virus recognition in electron microscope images using...

Virus Recognition in Electron Microscope Images using Higher

Order Spectral Features

by

Hannah Ong Chien Leing, BEng Medical (Hons)

PhD Thesis

Submitted in Fulfillment

of the Requirements

for the Degree of

Doctor of Philosophy

at the

Queensland University of Technology

Speech and Image, Video Technology (SAIVT)

School of Electrical and Electronic Systems Engineering

February 2006

Keywords

Virus recognition, electron micrograph, higher order spectra, bispectrum, invariant

features, feature averaging, texture and contour analysis.

Abstract

Virus recognition by visual examination of electron microscope (EM) images is time

consuming and requires highly trained and experienced medical specialists. For these

reasons, it is not suitable for screening large numbers of specimens. The objective of this

research was to develop a reliable and robust pattern recognition system that could be

trained to detect and classify different types of viruses from two-dimensional images

obtained from an EM.

This research evaluated the use of radial spectra of higher order spectral invariants to

capture variations in textures and differences in symmetries of different types of viruses

in EM images. The technique exploits invariant properties of the higher order spectral

features, statistical techniques of feature averaging, and soft decision fusion in a unique

manner applicable to the problem when a large number of particles were available for

recognition, but were not easily registered on an individual basis due to the low signal to

noise ratio. Experimental evaluations were carried out using EM images of viruses, and a

high statistical reliability with low misclassification rates was obtained, showing that

higher order spectral features are effective in classifying viruses from digitized electron

micrographs. With the use of digital imaging in electron microscopes, this method can be

fully automated.

iii

Contents

Abstract i

List of Tables ix List of Figures xi

Acronyms & Abbreviations xviii

Certification of Thesis xix

Acknowledgments xx

Chapter 1 Introduction 1

1.1 Motivation and Overview 1 1.2 Aims and Objectives 5

1.3 Thesis Outline 6

1.4 Original Contributions of the Thesis 9

1.5 Publications Resulting from this Research 11

iv CONTENTS

Chapter 2 Virus Morphology and Electron Microscopy (EM) 13

2.1 Introduction 13 2.2 Morphology of Virus 14

2.3 Preparation for Examination by EM 16

2.3.1 Negative Staining 16

2.4 Role of Electron Microscopy in Virology 17

2.5 Summary 19

Chapter 3 Towards Automated Virus Recognition 21

3.1 Introduction 21 3.2 Segmentation 22

3.3 Feature Extraction 25

3.3.1 Co-occurrence Matrices 27 3.3.2 Autocorrelation 28

3.3.3 Wavelet Features 28

3.3.4 Gabor Features 30

3.3.5 Higher Order Spectra 31

3.3.5.1 Time Domain Definition and Properties 31

3.3.5.2 Frequency Domain Definition and Properties 35

3.3.5.3 Motivations of using HOS in Feature Extraction 38

3.3.5.4 Rotation, Translation and Scaling Invariants Generation 40

3.3.5.4.1 Feature Extraction from 2-D Images 43

CONTENTS ___________ __________________________________________v 3.4 Classifiers 45

3.4.1 Parametric and Non-parametric Classifiers 46 3.4.2 Gaussian Mixture Model (GMM) 47

3.4.3 Support Vector Machines (SVMs) 50

3.5 Summary 54 Chapter 4 A Study of Texture and Contour 55

4.1 Introduction 55 4.2 The Relative Importance of Phase and Magnitude in Texture 57

4.2.1 Experimental Procedure 58 4.2.2 Results and Discussion 60

4.3 Texture and Contour Analysis using Indirect Method for HOS Feature

Extraction 63

4.3.1 Introduction 63

4.3.2 Experiment with a Large Database of Different Textures and

Contours 64

4.3.3 Experiment with Images of the Same Texture of Different

Contours 67

4.3.4 Experiment with Various Level of Noise 70 4.3.5 Experiment with Averaging of Features and Input Fusion of

Noisy Images 73

4.4 Summary 76

vi CONTENTS Chapter 5 Virus Recognition using Higher Order Spectral Features 79

5.1 Introduction 79 5.2 Higher Order Spectra 81

5.2.1 Illustration of the Indirect Method in obtaining Bispectral Features

using Synthetic Images 84

5.3 Gastroenteric Viruses 91 5.4 Image Analysis 92 5.5 GMM Modeling 96

5.5.1 Experimental Evaluation of Model Order and Dimensionality of

Training Observations 97

5.6 GMM Verification 100 5.7 Experiments 101

5.7.1 Experiment on a Pooled Population 104 5.7.2 Experiment on a Single Image Population 107

5.8 Virus of Similar Size 110 5.9 Evaluation using Support Vector Machine Classifier 112

5.9.1 Introduction 112 5.9.2 Experimental Procedure 113 5.9.3 Results and Discussion 114

5.10 3D Virus Reconstruction 115 5.11 Summary 116

Chapter 6 Relative Performance Evaluation 119

6.1 Introduction 119

CONTENTS vii 6.2 Gabor Filter 121 6.3 Discriminant Analysis and Results 122 6.4 Training and Classification using Support Vector Machine 124

6.4.1 Results and Discussion 125

6.5 Summary 126

Chapter 7 Conclusion and Further Work 129

7.1 Conclusion 129 7.2 Further Work 131

Bibliography 133 Appendix A A Study of Texture and Contour 143

A.1 Experimental Results of the Relative Importance of Phase and Magnitude

in Texture Analysis 143

A.2 Classification Results of a Large Database of Different Textures and

Contours using Higher Order Spectral Features 153

A.3 Classification Results of Images of the Same Texture but Different

Contours using Higher Order Spectral Features 155

A.4 Classification Results of Images with Various Level of Noise using Higher

Order Spectral Features 156

A.5 Classification Results with Averaging of Features and Input Fusion of

Noisy Images using Higher Order Spectral Features 157

Glossary 159

ix

List of Tables Table 3.1 Some commonly used kernels 53

Table 4.1 Misclassification rate (%) of the first 10 textures out of the 40 that were chosen

from the Brodatz album. The overall performance over forty textures shows an

average misclassification of 1.37%. 66

Table 4.2 Misclassification rate (%) of four different contours of (a) D5 and (b) D21 texture

images using higher order spectral features 69

Table 4.3 Misclassification rate (%) of four textures with added white Gaussian noise of

SNR equal to (a) -50 dB (b) -30 dB (c) -20 dB using higher order spectral

features 72

Table 4.4 Misclassification rate (%) when feature averaging of (a) 10 images (b) 20 images

were used for classification using higher order spectral features 74

Table 4.5 Misclassification rate (%) when M = (a) 4 and (b) 8 sets and N=5 images were

used for classification using higher order spectral features. Gaussian noise of

SNR = -30 dB was added to the image. 75

Table 5.1 Efficiency (%) of different combinations of number of mixture, M and

dimensionality of training observations, D used to examine the performance of

GMM 100

x LIST OF TABLES Table 6.1 Comparison of the Feature Space Separability of Gabor and HOS features using

FLD 123

Table 6.2 Efficiency (%) of higher order spectral features and Gabor features in verification

of Rotavirus, Calicivirus and Adenovirus 127

Table A.2 Misclassification rate (%) of a large database of different textures and contours

images that were chosen from the Brodatz album using higher order spectral

features. The overall performance over forty textures shows an average

misclassification of 1.37% 153

Table A.3 Misclassification rate (%) of four different contours of (a) D8 and (b) D17 texture

images using higher order spectral features 155

Table A.4 Misclassification rate (%) of four textures with added white Gaussian noise of

SNR equal to (a) -80 dB (b) -10 dB (c) 0 dB (d) 10dB using higher order spectral

features 156

Table A.5 Misclassification rate (%) when M = (a) 2 (b) 5 and (c) 10 sets and N=5 images

were used for classification using higher order spectral features. Gaussian noise

of SNR = -30 dB was added to the image. 157

xi

List of Figures

Figure 2.1 A basic structure of virus is the icosahedron which composed of 20 facets, each

an equilateral triangle and 12 vertices. Due to rotational symmetry it possesses

axes of (a) 5 fold (b) 3 fold and (c) 2 fold symmetry 15

Figure 2.2 Adenovirus after negative stain electron microscopy 16

Figure 3.1 An EM image of Adenovirus. A significant number of complex artificial objects

that normally present and non-uniform illumination of the image makes

segmentation of the virus particle a challenging task 23

Figure 3.2 The symmetry regions of the bispectrum (labeled 1). The region labeled 1

contains a unique set of values and those in the other labeled regions can be

mapped to these 38

Figure 3.3 Owing to symmetries of the bispectrum in equation (3.27), the bispectrum

possess redundancy and needs to be only computed for the triangular region

shown above. Features are extracted by integrating the bispectrum along a radial

line as shown and taking the phase of the complex-valued integral. 1f and 2f are

frequencies normalized by one half of the sampling frequency 42

Figure 3.4 The direct and indirect methods for computation of invariant parameters for a

1-D sequence 44

xii LIST OF FIGURES Figure 3.5 The Radon transform of a 2-D image yields 1-D parallel beam projections,

)n(x at various angles, θ 45

Figure 3.6 SVM Margin 53

Figure 4.1 A single virus particle of (a) Adenovirus (b) Astrovirus (c) Calicivirus. Note that

although there are small differences in texture and contour, it is difficult to tell

them apart by visual examination 57

Figure 4.2 Flow chart of analysis of two different textures to evaluate the importance of

phase or magnitude in representing the texture 59

Figure 4.3 Example of (a) homogeneous textures (b) inhomogeneous textures used in the

experiment. Two of the images above are randomly chosen and subjected to steps

in Figure 4.2 60

Figure 4.4 Results when images of (a) 2 inhomogeneous textures (b) 2 homogeneous

textures (c) a homogenous and inhomogeneous texture were used as input

textures after subjected to steps in Figure 4.2. The top images of each subfigure

are the input and the bottom images are the output 62

Figure 4.5 Four different texture images with four different contours (a) D5 with 5 fold

symmetry contour (b) D17 with 6 fold symmetry contour (c) D21 with 7 fold

symmetry contour (d) D33 with circular contour chosen out of the forty Brodatz

images that were used for classification 65

Figure 4.6 Four texture images from the Brodatz album (a) D5 (b) D8 (c) D17 (d) D21

used in the experiment. 4 different contours were applied to each of these texture

images 67

Figure 4.7 The 512 X 512 texture is tiled into 64 X 64 sized images. The texture

inhomogeneity between the tiles causes higher classification inaccuracy 70

LIST OF FIGURES xiii Figure 4.8 Gaussian noise added to texture D5 with SNR equal to (a) -50 dB (b) -30 dB (c)

-20 dB 71

Figure 4.9 Noise performance of bispectral features. Misclassification shown is an average

misclassification of textures D5, D8, D17 and D21 74

Figure 4.10 Average misclassification rate in percentage by input fusion where the features

are combined by averaging of M sets where each set consists of 5 images 77

Figure 5.1 Illustration of the inability of the power spectrum to retain phase information.

Figure 5.1(a) Non minimum phase of input sequence, h(k), Figure 5.1(b) Zeros of

the non-minimum phase, Figure 5.1(c) Power spectrum of the non-minimum

phase sequence. The zeros outside the unit circle in Figure 5.1(b) are inversed

conjugate to produce a minimum phase sequence. Figure 5.1(d) 1-D plot of the

minimum phase sequence, Figure 5.1(e) Zeros of the minimum phase sequence,

Figure 5.1(f) Power spectrum of the minimum phase sequence 83

Figure 5.2 The left top and bottom figures show the imaginary and real parts of the

bispectrum of Figure 5.1(a) and the right top and bottom figures show the

imaginary and real parts of the bispectrum of Figure 5.1(d). The differences

observed in the plots show the ability of bispectrum to retain the phase

information 84

Figure 5.3 Flow chart of computation of invariant parameters. ),( θaP is invariant to

scaling and translation and ),( θωaP is invariant to scaling, translation and

rotation. The algorithm was tested on a 5 fold symmetry and a 7 fold symmetry

image and results are presented in Figures 5.4, 5.5 and 5.6 86

Figure 5.4 Figure 5.4(c) and 5.4(d) show the Radon transform projection at 45 degree angle

of the 7 fold symmetry image, Figure 5.4(a) and the 5 fold symmetry image,

Figure 5.4(b) 87

xiv LIST OF FIGURES

Figure 5.5 Figure 5.5(a) and Figure 5.5(c) show the real and imaginary parts of the

bispectrum of the Radon transform projection at 45 degree angle of Figure 5.4(a).

Figure 5.5(b) and Figure 5.5(d) show the real and imaginary parts of the

bispectrum of Figure 5.4(b). The bispectrum is a triple product of Fourier

coefficients and is a complex valued function of two frequencies, f1 and f2, where

f1 and f2 are frequencies normalized by one half of the sampling frequency.

Different shaped projections result in different bispectra. Invariant features are

extracted by integrating along radial lines and taking the phase. The scale shown

at the colorbar above is the log of the absolute value of the real and imaginary

parts of the bispectrum. The above plots show that features, )a(P close to

21a = may capture differences as well 88

Figure 5.6 Figure 5.6(a) and 5.6(b) show plot of ))(2/1( θωP as a function of θω , (where

θω is a frequency in cycles per 180 degrees) of Figure 5.4(a) and Figure 5.4(b).

))(2/1( θωP is invariant to scaling, translation and rotation. Note that Figure

5.6(a) shows a dominant symmetry at 7 cycles per 180 degrees whereas Figure

5.6(b) shows a dominant symmetry at 5 cycles per 180 degrees 88

Figure 5.7 Figure 5.7(a) shows the radial spectrum of the bispectral features, ))(2/1( θωP

as a function of θω , ( θω is a frequency in cycles per 180 degrees) of a 7 fold

symmetry. White Gaussian noise has been added and SNR = 0dB to the image. In

Figure 5.7(b), the individual spectra are accumulated over 75 such images. Note

that Figure 5.7(a) does not demonstrate a dominant symmetry at 7 cycles per 180

degrees due to the low signal to noise ratio. As an ensemble of images is taken

and the spectra are accumulated, it eventually converges to a shape. A peak at 7

cycles per 180 degrees can be seen in Figure 5.7(b). Robustness to noise can thus

be achieved by averaging these features 89

Figure 5.8 Comparison between a 5 fold symmetry image and a 3D reconstructed virus

image using plots of radial spectra of the bispectral features, P(1/2). These

features which are invariant to translation, rotation and scaling contain

information from the contour and texture that are useful for verification 90

LIST OF FIGURES xv Figure 5.9 A sample image of each type of virus used for testing. These images are

different in magnification and resolution. (a) Adenovirus (b) Astrovirus (c)

Rotavirus (d) Calicivirus 93

Figure 5.10 A single virus of each type. (a) Adenovirus (b) Astrovirus (c) Rotavirus (d)

Calicivirus. These subimages are extracted from portions shown by square boxes

in figure 5.9 and a circular mask is applied to each. Note that although there are

small differences in texture, it is difficult to tell them apart by visual examination.

Pseudo colouring could be used to emphasize the differences in texture but the

difficulty arises when there is some variation in texture within the same virus

type on images that are obtained from various sources of different background,

scale, contrast and noise 94

Figure 5.11 Cluster plot of features from three different sets of Rotavirus images with

different backgrounds, contrast and scale. Each point is an average feature from a

subpopulation of 10 viral particles. The plot shows quite compact and isolated

clusters or modes in feature space 102

Figure 5.12 Illustration of selection of viral particles from different sets of EM images used

for testing and training in pooled population and single image population. In the

single image population, the testing and training is done on populations derived

from separate images. In a pooled population, the virus images pooled from all

the EM images of that type obtained from various sources 103

Figure 5.13 DET curve using the bispectral features from subpopulations of 5, 8, 10, 13 and

15 viral particles on a pooled population. As we increase the test ensemble size

for feature averaging, the EER drops. EER is the point on the DET curve where

the false alarm probability is equal to the miss probability. Refer to Figure 5.14

for EER values of each subpopulation size 105

Figure 5.14 Plot of EER versus ensemble size shows that as we increase the test ensemble for

feature averaging, the EER drops for N= 15 to 2.5% 107

xvi LIST OF FIGURES Figure 5.15 DET curve using the bispectral features from subpopulation of N=15 viral

particles on a pooled population. The solid line shows an average of 2 sets of

subpopulation of 15 viral particles while the dotted line shows the case for M = 1

(M, N, refer to equations 5.2, 5.3). The EER drops to less than 0.2%. The darker

solid line shows an output fusion of two test populations. In this case, false

acceptance rate will be the product of individual false acceptance rates and the

false rejection rate will be the sum of the individual ones. This shows that the

averaged scores yield better performance than output fusion in this case 108

Figure 5.16 DET curve using the bispectral features from subpopulations of 5, 8, 10, 13, 15

and 18 viral particles on a single image population. The EER drops as we

increase the feature averaging of the subpopulation size. Refer to Figure 5.17 for

EER values of each subpopulation size 109

Figure 5.17 Plot of EER versus ensemble size shows that as we increase the test ensemble for

feature averaging, the EER drops for 18 particles to 2% 110

Figure 5.18 A sample image of (a) Astrovirus and (b) Hepatitis A virus. The magnifications

of these images are the same 111

Figure 5.19 DET curve using the bispectral features from subpopulation of N = 5, 10, 15, 20

particles, M =1 and subpopulation of N = 20, M=2 on a pooled population. The

EER drops to less than 2% when features of 2 sets of subpopulation of 20

particles were averaged 112

Figure 5.20 DET curve using the bispectral features from subpopulations of 5, 10 and 15 viral

particles on a pooled population using SVM and GMM classifier 114

Figure 6.1 The plot of efficiency versus number of features for a subpopulation of 10 viral

particles trained using SVM classifier. A choice of 3 kernel widths were used,

0.001, 0.1 and 10 to train the features. The efficiency is calculated from miss and

false alarm probabilities 126

LIST OF FIGURES xvii Figure A.1(a) Subfigures of (a)-(l) Results when images of 2 homogeneous textures used as

input textures after subjected to steps in Figure 4.2. The top images of each

subfigure are the input and the bottom images are the output 143

Figure A.1(b) Subfigures (a)-(l) Results when images of 2 inhomogeneous textures used as

input textures after subjected to steps in Figure 4.2. The top images of each

subfigure are the input and the bottom images are the output 146

Figure A.1(c) Subfigures (a)-(l) Results when images of a homogenous and inhomogeneous

texture used as input textures after subjected to steps in Figure 4.2. The top

images of each subfigure are the input and the bottom images are the output 149

Acronyms & Abbreviations DFT Discrete Fourier Transform EER Equal Error Rate ELISA Enzyme-Linked Immunosorbent Assay EM Electron Microscopy E-M Expectation Maximization FLD Fisher Linear Discriminant GLCM Gray level Co-occurrence matrices GMM Gaussian Mixture Model HAV Hepatitis A Virus HOS Higher Order Spectra IFA Immunofluorescence Assay ML Maximum Likelihood OSH Optimal Separating Hyperplane PCA Principal Component Analysis PCR Polymerase Chain Reaction SNR Signal to Noise Ratio SRM Structural Risk Minimization SVM Support Vector Machine TEM Transmission Electron Microscope

Certification of Thesis This work contained in this thesis has not been previously submitted for a degree or

diploma at any higher educational institution. To the best of my knowledge and belief,

the thesis contains no material previously published or written by another person except

where due reference is made.

Signed: ________________________ Date: ________________________

Acknowledgments

First and foremost, my most sincere thanks must go to my principal supervisor Assoc.

Prof. Vinod Chandran, for his guidance, support, and most of all his infinite patience and

understanding without which this thesis may not have been completed at all. Honestly, I

could not think of a better supervisor. I also wish to acknowledge the support my

associate supervisors Professor Sridha Sridhran and Assoc. Prof. John Aaskov have

provided.

I would also like to thank the QUT super-computing services for their assistance in

providing their computing facilities, as well as all the members in SAIVT Laboratory, for

creating an enjoyable and fun atmosphere during the course of my study. In particular, to

Ronald Elunai for his invaluable help with a significant portion of work presented in this

thesis. I am also grateful to the Centre of Disease Control, USA and The Universal Virus

Database of the International Committee on Taxonomy of Viruses for their public domain

virus images and also to Prof. Hans Gelderblom for providing some of the electron

micrographs.

xxi ACKNOWLEDGMENTS

I’m very grateful to my family for their unconditional love and supporting me financially,

spiritually and emotionally the whole way through. I would also like to express my

gratitude to my friends here in Brisbane, who have been a constant source of support for

me while completing this work, through both the good times and the bad.

And finally to the most important person in my life, for You are the ultimate source of

our success, love, hope, dreams and future. I’m grateful for all that You have done not

only during the course of my study but my entire life.

Hannah Ong Chien Leing

Chapter 1 Introduction 1.1 Motivation and Overview Parallel to its technical development starting in the 1930s, electron microscopy (EM)

emerged as an important tool in basic and clinical virology [1] . EM has allowed a direct

demonstration of the particulate nature of viruses, as well as the description of their size

and morphology. The introduction of negative staining in the late 1950s and wider

availability of electron microscopes have encouraged broad application of EM to routine

viral diagnosis using cell cultures and clinical samples, such as stool, urine and biopsy

specimens. Within a short period of time, many viruses and bacteriophages were

characterized morphologically, and the differences observed in morphology were used as

criteria for virus classification [2].

2 1.1 Motivation and Overview

The value of EM in viral diagnosis soon became apparent, but over the years due to some

limitations of EM, other techniques and new kits have appeared in the market. Virus

recognition by visual examination of EM images is quite time consuming. To interpret a

micrograph, highly skilled and experienced medical specialists are needed. Success is

determined not only by the ability to carry mental images and compare them with what is

visible on the screen of the microscope, but also to see whether the observed image is

compatible with what is known of the particular virus, or one very like it, and, just as

importantly, when it is incompatible [3].

For these reasons, EM is not suitable for screening large numbers of specimens. Many

alternate methods have been developed to overcome this issue, including (a) detection of

viral antigen, e.g immunofluorescence assay (IFA), (b) detection of virus nucleic acid,

e.g polymerase chain reaction (PCR), and (c) detection of anti-viral antibody, e.g

enzyme-linked immunosorbent assay (ELISA).

Even though these techniques allow mass screening, they have several limitations

compared to EM. One of the primary disadvantages of immunologic tests such as ELISA

and IFA is that detectable antibodies may not be detectable in immunosuppressed patients

or early in the course of infection. Besides, the reagents may not exist that would permit

complete immunologic testing. Even when it is appropriate for the etiologic agent, the

sensitivity may only equal that of EM [4, 5].

This also is true for nucleic acid amplification techniques such as PCR that are capable

only of identifying genomic material for previously identified agents. Besides, nucleic

1.1 Motivation and Overview 3 acid amplification techniques will not identify subviral components such as empty virions

(viral particle) that may be present late in an infection. Furthermore, mutations in viruses

may cause this method to be less effective [2].

Although these techniques have taken over much of the diagnostic EM, they are not a real

substitute for, and therefore not comparative with EM diagnosis, because their objective,

e.g. viral antigen or nuclei acids, or antiviral antibodies, differs from that of EM, the virus

particle itself. Thus, so far, these modern diagnostic techniques can act only as

complementary and not alternatives to EM [3].

Automated recognition of viruses from EM images can make it possible to screen large

numbers of samples from various parts of the world. Besides, electron microscope images

can be transmitted without the risk of spreading a virus. With the advance and increase in

technology, the use of digital imaging with CCD cameras and powerful computers are

becoming common for Transmission Electron Microscope (TEM). This development

makes it possible to have a fully automated system, and thus it can be a useful tool in

assisting virus recognition.

To date, research has been done in this area to extract the individual virus cell from

electron microscope images for classification [6] and to automatically recognize the virus

extracted using methods such as topology [7] , template matching [8] and iterative

Bayesian approach [9]. Matuszewski [9] suggested classification of viruses based on

4 1.1 Motivation and Overview topology has a major disadvantage because the introduction of a new virus type to the

‘library’ of the recognizable viruses requires revision of the topological measures of all

the viruses in the library. Template matching has poor classification performance in

identifying a large number of different virus types.

In the iterative Bayesian approach, the multi-category multi-feature classification

problem is decomposed into a set of two-category classification sub-problems, with each

classification sub-problem solved based on this approach. However, this method

normalizes viral particles in size before feature extraction. Normalisation may not work

well for non-circular objects and often fails when the signal to noise ratio is low.

Registration of the image or its spectrum over a corresponding prototype is quite

computationally demanding and also error-prone. This method is not able to classify

viruses from different sources.

Viruses are the smallest infectious biological entities that depend on their host for

replication. They are classified on the basis of fundamental characteristics, the principal

ones being the nature of their genetic material or genome, either DNA or RNA, and their

morphology in terms of size, shape, and general appearance. The International

Committee on Taxonomy of Viruses (ICTV) recognizes about 1,550 virus species which

belong to 56 families, 9 subfamilies, and 233 genera [10].

Viruses in EM images vary in orientation, position and size. EM images of different

viruses also exhibit fine differences in texture that arise from differences in their 3D

surfaces and internal structures. Symmetries are commonly observed in biological

1.2 Aims and Objectives 5

reproduction processes. Textures on images of viral particles tend to exhibit different

rotational symmetries as well. However, the variation in texture and any differences in

symmetry are difficult to visualize in any single specimen because images of virus taken

from TEM often are noisy due to the high resolution and the low dose of electrons used in

the microscope. Consequently not much information can be extracted by simple visual

inspection of a single particle or image. Additional processing such as averaging an

ensemble of virus particles is necessary to obtain a better result. Averaging can be done

only if the features are robust to translation, size, rotation and noise. Thus, features that

have these invariant properties are important in this application. In addition, these

features need to capture contour and texture properties.

Automated virus recognition using EM will speed up the diagnostic process, release

medical specialists’ time by de-skilling the diagnostic task to allow the use of non-

specialist medical staff, and allow screening a large number of specimens. This work

attempted to address this vision by developing a method that could be used to detect and

classify different types of viruses from negative stained EM images.

1.2 Aims and Objectives The general aim of this project, as a result of the discussion in Section 1.1, is to develop a

reliable and robust pattern recognition system that can be trained to detect and classify

different types of viruses, in particular viruses that are difficult to distinguish visually

from two-dimensional images obtained from an electron microscope. The methods

6 1.3 Thesis Outline

proposed are based on higher order spectral features that capture contour and texture

information, while providing robustness to shift, rotation, changes in size and noise. This

method also can be applied to other microorganisms such as bacteria and biological cells.

The specific goals of this work are to:

(i) Conduct a study on contour and texture using higher order spectral features to

have a better understanding of this application in virus classification from EM

images.

(ii) Investigate the use of higher order spectral features in automated virus recognition

system from 2-D EM images.

(iii) Evaluate and compare other texture and contour based features in the application

of virus classification.

(iv) Evaluate and seek improvement of results by using different classifiers and

additional processing such as fusion of features and fusion of classifier scores.

1.3 Thesis Outline The remainder of the thesis is organized as follows: Chapter 2 discusses the morphology of virus, preparation method, and the role of

electron microscopy in virus recognition, including a brief history of diagnostic electron

microscopy. The use of EM as a diagnostic tool was compared with current

1.3 Thesis Outline 7 diagnostic kits such as enzyme-immunoassay and latex agglutination tests, and various

molecular techniques.

Chapter 3 covers the basic recognition steps such as segmentation, feature extraction

and classification. The feature extraction methods that are fundamental and used in many

pattern recognition systems, particularly in texture analysis are presented. The classifiers

that will be used in this thesis also are reviewed. This chapter also provides a brief

background on Higher Order Spectra (HOS), highlighting the time and frequency domain

definitions, properties, and naming convention and notations used. The applications of

HOS and motivations of using HOS in feature extraction also are discussed, followed by

feature extraction from a 2-D image and generation of the bispectral invariant features.

Chapter 4 studies the relative importance of phase and magnitude in texture and

contour using a set of images from the Brodatz album. Subsequently, further analysis of

texture and contour was carried out on these images using the indirect method for HOS

feature extraction as outlined in Chapter 3. Noise was added to the images to reflect EM

images that are normally noisy due to the high magnification used to capture the virus.

Averaging of features was used to improve the classification results. The evaluation of

texture and contour features is important for virus recognition because different viruses

appear differently on electron micrographs. The morphological (texture and contour)

8 1.3 Thesis Outline differences appear on the micrograph are useful in distinguishing one virus group from

another.

Chapter 5 presents the verification results of gastroenteric viruses using higher order

spectral features. Experiments were conducted to identify virus population from digitized

EM images of four types of viruses; rotavirus, adenovirus, astrovirus and calicivirus,

whose morphologies are quite similar. Experiments were also conducted on viruses with

similar size. Results are presented in detection error trade-off (DET) plots. Gaussian

Mixture Model (GMM) and Support Vector Machine (SVM) classifiers were used

separately to train for viruses and comparison of results were made. This chapter also

explores the possibility of using higher order spectral invariant features in the application

of 3D virus reconstruction from 2D images.

Chapter 6 compares the bispectral features with Gabor features in virus recognition.

SVM was used to train and classify detectors for virus population from EM images of

Rotavirus, Adenovirus, Astrovirus and Calicivirus. Optimal results were achieved by

trying different kernel widths and number of training features.

Chapter 7 concludes with a discussion of contributions made in this thesis. The

possibilities for future work, which extend upon this thesis, also are included.

1.4 Original Contributions 9 1.4 Original Contributions of the Thesis This research provides original contributions in these areas; (i) A new method of identifying viruses from negative stained EM images.

(ii) New methodologies that take advantage of the large numbers of viral particles in

these images to improve classification accuracy.

A methodology has been developed to recognize viruses from negative stained images

using higher order spectral features. This methodology exploits invariant properties of the

higher order spectral features, statistical techniques of feature averaging, and soft

decision fusion in a unique manner applicable when a large number of particles are

available for recognition, but are not easily registered on an individual basis. Higher order

spectral features that are invariant to similarity transformations and robust to noise have

been defined and applied in previous pattern recognition work, but have not been used in

this application before. In this thesis, the radial spectra of higher order spectral features

were used for classification of viral populations. There are no pervious reports of batch

training and testing over populations of viral particles.

More specifically, the detailed smaller contributions that are associated with the broad

ones listed above are as stated below:

10 1.4 Original Contributions (i) Texture and contour analysis

The evaluation of texture and contour features is important for virus recognition. This

forms a basis for creating an automated virus recognition system because different

viruses appear differently on electron micrographs. The morphological (texture and

contour) differences appearing on the micrograph are useful in distinguishing one virus

group from another. The analysis was carried out using a set of synthetic textures from

the Brodatz album with noise added to the images to reflect the EM images that are

normally noisy. The analytical and empirical evaluations show that the indirect method in

obtaining higher order spectral features as proposed by Chandran et. al. [11] is suitable in

classifying homogeneous texture. This analysis also shows the ability of higher order

spectral features in discriminating a large database of different textures and contours and

averaging of features and input fusion for improvement of classification accuracy.

These experiments have enhanced our understanding of texture and contour classification

of noisy images using higher order spectral features. This knowledge is useful and

provides a foundational work in virus recognition.

(ii) Comparative studies

This study indicates that higher order spectral features perform better than Gabor features

in the application of virus recognition. Comparison of Support Vector Machine (SVM)

and Gaussian Mixture Model (GMM) classifiers to train and classify the viruses shows

1.5 Publications 11

that there is not much difference between these two classifiers in terms of Equal Error

Rate (EER) in classifying subpopulations of 5, 10 and 15 viral particles.

1.5 Publications Resulting from this Research Conference Publications

(i) V. Chandran and H.Ong , “Identification and Classification of viruses in electron

microscope images using higher order spectral features,” Proceedings of Fourth

Australasian Workshop on Signal Processing and Applications (WOSPA), Brisbane,

Australia, 17-18 December, pp. 55-59, 2002.

(ii) H.Ong and V.Chandran, ‘Recognition of viruses by electron microscopy using

higher order spectral features,’ Proceedings of the International Society for Optical

Engineering (SPIE) - Medical Imaging, San Diego, USA, 15-20 February, pp 234-42,

2003.

Journal Publication (i) H.Ong and V.Chandran, ‘Identification of gastroenteric viruses by electron

microscopy using higher order spectral features’ Journal of Clinical Virology,

vol. 34, pp.195-206, 2005.

Chapter 2 Virus Morphology and Electron Microscopy 2.1 Introduction This chapter begins by discussing the morphology of viruses, preparation methods and

the role of electron microscopy in virus identification. The use of electron microscopy as

a diagnostic tool was compared with other current diagnostic kits such as enzyme-

immunoassay and latex agglutination tests, and various molecular techniques. The

advantages and disadvantages of using electron microscopy as a virus recognition tool are

also discussed.

14 2.2 Morphology of Virus 2.2 Morphology of Virus

Viruses come in two basic structures; icosahedral structure of isometric viruses and

helical structure [12]. All known animal viruses, except poxviruses, belong to either of

these two structural types. Icosahedral structure is also known as 5:3:2 symmetry because

it possesses axes of 5-fold, 3-fold and 2-fold symmetry (Figure 2.1). Icosahedral structure

is found in both DNA and RNA viruses. In some virus groups the icosahedral structure

exists as a naked nucleocapsid, while in others it is surrounded by an envelope studded

with projections. The morphological units, or capsomers, of icosahedral viruses are

arranged such that they result in a rigid geometric configuration, an icosahedron, which

has 12 vertices (points), 20 faces (flat sides), and 30 edges. Each vertex, face or edge is

an axis of symmetry. The icosahedral viruses have a relatively constant size and shape

within each genus [13] .

In most icosahedral viruses, the protomers are arranged in oligomeric clusters

(capsomeres), that are readily delineated by negative staining electron microscopy and

form the closed capsid shell as shown in Figure 2.2. The arrangement of capsomeres into

an icosahedral shell permits the classification of such viruses by capsomere number and

pattern. This requires the identification of the nearest pair of vertex capsomeres (called

penton: those through which the fivefold symmetry axes pass) and the distribution of

capsomeres between them. Today, the International Committee on Taxonomy of Viruses

(ICTV) recognizes about 1,550 virus species comprising of 56 separate families and

humans have been found to host 21 of the 26 families specific for vertebrates [10].

2.2 Morphology of Virus 15

Viral morphology has provided the basis for grouping viruses into families. Most viruses

have sufficiently distinctive morphology such that this property can be used to distinguish

one virus group from another.

(a) (b) (c)

Figure 2.1: A basic structure of virus is the icosahedron which composed of 20 facets, each an equilateral triangle and 12 vertices. Due to rotational symmetry it possesses axes of (a) 5 fold symmetry (b) 3 fold symmetry and (c) 2 fold symmetry.

The helical viruses, another virus structure contain RNA which is assembled with protein

subunits into a helical nucleocapsid with the RNA located in a channel in the centre of

the helix. The single axis of symmetry passes longitudinally down this helical centre [13].

Whereas the icosahedral viruses have a relatively constant size and shape within each

family, the helical viruses tend to be heterogeneous in size and are frequently

pleomorphic.

16 2.3 Preparation for Examination by EM

Figure 2.2: Adenovirus after negative stain electron microscopy.

2.3 Preparation for Examination by EM

There are numerous ways to prepare biological material for examination or identification

in the TEM. Technical methodology has reached a point where reproducibility of

specimen preparation is possible. A basic aim is to obtain morphological information

by methods that can be repeated anywhere in the world. Reproducibility strengthens the

belief that micrographs are faithful reflections of the native state of the specimen. One

type of preparation that is used for routine identification of viruses in EM is negative

staining.

2.3.1 Negative Staining

The introduction of negative staining [14] revolutionized the field of electron microscopy

of viruses. Within just a few years, much new and exciting information about the

architecture of virus particles was acquired. The negative stain moulded round the virus

particle, outlining its structure, and also is able to penetrate between small surface

projections and to delineate them. If there are cavities within the virus particle that are

accessible to the stain, they will be revealed and some of the internal structure of the virus

2.4 Role of Electron Microscopy in Virology 17 may be disclosed. Thus, it does not only reveal the overall shapes of particles, but also the

symmetrical arrangement of their components. This information is important to

distinguish one group of viruses from another.

The negative staining technique is simple, rapid and requires a minimum of experience

and equipment. A negative staining technique uses heavy metal salts to enhance the

contrast between the background and the virion’s image. A variety of heavy metal

compounds are available for negative staining. Among the most commonly used stains

are uranyl and tungstate stains and ammonium molybdate [15].

Besides the simplicity, rapidity and minimum of experience needed, negative staining

also has other benefits over the more recent techniques such as vitrification. Viruses

prepared by vitrification usually adopt random orientations in the amorphous ice layer.

Whereas negative staining tends to induce preferred orientations of the molecules on the

carbon support film [16]. This is an advantage because less heterogeneity among the

same virus will increase the classification accuracy when averaging of particles is made

to improve the signal to noise ratio in automated virus recognition.

2.4 Role of Electron Microscopy in Virology

Since the 1930s, electron microscopy (EM) has become an important tool in basic and

clinical virology. The first electron micrograph of poxvirus was published in 1938 [17].

In the early 1940s, immune EM techniques were developed and used in electron

microscopic study of the tobacco mosaic virus [18]. Within a short period of time, EM

18 2.4 Role of Electron Microscopy in Virology was successfully introduced in the differential diagnosis of smallpox and chickenpox

infections [19, 20].

The introduction of negative staining and wider availability of electron microscopes has

encouraged a broad application of EM. In the following years, a great number of

clinically important, previously undescribed agents such as adeno-, entero-, myxo-,

paramyxo-, and reoviruses were indentified. Virus diagnosis by electron microscopy that

relies on the detection and identification of viruses on the basis of size and particle

morphology leads to rapid identification of infection agents. The initial classification of

many agents was therefore based on a combination of morphology and genome structure.

The virions of each of these families display distinct morphologies and this feature can be

used to group them accordingly. In fact, in most cases, this morpho-diagnosis combined

with clinical information is sufficient to permit a provisional diagnosis or rule out a more

serious infection and to initiate treatment without waiting for other test results [2].

EM is not suitable for a mass screening of clinical specimens because virus identification

by visual examination is quite time consuming. In addition, the identification of the

viruses is critically dependent on the skill and experience of the microscopist or

virologist. Therefore, in the following years a number of ‘modern’ techniques, such as

immunologic and molecular methods based on nucleic acid amplification have been

developed. Both of these techniques have several limitations compared to EM. (discussed

in Section 1.1). One of the primary limitations is that a priori notion of the virus identity

must be known to be able to select the appropriate reagents.

2.5 Summary 19

When compared to these diagnostic tests, diagnostic EM differs in its rapidity and its

undirected ‘open view’ [2]. A specimen can be ready for examination and an

experienced virologist or technologist can identify a viral pathogen morphologically

within 10 minutes. Nucleic acid amplification and enzyme assays normally have to wait

overnight.

Nevertheless, there are several limitations that exist in the identification of viral agents

using negative stain electron microscopy. First is the need for high particle concentrations

(106 ml-1), which means this method might not suit all viruses. It has been widely

accepted that this threshold of virus concentration is too high and may be reduced [3].

Many researchers have tried different methods such as using different coating on the

grids [21] to improve virus concentration on the grids. Other techniques include agar

filtration [22], sedimentation [23] and bioaffinity [24] which have successfully increased

the concentration of virus particles on the grid.

Other disadvantages of EM include the high maintenance cost of the equipment, other

capital expenses such as room or space, labor intensive nature and lack of career structure

for operators. Biel and Madeley [3] have discussed and addressed most of these issues.

2.5 Summary This chapter explores the morphology of virus, which comes in two basic structures;

icosahedral structure of isometric viruses and helical structure. Some of the current

diagnostic techniques also were discussed and compared with EM. One of the limitations

20 2.5 Summary

of EM includes the skill and experience needed by the microscopist or virologist in

interpreting these images. This aspect of EM (ultrastructural interpretation) can take

many years of training to master. To examine every specimen individually is quite time

consuming and can be a burdensome task. Thus, having an automated virus recognition

that can identify viruses from EM images can help to overcome these issues.

Chapter 3

Towards Automated Virus

Recognition 3.1 Introduction

Virus recognition is the process of recognizing a virus particle or population based on

their morphology (texture and contour). As stated in Chapter 2, the morphological

differences arise from the arrangement of protomers in oligomeric clusters or capsomeres

that are evidenced through negative staining of the viral particle.

Virus recognition may be classified into two main areas, that is, virus identification and

verification. Virus identification is the means of identifying a virus from a group of

viruses. Virus verification is the systematic process of accepting or rejecting (as a binary

decision) the claimed identity of a virus based on the sample morphology.

22 3.2 Segmentation

Automated virus recognition system involves steps such as segmentation of the viral

particles, feature extraction and also classification. In this thesis, the major focus will be

on feature extraction methods and classification. Segmentation methods proposed by

Shark [6] and Utagawa [25] that automatically segment the individual virus particles can

be incorporated to make the system fully automated. In this chapter, feature extraction

methods that are fundamental and used in many pattern recognition systems, particularly

in texture analysis are presented. The core method of virus recognition system developed

for this thesis is also addressed in this chapter.

A brief background on Higher Order Spectra (HOS), highlighting the time and frequency

domain definitions, properties, and naming convention and notations used are discussed.

This chapter also discusses the applications of HOS and motivations of using HOS in

feature extraction. This is followed by feature extraction from 2-D images and generation

of the bispectral invariant features using the direct and indirect method as proposed by

Chandran et. al. [11]. Classifiers that will be used in this thesis are also reviewed.

3.2 Segmentation Segmentation refers to the process of differentiating between the objects of interest (the

foreground objects) and the background. Segmentation of the negative stained EM

images of viruses is complicated because a significant number of complex artificial

objects usually are present and the images have non-uniform illumination. This can be

3.2 Segmentation 23

illustrated by a typical virus image taken from an electron microscope as shown in Figure

3.1.

It can be seen that a virus image contains not only good virus cells (approximately

circular in shape with a non-uniform internal structure consisting of a characteristic

pattern or texture), but also some corrupted virus particles with no diagnostic value, and

some unwanted artificial objects. The image also reveals non-uniform illumination. All

these factors must be taken into consideration to ensure that the virus particles can be

distinguished from the dark background and from the unwanted objects in the image, as

well as ensuring the size of the segmented viruses is accurate [6].

Figure 3.1: An EM image of Adenovirus. A significant number of complex artificial objects that normally present and non-uniform illumination of the image makes segmentation of the virus particle a challenging task.

24 3.2 Segmentation Researchers [6] in this area have developed a method of segmentation of viruses from

electron microscope images based on two main strategies a) Image histogram shaping by

a combination of filtering, edge detection and morphological operations, thereby

enabling regional threshold values to be accurately estimated via model fitting with the

initial parameters derived from the fuzzy c-means clustering technique, and b) image

segmentation based on a threshold value adaptive to local image brightness, thereby

resulting not only in the removal of artificial objects, but also in the accurate estimation

of the size and the position of virus cells. The effectiveness of this method was tested on

actual images of viruses such as Rota-, Adeno-, Astro- and Calicivirus. All the viruses

were extracted correctly with accurate size estimation except for one virus in one of the

images tested.

Recently an automated specimen search system in which a microtracing device is

installed on a Transmission Electron Microscope (TEM) has been developed and is

commercially available. Utagawa [25] demonstrated the possibility of applying the

automated specimen search system installed in an electron microscope to virological

studies, especially the detection of caliciviruses in semipurified stool samples.

In this system, TEM images of inspection specimens are recorded using a built-in TV

camera. The particles are automatically detected from digitized images and input

parameters such as diameters and the roundness of particles of interest. The detected

images are automatically stored in memory with their specimen positions (X,Y

coordinates), operating magnifications, accelerating voltages and other TEM operating


conditions put into a database. The result shows an accuracy of more than 95% for

detection of a single Calicivirus particle in a purified virus fraction. This system is useful

for clinical diagnosis without the need for operator intervention. These segmentation

methods can be applied and incorporated with our system to have a fully automated virus

recognition system in the future.

3.3 Feature Extraction Feature extraction is an essential component in any recognition system. The goal of a

feature extractor is to characterize an object to be recognized by measurements whose

values are similar for objects in the same category, and different for objects in different

categories. In a broad sense, features may include both text-based descriptions

(keywords, annotations, etc) and visual features (color, texture, shape, spatial

relationships etc). This section overviews some of the feature extraction methods that are

fundamental and used in many pattern recognition systems, particularly in texture

analysis. The core approach or method used in this thesis will be largely addressed in this

section as well.

According to Tuceryan and Jain [26], methods for texture feature extraction are

categorized into four classes i.e statistical, model-based, geometrical, and signal

processing or filtering methods. Statistical and signal processing methods are the ones

that are widely used. Statistical methods are comprised of techniques such as

co-occurrence matrices and autocorrelation (or power spectrum) function features. The

26 3.3 Feature Extraction co-occurrence matrix estimates the image properties based on the orientation and the

distance between the pixels and summarizes them into meaningful statistics.

The autocorrelation method is based on finding the linear spatial relationships between

primitives. If the primitives are large, the function decreases slowly with increasing

distance, whereas it decreases rapidly if texture consists of small primitives. For periodic

primitives, the autocorrelation increases and decreases periodically with distance. The

power spectrum, which is the Fourier transform of the autocorrelation function, shows the

directionality of the texture. Bispectral (or bicorrelation) features also were used in

texture analysis [27].

Most techniques in the signal processing method try to compute certain features from the

transformed images which are then used in classification or segmentation tasks. In the

early 90’s, the wavelet transform was investigated for texture representation [28] by

decomposing the texture into its frequency components. Another filtering technique,

Gabor filters also was applied in texture analysis. Gabor filters are frequency and

orientation selective and have some desirable optimization properties.

Following is a detailed review of some of the techniques for feature extraction that are

commonly used in texture analysis.

3.3 Feature Extraction 27 3.3.1 Co-occurrence Matrices

To capture the spatial dependencies in the image gray levels, a simple histogram is not

adequate because the image is 2-D [29]. This is the motivation behind the development of

Gray Level Co-occurrence Matrices (GLCM), which along with the autocorrelation

function is the most extensively used statistical method for texture

analysis. The co-occurrence matrix ),( jiPd of an N x N image I is defined mathematically

as the probability of two pixels, (r, s) and (t, v) that are separated by distance d, having

grey level values of i and j respectively. This can be expressed as

NNjvtIisrIvtsrjiPd

|}),(,),(:)),(),,{((|),( === (3.1)

where | | represents the cardinality of a set. Although GLCM features have proven to be

useful in many texture classification tasks, they have a number of disadvantages [26]. The

features extracted depend heavily on the choice of the displacement parameter and

currently there is no established method of choosing these parameters for optimal texture

characterization. Calculating the GLCM for a large number of distances and angles is

computationally expensive, and leads to an excessive number of total features.

28 3.3 Feature Extraction 3.3.2 Autocorrelation

The autocorrelation of an image ),( yxI can be given by

∑ ∑∑ ∑

= =

= = ++= N

0uN

0v2

N0u

N0v

vuyvxuIvuIyx

I ),(),(),(),(ρ (3.2)

Autocorrelation has been used in a wide range of applications such as character

recognition [30], affine-invariant texture classification [31], time series classification [32]

and face detection and recognition [33]. However, in most cases, the applicability of the

autocorrelations have been limited to first or second order due to high computational

costs. In texture analysis, the autocorrelation function is useful for capturing

repetitiveness in texture patterns. It can also be used to measure the scale of the texture

primitives from spacing of the repetitiveness.

3.3.3 Wavelet Features

Wavelet features have demonstrated good discriminance in the analysis and classification

of textures [34, 35]. There are a number of ways to approach wavelet transform [36]. It

can be approached from the mathematical standpoint of scaling functions and wavelets

[37], as well as in terms of averaging and detail of discrete sequences [38], filtering

operations [39] or multiresolution analysis [34]. Even though a researcher may focus on a

particular approach in interpreting wavelets, all the other remaining approaches are still

evident, as they are all interrelated. The concept of multiresolution for instance, is

3.3 Feature Extraction 29 closely related to the space spanned by scaling functions and wavelets, which is related to

the filter coefficients of these functions.

The wavelet transform is defined as decomposition of a signal )()( 2 RLtf ∈ into a family

of functions )(, tnmψ obtained through translation and dilation of a kernel function

)(tψ known as mother wavelet:

(3.3)

where m and n are the scale and translation indices, respectively. The mother wavelet is

constructed from the scaling functions )(tφ as follows:

)2()(2)( ktkhtk

o −= ∑∞

−∞=

φφ (3.4)

)2()(2)( 1 ktkhtk

−= ∑∞

−∞=

φψ (3.5)

where )(kho and )(1 kh are coefficients for low-pass and high-pass filters, respectively.

)1(*)1()(1 khkh o

k −−= (3.6)

The earliest such features involved calculating the energy, or a similar measure, present

in each of the subbands resulting from the wavelet decomposition of an image [40, 41]. It

has been shown that such features perform reasonably well in classification and

segmentation tasks. Using multiple analyzing, wavelets have also been shown to improve

)2(2)( 2/ ntt mm −= −− ψψ

30 3.3 Feature Extraction

the overall classification accuracy, as each can detect different characteristic features of

textures [42].

Other first order statistics are computed by constructing a histogram of the wavelet

coefficients at each level [34]. To obtain such a histogram, uniform quantization of the

coefficients is used. The wavelet packet transform has been extensively used in texture

analysis as it allows greater resolution in the frequency domain. Lee and Pun [43] use the

wavelet packet transform to select only the dominant energy band for use as texture

features, allowing for good classification accuracy at reduced computational expense.

3.3.4 Gabor Features

Gabor functions were introduced by Dennis Gabor in 1946 in his ‘Theory of

Communication’. The purpose was to represent a signal in both the time and frequency

domains simultaneously. The work of Gabor was extended to 2-D by Daugman [44]. The

Gabor filter takes the form of a 2-D Gaussian modulation complex sinusoidal grating in

the spatial domain [45], which is given by:

)(2exp),(),( VyUxjyxgyxh +−′′= π (3.7)

where ),( VU defines the position of the filter in the Fourier domain with a centre

frequency of 22 VUf += and an orientation of )/arctan( UV=θ . The term

),( yxg ′′ represents a Gaussian function orientated at an angle φ , where ),( yx ′′ are the

3.3 Feature Extraction 31 rotated co-ordinates given by φφ sincos yxx +=′ and φφ cossin yxy +−=′ . The general

form of the Gaussian function is:

⎥⎥

⎦

⎤

⎢⎢

⎣

⎡

⎟⎟

⎠

⎞

⎜⎜

⎝

⎛

⎟⎟⎠

⎞⎜⎜⎝

⎛+⎟⎟

⎠

⎞⎜⎜⎝

⎛−=

22

5.0exp2

1),(yxyx

yxyxgσσσπσ

(3.8)

where yx σσ / is known as the aspect ratio, which determines the eccentricity of the

Gaussian envelope. The product of xfσ determines the spatial frequency bandwidth b.

In recent times, Gabor filters have emerged as one of the most commonly used techniques

in the field of texture analysis. They are useful because they capture frequency and

orientation, which are important properties. By applying a rotation-invariant transform to

these features, it is then possible to create a set of texture descriptors that is invariant to

rotation. In this thesis, Gabor features will be compared with higher order spectral

features in virus recognition.

3.3.5 Higher Order Spectra 3.3.5.1 Time Domain Definition and Properties

Higher order spectra [46] consist of moment and cumulant spectra and can be defined for

both deterministic signals and random processes. If {X (k)}, k = 0, ±1, ±2, ±3…. is a real,

stationary, discrete-time signal and its moments up to order p exist, then

( ) ( ) ( ) ( ){ }11121 ...,...,, −− ++= pp

xp kXkXkXEm τττττ (3.9)

32 3.3 Feature Extraction represents the pth-order moment function of the signal, where E is the expectation

operation. The expectation operation can be performed over the ensemble (ensemble

averaging) or along the time dimension (time averaging). For ergodic processes, the two

expectations are the same. For deterministic signals, there is no ensemble averaging

possible. The first order moment xm1 is the mean value and second order moment )(2 τxm

is the auto-correlation function. The third-order moment ),(3 kjxm ττ is often called

bicorrelation function, and fourth order moment function ),,(4 srqxm τττ is often called

tricorrelation function, and so on.

There exists a general relationship between moment and cumulant functions. If we

consider a zero-mean stationary random process )(tx , then the relationship between these

two functions (or sequences) becomes quite simple. Specifically, the second and third

order moment are the same as the second and third order cumulant, respectively [47]

given by:

( ) ( ){ }τττ +== txtxEmc xx )()( 22 (3.10)

( ) ( ) ( ) ( ) ( ){ }2133 ,, ττττττ ++== txtxtxEmc kjx

kjx (3.11)

The relationship between the fourth order cumulant and moment is as follows:

)()()()()()(),,(),,( 22222244 qr

xs

xqs

xr

xrs

xq

xsrq

xsrq

x mmmmmmmc τττττττττττττττ −−−−−−= (3.12)

3.3 Feature Extraction 33 By putting 0=== srq τττ into the equations above, we obtain;

( ){ } )0(222

xckXE ==γ (variance) (3.13)

( ){ } )0,0(333xckXE ==γ (skewness) (3.14)

( ){ } ( ) )0,0,0(3 4

2244

xckXE =−= γγ (kurtosis) (3.15)

The following are important properties that any pth-order cumulants satisfy [48]

(i) Scaled quantities: The cumulants of scaled quantities equal the product of all

the scale factors times the cumulant of the unscaled quantities, i.e., if iλ , i = 1,2, …, p

are constants and ix , i = 1,2, …, p are random variables, then:

),...,,(),....,,( 21

p

1i2211 Π ppp xxxcumxxxcum

i⎪⎭

⎪⎬

⎫

⎪⎩

⎪⎨

⎧

==

λλλλ (3.16)

(ii) Symmetry: Cumulants are symmetric in their arguments, i.e.,

),...,,(),....,,( 2121 ipiip xxxcumxxxcum = (3.17)

where ( 1i ,..., pi ) is a permutation of (1,…, p); interchanging the arguments of the

cumulant in any way does not change its value, e.g.:

),,(),,(),,( 132412343214 τττττττττ CCC ==


(iii) Additivity: Cumulants are additive in their arguments, that is the cumulants of

sums equal sums of cumulants. For example, even if ox and oy are not statistically

independent, it is true that

),...,,(),...,,()....,,( 111 popopoo zzycumzzxcumzzyxcum +=+ (3.18)

(iv) Additive constants: Cumulants are insensitive to additive constants, that is, for

α constant:

),...,(),....,( 11 pp zzcumzzcum =+α (3.19)

(v) Sums: The cumulants of a sum of statistically independent quantities equals the

sum of the cumulants of the individual quantities, i.e., if the random variable [xi] are

independent of the random variables [ iy ] for i = 1,2, …, p then:

),...,,(),...,,(),...,,( 21212211 pppp yyycumxxxcumyxyxyxcum +=+++ (3.20)

Note that if ii yx ... were not independent, then from equation 3.18 there would be 2p terms

on the right hand side. Statistical independence reduces these terms to just 2.

(vi) Independent subsets: If a subset of the random variables is independent from the

rest, then

0)....,,( 21 =pxxxcum (3.21)

3.3 Feature Extraction 35 3.3.5.2 Frequency Domain Definition and Properties The Weiner-Khintchine relation [49] indicates that the spectral density function

)(wM xp and the correlation function )(τx

pm constitute of Fourier transform pair, that is

)()( wMm x

pxp ↔τ (3.22)

where w denotes frequency, and ↔ denotes a Fourier transform pair. The second order

moment spectrum is the classical power spectrum, and the third order moment spectrum

is the bispectrum and fourth-order is frequently referred to as the trispectrum. However,

the words bispectrum and trispectrum also are used to describe third-order and fourth

order cumulant spectra. The second-, third-, and fourth-order cumulant spectra also are

known as the power spectrum, bispectrum, and trispectrum, respectively as shown below:

General formula

⎥⎦

⎤⎢⎣

⎡−= ∑∑∑

−

=

∞

−∞=−

∞

−∞=−

−

1

1121121

1

exp),...,(...),...,,(p

iiipppp wjCwwwS

p

ττττττ

(3.23)

Power Spectrum: p =2

[ ]∑∞

−∞=

−=1

111212 exp)()(τ

ττ jwCwS (3.24)

In the above definitions, it is assumed that the moment or cumulant functions satisfy the

conditions necessary for a Fourier (spectral) representation. This implies that they decay

36 3.3 Feature Extraction and are at least square integrable. For discussion on existence of polyspectra for random

processes, refer to [50]. For a deterministic signal x(n), the power spectrum can be

expressed in terms of the Fourier transform of the underlying signals as:

)()(*)(2 wXwXwS =

Bispectrum: p =3

The bispectrum is the 2D-Fourier transform of the third cumulant function:

( ) ( ) ( )[ ]2211213213 exp,,1 2

τττττ τ

wwjCwwS +−= ∑ ∑∞

−∞=

∞

−∞=

(3.25)

for πππ ≤+≤≤ 2121 and,, wwww . For a deterministic, zero-DC signal the bispectrum

may be expressed in terms of the Fourier transform of the underlying signal since:

( ) ( ) ( ) ( ) ( )[ ]221121213 exp,1 2

τττττ τ

wwjnxnxnxwwSn

+−++= ∑ ∑ ∑∞

−∞=

∞

−∞=

∞

−∞=

(3.26)

setting knmn =+=+ 21 and ττ and splitting the exponent yields:

( ) ( ) [ ] ( ) [ ] ( ) ( )[ ]⎭⎬⎫

⎩⎨⎧

+⎭⎬⎫

⎩⎨⎧

−⎭⎬⎫

⎩⎨⎧

−= ∑∑∑∞

−∞=

∞

−∞=

∞

−∞= nkm

nwwjnxkjwkxmjwmxwwS 2121213 expexpexp,

)(*)()( 2121 wwXwXwX += (3.27)

Note that in the expressions above for the power spectrum and the bispectrum of a

deterministic signal, these spectra are Fourier transforms of the time averaged (or sample)

3.3 Feature Extraction 37 correlations of order 2 and 3 respectively, and there is no ensemble averaging. The

sample correlations are themselves deterministic functions of the lag variables in these

cases, and must satisfy conditions for existence of their Fourier transforms. If x(n) is a

finite duration sequence (as is the case for all cases in this thesis and for finite 1-D

patterns or finite length projections of 2-D patterns) the existence is guaranteed.

The symmetry conditions of ),( 213 wwS follow from those of the third cumulant, namely:

),(),( 123213 wwSwwS =

),(*),(* 213123 wwSwwS −−=−−=

),(*),(* 21132213 wwwSwwwS −−=−−=

),(*),(* 21231213 wwwSwwwS −−=−−=

Thus, knowledge of the bispectrum in the triangular region π≤+≥≥ 21122 ,,0 wwwww is

sufficient to describe the rest (Figure 3.2). This region (labeled 1) is often termed the

principal region of the bispectrum.


Figure 3.2: The symmetry regions of the bispectrum (labeled 1). The region labeled 1 contains a unique set of values and those in the other labeled regions can be mapped to these.

3.3.5.3 Motivations for Using Higher Order Spectra in Feature Extraction A wide range of applications has developed due to these unique properties of higher order

spectra such as image reconstruction, pattern recognition, image restoration and edge

detection. As mentioned by Chandran et. al. [11], the motivations for using higher order

spectra in feature extraction are as below:

(i) Higher order spectra preserve both amplitude and phase information from the

Fourier transform of a signal, unlike the power spectrum. The phase of the Fourier

transform contains important shape information [51].

1

2

34

5

6

7

8

9 10 11

12

w2

w1

w2=w1

w2+w1= π

-(w2+w1)= π

w1= - π

w2= π

w2= - π

w1= π

3.3 Feature Extraction 39 (ii) The Fourier phase of a one-dimensional (1-D) pattern is a shape-dependent

nonlinear function of the frequency and higher order spectra can extract this

information.

(iii) Finite-length patterns that are symmetric about their centres of support have a

Fourier phase that is a linear function of frequency. Therefore, the shape

information resides in the Fourier magnitudes. However, the Fourier magnitude

for positive frequencies is an asymmetric function whose shape is related to the

shape of the original input. Therefore, higher order spectra can still be used to

extract features indirectly from Fourier magnitudes.

(iv) Higher order spectra are translation invariant because linear phase terms are

cancelled in the products of Fourier coefficients that define them. Functions that

can serve as features for pattern recognition can be defined from higher order

spectra that satisfy other desirable invariance properties such as scaling,

amplification and rotation invariance.

(v) Higher order spectra are zero for Gaussian noise and, thus provide high noise

immunity to features.

(vi) Multidimensional signals can be decomposed into 1-D projections.

Transformations such as shift, scaling, or rotation of the multidimensional signal

can be related to shift or scaling of the projections. Higher order spectral features


derived from the projections can be used to derive invariant features for the

multidimensional signal.

3.3.5.4 Rotation, Translation and Scaling (RTS) Invariants Generation The bispectrum of a 1-D deterministic sequence, x(n) may be defined as in (3.27). It is

assumed that the sequence is oversampled for all scales of interest such that X(f) = 0 and

for f ≤ 1/2 , with the frequency f normalized by the Nyquist frequency.

The bispectrum (3.27) is a triple product of Fourier coefficients, and is a complex-valued

function of two frequencies, similar to the power spectrum, )(*)()( fXfXfP = , a

function of only one frequency. As mentioned earlier, the bispectrum retains information

about the phase of the Fourier transform of a sequence. For a symmetric sequence of

finite extent, the phase of the Fourier transform is a linear function of frequency, thus the

biphase is zero. As for an asymmetric sequence, the phase of the Fourier transform is a

nonlinear function of frequency and this nonlinearlity is extracted by the biphase.

Based on these properties, Chandran and Elgar [52] proposed a type of bispectral

projection that yields DC level, amplification, scale and translation invariant features

from the input.

These features are defined as;

))(/)(arctan()( aIaIaP ri= (3.28)

where


∫+

+==+= )a1/(10f 111ir 1

df)af,f(B)a(jI)a(I)a(I (3.29)

for 0< a ≤ 1, and j = √-1. The bispectral values are integrated along straight lines with

slope a passing through the origin in the bifrequency space are shown in Figure 3.3. Refer

to [52] for the discrete-time version of )a(I . In practice, the fast Fourier transform (FFT)

is used to obtain )K(X where NKf = , 12N,,....1,0K −= and the integral in (3.29) is

computed as a summation.

Figure 3.4 shows the flow chart of computation of these invariant parameters. P(a) is

invariant to translation and scaling. The direct and indirect methods can be used to

compute these invariant parameters. It has been shown [52] that the indirect method that

discards all the phase information from the original sequence achieves better scale

invariance. For different sequences that have the same DFT magnitude, the direct

procedure can be use to classify them.


Figure 3.3: Owing to symmetries of the bispectrum in equation (3.27), the bispectrum possesses redundancy and needs to be only computed for the triangular region shown above. Features are extracted by integrating the bispectrum along a radial line as shown and taking the phase of the complex-valued integral. 1f and 2f are frequencies normalized by one half of the sampling normalized frequency.

Invariance properties of the bispectral features that have been proved in [11] is shown

below:

Claim: P(a) are translation invariant

Proof: Translation produces linear phase shifts of sequence x(n) that cancel in (3.27).

Integrating the bispectrum along lines passing through the origin in bifrequency space

preserves the translation because the integral is translation invariant if the integrand is.

The phase of this complex entity I(a) must also be translation invariant because its real

and imaginary parts are. Thus, P(a) are translation invariant.


Claim: P(a) are scale invariant

Proof: Scaling the sequence x(n) results in an expansion or contraction of the Fourier

transform that is identical along the f1 and f2 directions. The real and imaginary parts of

the integrated bispectrum along a radial line are multiplied by identical real-valued

constants upon scaling and therefore the phase, P(a) of the integrated bispectrum is

unchanged.

Rotation invariance is achieved by deriving invariants from the Radon transform of the

image and using the cyclic-shift invariance property of the discrete Fourier transform

magnitude [11, 52].

3.3.5.4.1 Feature Extraction from 2-D Images The 1-D bispectral invariant features can be applied to 2-D images by taking Radon

transform projections and computing features from these projections [11]. Let g(u,v) be

an N x N image and {xθ(n)} be the Radon transform of the image, that is, a set of parallel

beam projections of the image at angles θ with respect to the horizontal axis as shown in

Figure 3.5. The 2-D image thus is reduced to a set of 1-D projections by computing

projections at equal increments of angle θ, or θi = iπ/ Nθ for i = 0 to Nθ – 1.

Features P(a) that are invariant to shift, scaling, or amplification of the 1-D function, x(n)

will therefore provide a set {P(a)(θ), a=1, Na } of 1-D functions of θ, which are cyclically

shifted when the image is rotated. The radial spectra of the bispectral invariants, P(a,ωθ)


where ωθ is a frequency in cycles per 180 degrees is a set of features that are invariant to

rotation, translation and scaling.

Figure 3.4: The direct and indirect methods for computation of invariant parameters for a 1-D sequence.

Input n

x(n)

DIRECT INDIRECT

FFT

Triple products X(f1)X(f2)X*(f1+f2)

Integrate along line of slope a

Parameter P(a)

DFT Magnitude For positive frequencies

3.4 Classifiers 45

Figure 3.5: The Radon transform of a 2-D image yields 1-D parallel beam projections, )n(x at various angles, θ .

3.4 Classifiers

An important consideration in the problem of texture classification is that of classifier

design. Most evaluations of texture features rely on simple classifiers, such as minimum

distance and nearest neighbour classifiers, while other researchers have used artificial

neural networks to good effort.

Classifiers for pattern recognition tasks have been widely studied. In theory, the Bayes

classifier is optimal for any problem, as it minimizes the probability of error. The true a

posteriori probability that an observation x belongs to a class iw is given by Bayes rule

∑ =

= Nn nn

iii

wxpwP

wxpwPxwPr

1)|()(

)|()()|( (3.30)

46 3.4 Classifiers

where N is the total number of classes, )( iwP is the a priori probability of being in class

iw and )|( iwxp is the true conditional density function for the class iw .

In practical applications, this true a posteriori probability can never be achieved, because

the true conditional density functions )|( nwxp can never be known with finite training

data. An estimate of this probability is given, such that

)()|()|( xxwPrxwPr ii ∈+=∧

(3.31)

where )(x∈ is an error term due to the limitations stated above. Thus the aim of a

classifier system is to provide an estimate of )|( iwxp such that this error is minimized.

The following section discusses some of the classifiers that are commonly used in texture

analysis.

3.4.1 Parametric and Non-parametric Classifiers

Classifiers are categorized into two types, parametric and non-parametric classifiers

which depend on the method used to find this decision function. Parametric classifiers

use the statistics of the data to implement the best discriminant function. The error of

classification in both supervised and unsupervised learning can be minimized with the

parametric approach, because this becomes a deterministic optimization problem. Non-

parametric classifiers do not use such parameters, but classify the features in feature

space using statistical optimality criteria.

3.4 Classifiers 47

3.4.2 Gaussian Mixture Models

A Gaussian Mixture Model (GMM) is a parametric model used to estimate a continuous

probability density function from a set of multi-dimensional feature observations. A

GMM probability density is described by the additive contribution of N multi-

dimensional Gaussian components. The Gaussian mixture model is described by mixture

component weights iw , means iµ and covariances iΣ . For a single observation, x, the

probability density given a GMM described by λ given by:

( ) )Σ,|(| iiµxx gwpN

ii∑

=

=1

λ (3.32)

The probability density of a single Gaussian component of D dimensions is given by:

( )( )

( ) ( )⎟⎠⎞

⎜⎝⎛ −−−= −

iiii µxµxµx 1i

iD 2

1exp2

1g Σ'|Σ|

Σ,|π

(3.33)

The vector or matrix transpose is represented by (').

The solution for determining the parameters of the GMM is by the Maximum Likelihood

(ML) parameter estimation criterion. The joint likelihood of T independent and

identically distributed feature vector observations, { }T21 xxxX ....,,= , may be specified

according to Equation 3.34,

( ) ( )∏=

=T

t

pp1

λλ |x|X t (3.34)

48 3.4 Classifiers This may conveniently be represented in log form as

( ) ( ) ( )∑=

==T

t

ppL1

|log|log λλλ txX (3.35)

In terms of the mixture component densities, the log-likelihood function to be maximized

is given by:

( ) ( )⎟⎟⎠

⎞⎜⎜⎝

⎛= ∑∑

==

N

iii

T

t

gwL11

log Σ,| it µxλ (3.36)

The model parameters are estimated such that they maximize the likelihood of the

observations. A method for maximizing the log-likehood of the observations is by the

general form of the Expectation-Maximization (E-M) algorithm. The E-M algorithm,

given the parameters of an initial estimate ⎭⎬⎫

⎩⎨⎧

⎭⎬⎫

⎩⎨⎧

⎭⎬⎫

⎩⎨⎧

⎭⎬⎫

⎩⎨⎧=

∧∧∧∧∧∧∧

NNww Σ,...,Σ,,...,,..., 11 N1 µµλ ,

will determine new estimates of the parameters, { } { } { }{ }NNww Σ,...,Σ,,...,,,..., 111 Nµµ=λ

such that ( ) ⎟⎠⎞

⎜⎝⎛≥

∧

λλ || XX pp . On each EM iteration, the parameters are updated using

the following equations:

Mixture Component Weights:

∑=

∧

⎟⎠⎞

⎜⎝⎛=

T

ti iPr

Tw

1

1 λ,| tx (3.37)

3.4 Classifiers 49 Mixture Component Means:

∑

∑

=

∧

=

∧

⎟⎠⎞

⎜⎝⎛

⎟⎠⎞

⎜⎝⎛

=T

t

T

t

iPr

iPr

1

1

λ

λ

,|

,|

t

tt

i

x

xxµ (3.38)

Mixture Component Covariances:

( )( )

∑

∑

=

∧

=

∧

⎟⎠⎞

⎜⎝⎛

′−−⎟⎠⎞

⎜⎝⎛

=T

t

T

t

i

iPr

iPr

1

1

λ

λ

,|

,|Σ

t

ititt

x

µxµxx (3.39)

The a posteriori probability for the Gaussian mixture component class i is given by

∑ =

∧∧∧∧

∧∧∧∧

∧

⎟⎠⎞

⎜⎝⎛

⎟⎠⎞

⎜⎝⎛

=⎟⎠⎞

⎜⎝⎛

N

j jjj

ii

ggw

ggwiPr

1Σ|

Σ|,|

µx

µxx

t

it

t λ (3.40)

One of the important attributes of the GMM is its ability to form smooth approximations

for any arbitrarily-shaped densities. As ‘real world’ data has multi-modal distributions,

GMM provide an excellent tool to model the characteristics of the data. Another

extremely useful property of GMM is the possibility of employing a diagonal covariance

matrix instead of the full covariance matrix [53]. Thus, the amount of computational time

and complexity can be reduced significantly. GMMs have been used widely in many

areas of pattern recognition and classification, and with great success in the area of

speaker identification and verification [54, 55].

50 3.4 Classifiers 3.4.3 Support Vector Machines

In the recent years, Support Vector Machines (SVMs) classifiers have demonstrated

excellent performance in a variety of pattern recognition problems [56-58]. Support

vector machines are particularly suited for binary classification tasks. In SVMs, patterns

from each class are categorized based on their location with respect to a hyperplane. The

hyperplane is obtained from the training data, in such a way that the best discriminance is

achieved even to unseen data. The advantage of SVMs is that complexity of the classifier

is defined not by the dimensionality of the transformed space, but rather by the number of

support vectors used to define the boundary hyperplane.

An SVM binary classifier selects an indicator function { }1,1: −aNRf from a class of

functions Λ∈αα ),,(xf , such that the function f correctly classify the test

examples ( )y,x . Like all learning machines, an SVM seeks to minimize the expected

error of classification. Since the underlying probability distribution of the data in each

class ),( yxP is unknown, the observed training data ( ) ( ) ( ){ }nn yxyxyx ,,...,,,, 2211 is used

to approximate it. This, implies approximating the actual risk by the empirical risk

(empirical in the sense that it is obtained from the data and not the distribution). Hence,

minimizing the empirical risk somehow contributes to the minimization of the actual risk.

A better estimation of the actual risk can be obtained in addition to the empirical data, the

confidence interval is considered. Hence the actual risk is bounded by the empirical risk

and the confidence interval as the following equation shows:

3.4 Classifiers 51

),(][][ hnfRfR emp Φ+≤ (3.41)

where R[ f ] is the actual risk, Remp[ f ] is the empirical risk and Φ(n,h) is the confidence

interval and is explicitly given by

( )

nnnh

hn4ln12ln

),(η−⎟

⎠⎞

⎜⎝⎛ +

=Φ (3.42)

which is a function of the training sample count n and the VC-dimension h of the

function class we seek. The probability that the bound in equation (3.41) holds is η−1 .

The VC-dimension h of a function is defined as the largest number of points that it can

correctly classify, when the training examples are drawn from an underlying distribution

( ) { }1, ±×∈ Nii Ryx hi ,....,2,1= in all the possible 2h ways.

The minimization of the right hand side of (3.41) is known as Structural Risk

Minimization (SRM), where we seek to minimize the upper bound on the actual risk, by

minimizing either Remp[ f ] or Φ(n,h). This principle of SRM is implemented by

expressing the concept of VC dimension in practical terms, such as margin of the optimal

separating hyperplane (OSH). The margin is defined as the minimum distance of a

sample to the decision surface as in Figure 3.6.

52 3.4 Classifiers The OSH f(x) is a linear function expressed as:

f(x) = (w.x) + b (3.43)

where the length of weight vector w can be used as a measure of the margin length, and b

is an offset parameter. The weight vector may not be easily found in the input space. The

coefficients w and b are found by solving the quadratic programming problem [58, 59].

The solution (or hyperplane) is generally sought in a feature space that is higher than the

input space. This feature space of higher dimension is a result of a non-linear transform

of the input space. It is easier to obtain a linear hyperplane in the higher dimensional

space. The solution is obtained using optimization theory and involves the inner product,

which appears as we proceed in the quest of obtaining w. This ubiquitous inner product

expression is called the kernel. There is a freedom of choice of kernels depending on the

nature of the data being handled. Some of the common kernels are polynomial kernels,

Gaussian RBF's and the Sigmoidal [60]. Table 3.1 shows the descriptions of these

kernels.

3.4 Classifiers 53

-5

0

10

5

5

0 10

*1

*6

*8

*4

*5

o

2

o

7 o

9

o10o

3

Margin

-5

0

10

5

5

0 10

*1

*6

*8

*4

*5

o

2

o

7 o

9

o10o

3

Margin

Figure 3.6: SVM Margin

Kernel Description k(x,y) Polynomial dyx )).(( θ+

Gaussian RBF ⎟⎟⎠

⎞⎜⎜⎝

⎛ −−β

2||||exp yx

Sigmoidal )).(tanh( θ+yxk Inverse Multiquadric

22||||1

β+− yx

Table 3.1: Some commonly used kernels. The method to determine these kernels parameters are illustrated in [60].

54 3.5 Summary 3.5 Summary

In this chapter, the process of creating an automated recognition system was discussed

with emphasis on feature extraction and classification methods. Of particular interest is

the Gabor features which will be compared with higher order spectral features in virus

recognition and Support Vector Machine (SVM) and Gaussian Mixture Model (GMM) as

classifiers. The remaining sections of the chapter outlined a number of popular feature

extraction techniques which have been used over the years such as co-occurrence

matrices, autocorrelation and wavelet. Only a brief summary of each technique is

presented due to the large body of material on the subject in the literature and research

activity currently in progress.

This chapter provides a brief background of HOS and its properties. This chapter also

presents an algorithm for invariant feature extraction from 1-D sequence and extends the

algorithm to 2-D images. This algorithm used radial spectra of higher order spectral

features to provide desirable invariance properties such as rotation, translation and

scaling and to provide noise immunity. The virus recognition system developed for this

thesis incorporates the method used to extract these features.

Chapter 4 A Study of Texture and Contour

4.1 Introduction

This chapter follows the review of virus morphology, the role of electron microscopy in

virology in Chapter 2 and the steps of creating an automated virus recognition system that

includes the approach to texture analysis in Chapter 3. Chapter 3 also discussed a brief

background on Higher Order Spectra (HOS), the motivations for using HOS in feature

extraction and generation of the bispectral invariant features. In this chapter, the goal is

to involve knowledge of feature extraction using HOS, the direct and indirect methods to

a set of synthetic images with different textures and contours. The knowledge gained will

then be applied to virus recognition.

56 4.1 Introduction

Texture is an important term used to characterize the surface of an object and is a

significant feature used in many applications of image processing and pattern recognition.

The evaluation of texture and contour features is important for virus recognition. This

forms a basis for creating an automated virus recognition system because different

viruses appear differently on electron micrographs. The morphological (texture and

contour) differences appearing on the micrograph are useful in distinguishing one virus

group from another. As mentioned in the earlier chapter, the morphology differences

arise due to the arrangement of capsomeres that are evidenced through negative staining

of the viral particle. Some of the negative-stained virus particles are shown in Figure 4.1.

When stained, adenoviruses appear as hexagonal shaped with distinct, closely packed

capsomers. Astroviruses appear circular in outline and a 5- or 6-pointed white star

configuration in certain orientations; Caliciviruses giving a ‘Star of David’ appearance

(refer to Figure 4.1). These differences might not be visible to the naked eye, thus

making virus recognition a challenge.

In this chapter, the analysis of texture and contour was carried out using a set of synthetic

texture images from the Brodatz album. The first segment of work is to investigate the

relative importance of phase and magnitude in texture. In the subsequent experiments,

noise was added to the images to stimulate EM images that are normally noisy due to the

high magnification used to capture the viruses. These experiments will enhance our

understanding of texture and contour classification of noisy images using higher order

spectral features and also will help to determine the effectiveness of using processing

4.2 The Relative Importance of Phase and Magnitude in Texture Analysis 57

techniques such as averaging of features and input decision fusion for improvement of

classification results.

(a) (b) (c)

Figure 4.1: A single virus particle of (a) Adenovirus (b) Astrovirus (c) Calicivirus. Note that although there are small differences in texture and contour, it is difficult to tell them apart by visual examination.

4.2 The Relative Importance of Phase and Magnitude in

Texture Analysis

Phase and magnitude-only have been studied in acoustical and optical holograms [51].

Research has shown that reconstructed objects from the magnitude-only holograms are

not of much value in representing the original object, whereas reconstructions from

phase-only holograms have many important features in common with the original objects.

Similar observations also have been made in the context of speech signals, X-ray

crystallography and images. As with holograms, only phase-only images have Fourier

transform phase equal to that of the original image. These studies suggest very strongly

58 4.2 The Relative Importance of Phase and Magnitude in Texture Analysis

that in many contexts the phase contains much of the essential information in a signal

[51, 61, 62] .

Currently no research has been done in the area of investigating the relative importance

of Fourier phase and magnitude in texture analysis. Thus, the aim of this section is to

compare the best representation of texture when magnitude and phase information are

used in isolation and to compare the importance of phase and magnitude in different

types of textures.

4.2.1 Experimental Procedure

Two images or textures, known as Texture 1 and Texture 2 were selected from the

Brodatz album. Each of the 512 X 512 textures was reduced to 256 X 256, and a circular

mask was applied to the image. A Fourier transform was computed to obtain the

magnitude and phase of the textures. The magnitude of Texture 1 was combined with

phase of Texture 2 and the magnitude of Texture 2 with phase of Texture 1. Contrast

stretching was applied to the images after inverse fast Fourier transform (FFT) was

performed on these images. These steps are shown in the flow chart in Figure 4.2.

The textures used in this experiment can be divided into 2 categories, spatially

homogeneous (pseudo periodic and periodic) and inhomogeneous. Tests were conducted

with 2 randomly chosen images of (a) homogeneous and homogeneous textures, (b)

inhomogeneous and inhomogeneous textures, and (c) homogeneous and inhomogeneous


textures. Examples of homogeneous and inhomogeneous textures used are shown in

Figure 4.3. This analysis was evaluated with 12 sets of two different types of textures

using the combinations stated above. In each set, two of these textures were subjected to

steps shown in Figure 4.2. If magnitude information is more important, the inverse FFT

of the magnitude of Texture 1 and phase of Texture 2 will represent Texture 1. This is

opposite when phase information is more important.

Figure 4.2: Flow chart of analysis of two different textures to evaluate the importance of phase or magnitude in representing the texture.

INPUT Texture 1

Fourier-transform

Combine Mag1 with Phase2

INPUT Texture 2

Fourier-transform

Combine Mag2 with Phase1

Inverse FFT Inverse FFT

Contrast stretching Contrast stretching

Does it represent Texture1 or Texture 2?

Does it represent Texture1 or Texture 2?

OUTPUT If Texture 1,magnitude is important

If Texture 2,phase is important

OUTPUT If Texture 1,phase is important

If Texture 2,magnitude is important


(a)

(b)

Figure 4.3: Examples of (a) homogeneous textures (b) inhomogeneous textures used in the experiment. Two of the images above are randomly chosen and subjected to steps in Figure 4.2.

4.2.2 Results and Discussion

Some of the results presented in terms of input and output textures are shown in Figure

4.4. The rest can be found in Appendix A.1. In all cases, the magnitude information

seems to be more important when both input textures are homogeneous. As shown in

Figure 4.4(b), combining the magnitude of a homogenous texture (Texture 1) with the

phase of another homogenous texture (Texture 2) shows an output texture of Texture 1.


This is opposite when testing with 2 inhomogeneous textures, where phase information is

more important (Figure 4.4(a)). Whereas, combining the magnitude of a homogeneous

texture with the phase of an inhomogeneous texture shows a clearer representation of the

homogeneous texture at the output (Figure 4.4(c)), it contains more features of the

homogeneous pattern than the inhomogeneous pattern. In contrast, combining the phase

of a homogeneous texture with the magnitude of an inhomogeneous texture represents

neither of the images at the output (Figure 4.4(c)).

This analysis shows that the importance of phase and magnitude dependents largely on

the pattern of the textures and does not necessarily reside on phase-only. The results

illustrate that magnitude information will better represent the texture when both the input

textures are homogeneous, and that if the magnitude information is eliminated, many of

the important characteristics of texture will not be retained. As outlined in Chapter 3,

although the direct method uses both magnitude and phase information, it emphasizes

phase information. Most of the magnitude information is lost in the integration over the

bifrequency plane and the division to obtain phase parameters. Relative performance of

the direct features for phase-only and magnitude-only speech data can be found in [63].

The indirect method discards all phase information because it uses the magnitude of the

DFT for positive frequencies of the input. However, it extracts the magnitude information

in a manner superior to mere extraction of energy in spectral bands. Virus images show

homogeneous textures, and thus the indirect method is used in this thesis and in the

evaluation of the following sections.


Figure 4.4: Results when images of (a) 2 inhomogeneous textures (b) 2 homogeneous textures (c) a homogenous and inhomogeneous texture were used as input textures after subjected to steps in Figure 4.2. The top images of each subfigure are the input and the bottom images are the output.

(b) (a)

(c)

4.3 Texture and Contour Analysis using HOS 63 4.3 Texture and Contour Analysis using Indirect Method for

HOS Feature Extraction

4.3.1 Introduction The performance of using the indirect method to obtain bispectral features is evaluated

experimentally using a selection of images from the Brodatz album, which can be

downloaded from http://www.ux.his.no/~tranden/brodatz.html. These images were

chosen on the basis of being relatively uniform and regular in appearance, or in other

words, they are homogeneous textures.

In this section, four experiments were carried out. In the first experiment, 40 different

texture images with different contours were used to perform classification to determine

the ability of higher order spectral features to discriminate a large number of images with

different textures and contours. In the second experiment, 4 texture images were chosen

and 4 different contours were applied to each image to distinguish images with the same

texture but different contours. In the third experiment, images with different levels of

signal and noise ratio were used to investigate the robustness of higher order spectral

features to noise. The final experiment seeks to improve the classification results by

averaging the features and the performance of input fusion.

In the following experiments, each of the 512 X 512 textures was tiled into 64 X 64 sized

images, resulting in 64 sample images for each texture. Each of the 64 X 64 images was

rotated at 3 random angles to produce a total of 192 images for each texture. Noise was

64 4.3 Texture and Contour Analysis using HOS

added to the images. 150 bispectral features were then extracted from each image.

Section 3.3.5.4 outlined the procedure of extracting the features using the indirect

method. These features extracted are invariant to rotation, translation, scaling and robust

to noise.

The features used for training and testing were randomly chosen, and 15 realizations of

the experiments were undertaken for each binary classification task, and the results were

averaged. Forty were used for training and the remaining for testing. The training and test

images were extracted from separate parts of the image such that no overlap between the

two sets is possible. In all cases, a RBF kernel with width = 0.1 in the Support Vector

Machine (SVM) was used for classification.

4.3.2 Experiment with a Large Database of Different Textures and

Contours

The experiment was carried out on 40 texture images chosen from the Brodatz album; 10

of these textures has a circular contour, 10 of 5-fold-symmetry, 10 of 6-fold-symmetry

and 10 of 7-fold-symmetry contour. Figure 4.5 shows some of the different texture

images used with different contours. Each image is labeled using the standard notation in

this texture database. White Gaussian noise was added to the image with signal to noise

ratio (SNR) equal to 5dB. Each trial used average features from 5 images.

4.3 Texture and Contour Analysis using HOS 65

(a) (b)

(c) (d)

Figure 4.5: Four different texture images with four different contours (a) D5 with 5 fold symmetry contour (b) D17 with 6 fold symmetry contour (c) D21 with 7 fold symmetry contour (d) D33 with circular contour chosen out of the forty Brodatz images that were used for classification.


The misclassification results of the first 10 textures are tabulated as shown in Table 4.1.

The rest are in Appendix A.2. The overall performance over 40 textures shows an

average misclassification of 1.37%, demonstrating that low misclassification can be

achieved in a large database of different textures and contours. Thus, bispectral features

are able to distinguish images of different textures and contours.

D1 D2 D3 D5 D6 D8 D9 D11 D16 D17

D1

D2 1.88

D3 0.35 0.27

D5 0.79 3.54 0.08

D6 0.02 0.06 0.33 0

D8 0 0.98 0 0.69 0

D9 1.00 0.54 1.94 0.04 1.06 0

D11 6.23 1.69 0.94 0.27 0 0.21 1.25

D16 0 0 0.04 0 1.02 0.04 2.25 0.04

D17 0 0 0 0 1.48 0.02 0.42 0 0.33

Table 4.1: Misclassification rate (%) of the first 10 textures out of the 40 that were chosen from the Brodatz album. The overall performance over 40 textures shows an average misclassification of 1.37%.

4.3 Texture and Contour Analysis using HOS 67 4.3.3 Experiment with Images of the Same Texture of Different

Contours

Four texture images from the Brodatz album, D5, D8, D17, D21 were chosen as shown in

Figure 4.6. Four different contours (circular, 5-,6-,7-fold symmetry) were applied to each

texture image. Similar to the previous section, white Gaussian noise of SNR equal to 5dB

was added to the images and feature averaging of 5 images were used for each trial.

(a) (b)

(c) (d)

Figure 4.6: Four texture images from the Brodatz album (a) D5 (b) D8 (c) D17 (d) D21 used in the experiment. 4 different contours were applied to each of these texture images.


The classification results of D5 and D21 using higher order spectral features are

presented in Table 4.2 and the rest are in Appendix A.3. It shows the percentage of

misclassification. The misclassification among the 5-6-7 fold symmetry is slightly higher

than the misclassification of circular against the 5-6-7 fold symmetry, which is as

expected. It also is observed that misclassification of textures D5 and D8 is slightly

higher than D17 and D21, because in low spatial frequency textures (both D5 and D8)

and in texture images that are homogeneously random (D5), each of the extracted tiles

contains only part of the texture and thus does not represent the underlying pattern that

spans the entire source image (Figure 4.7).

4.3 Texture and Contour Analysis using HOS 69 Circular 5 fold sym 6 fold sym 7 fold sym

Circular

5 fold sym 8.06

6 fold sym 7.64 12.58

7 fold sym 4.47 7.94 9.94

(a)

Circular 5 fold sym 6 fold sym 7 fold sym

Circular

5 fold sym 2.92

6 fold sym 0.92 4.77

7 fold sym 1.60 5.98 4.48

(b)

Table 4.2: Misclassification rate (%) of four different contours of (a) D5 and (b) D21 texture images using higher order spectral features.


Figure 4.7: The 512 X 512 texture is tiled into 64 X 64 sized images. The texture inhomogeneity between the tiles causes higher classification inaccuracy. 4.3.4 Experiment with Various Level of Noise The robustness against noise of the methodology is studied in this section. The textures

are degraded with noise at different levels. The amount of noise added is measured using

signal to noise ratio (SNR), which is the average signal to noise ratio. White Gaussian

noise was added to four different textures with SNR equal to -80dB, -50dB, -40dB,

-30dB, -20dB, -10dB and 0dB. The texture images chosen were D5, D8, D17 and D21

from the Brodatz album (Figure 4.6). Each trial consists of feature averaging of 5

different images. Figure 4.8 shows the texture of D5 with added noise of SNR equal to

4.3 Texture and Contour Analysis using HOS 71

-50dB, -40dB and -30dB. The results in percentage of misclassification of these images

using higher order spectral features is presented in Table 4.3. The rest is in Appendix A.4.

(a) (b)

(c) Figure 4.8: Gaussian noise added to texture D5 with SNR equal to (a) -50 dB (b) -30 dB (c) -20 dB


The misclassification in percentage when SNR equal to -50dB is fairly high. This is

expected because the original image is barely visible when noise is added (Figure 4.8(a)).

The misclassification improves with decreasing noise as shown in Figure 4.9. An average

misclassification of textures D5, D8, D17 and D21 was used for this plot, and shows that

the method is robust down to a SNR of -30dB.

D5 D8 D17 D5 D8 27.1 D17 22.5 21.0 D21 29.2 22.1 23.7

(a)

D5 D8 D17 D5 D8 6.10 D17 0.42 0.44 D21 0.46 0.56 14.4

(b)

D5 D8 D17 D5 D8 5.90 D17 0.23 0.33 D21 0.31 0.77 12.6

(c)

Table 4.3: Misclassification rate (%) of four textures with added white Gaussian noise of SNR equal to (a) -50 dB (b) -30 dB (c) -20 dB using higher order spectral features.

4.3 Texture and Contour Analysis using HOS 73 4.3.5 Experiment with Averaging of Features and Input Fusion of Noisy Images

In the previous sections, feature averaging over 5 images was used in all testing. In this

section, we increased the test ensemble for feature averaging from 5 images to 10 and 20

images. White Gaussian noise was added to the images (D5, D8, D17, D21) with SNR

equal to -30dB.

The results are presented in Table 4.4, which shows the percentage of misclassification of

feature averaging of 10 images and 20 images with SNR = -30dB using higher order

spectral features. As clearly seen (Table 4.4), as the number of test ensemble increases,

the misclassification rate drops.

The result of feature averaging of 5 images (Table 4.3(b)) produces an average

misclassification of 3.6%. Feature averaging of 10 images gives an average

misclassification of 1.8% and averaging of 20 images has a 0.8% misclassification rate

(Table 4.4). This shows that averaging of features improve the classification

performance.


-80 -70 -60 -50 -40 -30 -20 -10 0 100

5

10

15

20

25

30

35

Signal to Noise Ratio (dB)

Mis

clas

sific

atio

n Ra

te (%

)

Figure 4.9: Noise performance of bispectral features. Misclassification rate shown is an average misclassification of textures D5, D8, D17 and D21.

D5 D8 D17 D5 D8 1.69 D17 0 0.5 D21 0 0.52 8.14

(a)

D5 D8 D17 D5 D8 1.48 D17 0 0.44 D21 0 0.27 2.4

(b) Table 4.4: Misclassification rate (%) when feature averaging of (a) 10 images (b) 20 images were used for classification using higher order spectral features.

4.3 Texture and Contour Analysis using HOS 75 Another method to reduce the percentage of misclassification is by input fusion where the

features are combined from N images, and soft decisions (likelihoods) are averaged from

M such sets of N images. In the following experiments, different numbers of M were

chosen while N was fixed at 5. Table 4.5 presents the misclassification percentage when

M = 4 and 8 and N = 5 using higher order spectral features. The rest of the results, where

M = 2, 5 and 10 is in Appendix A.5. From the results, it can be seen that the average

misclassification of textures D5, D8, D17 and D21 with added noise (SNR = -30dB)

decreases as M increases. Figure 4.10 shows the misclassification in percentage with

different M.

D5 D8 D17

D5 D8 0.5 D17 0.083 0 D21 0.083 0.25 4.42

(a)

D5 D8 D17

D5 D8 0 D17 0 0 D21 0 0 1.2

(b)

Table 4.5: Misclassification rate (%) when M = (a) 4 (b) 8 sets and N=5 images were used for classification using higher order spectral features. Gaussian noise of SNR = -30 dB was added to the image.

76 4.4 Summary

4.4 Summary This chapter begins by investigating the relative importance of Fourier phase and

magnitude. Experimental evaluations were carried out using a set of texture images from

the Brodatz album. This analysis shows that the importance of phase and magnitude

dependents largely on the pattern of the textures. Through this investigation, the indirect

method of obtaining bispectral features was used for the subsequent experiments.

A large number of experiments were conducted to illustrate the effectiveness of the

proposed bispectral features for classification of texture and contour. The experimental

results show the ability of bispectral features in classifying a large database

of different texture images with different contours, as well as images with the same

texture, but different contours. Since it is important that any texture classification scheme

can operate successfully in a noisy environment, particularly in the application to EM

virus images, the robustness of this feature against noise was evaluated. The method

shows robustness to noise down to a SNR of -30dB.

This chapter has presented two approaches for improving the classification accuracy

particularly the noisy images. Experimental evaluations were carried out by increasing

the feature averaging of N number of images and input fusion, where the features are

combined by averaging of M sets where each set consists of N number of images. Both

methods have shown the ability to reduce the percentage of misclassification. The

analytical and experimental study of texture and contour in this chapter has provided an

important foundational knowledge that can be applied to virus recognition.

4.4 Summary 77

1 2 3 4 5 6 7 8 9 100

0.5

1

1.5

2

2.5

3

3.5

4

Mis

clas

sific

atio

n ra

te (%

)

M sets

Figure 4.10: Average misclassification rate in percentage by input fusion where the features are combined by averaging of M sets where each set consists of 5 images.

Chapter 5 Virus Recognition using Higher

Order Spectral Features

5.1 Introduction Viruses can be viewed only by using electron microscopes, and although large

populations can be imaged, the individual images often are noisy and viral particles can

vary in orientation and size. Additional processing such as averaging an ensemble of

particles is necessary to get a better result. Higher order spectral features, that are

invariant to translation, rotation and scaling and robust to noise, have been defined and

applied in previous pattern recognition work, but not in virus recognition.

80 5.1 Introduction

This segment of work examines the use of radial spectra of higher order spectral invariant

features to capture information about symmetries and asymmetries of different types of

viruses in electron microscope images. Biological reproduction processes often impart

symmetries to the forms of organisms, and viruses are even seen assembled in crystal-like

structures. Radial spectra of invariant higher order spectral features can be averaged over

an ensemble of particles regardless of the orientation and size changes. Shape information

can thus be extracted and used for classification even when an individual segmented virus

image is difficult to classify on its own.

In the chapter, experiments were carried out to identify gastroenteritis virus population

from digitised EM images of four types of viruses; Rotavirus, Adenovirus, Astrovirus and

Calicivirus, whose morphologies are quite similar. The performance of the method on

viruses of similar size was separately evaluated using Astrovirus, Hepatitis A virus

(HAV) and Poliovirus. The viral particles from one or more images are segmented and

analyzed to verify whether they belong to a particular class (such as Adenovirus,

Rotavirus etc) or not. Two experiments were conducted - depending on the populations

from which virus particle images were collected for training and testing, respectively. In

the first, disjoint subsets from a pooled population of virus particles obtained from

several images were used. In the second, separate populations from separate images were

used.

5.2 Higher Order Spectra 81

A Gaussian Mixture Model (GMM) and Support Vector Machine (SVM) were used

separately to train the viruses and results were compared. A threshold on the log

likelihood is varied to study false alarm and false rejection trade-off. Features from many

particles and/or likelihoods from independent tests are averaged to yield better

performance. Results are presented in detection error trade-off (DET) curves.

5.2 Higher Order Spectra (HOS) As outlined in Chapter 3, the bispectrum is a function of two frequencies and in contrast

to the power spectrum this function is complex-valued in general and thus retains some of

the phase information in the Fourier transform. Figure 5.1 presents an illustration of two

different signals which that identical power spectra but different bispectra. A one-

dimensional input sequence that is finite in length and has a z-transform with zeros inside

and outside the unit circle (non-minimum phase) is used in this illustration (Figures 5.1(a)

and 5.1(b)). All the zeros that are outside the z-plane are inversed conjugate to produce a

sequence that is of minimum phase. The z-transform of the minimum phase is shown in

Figure 5.1(e). The power spectrum of the minimum and non-minimum phase sequence is

identical (Figures 5.1(c) and 5.1(f)). A distinct difference can be seen in the plot of the

real and imaginary parts of the bispectrum (Figure 5.2) showing that the information of

phase only be captured only by higher order spectra.

Especially for asymmetric sequences the phase is nonlinear and higher order spectra

retain the nonlinear phase information. Higher order spectra also are unaffected by a

82 5.2 Higher Order Spectra

translation of the input. These unique properties of higher order spectra are useful in

pattern recognition. If an input is even (or odd) symmetric, the phase of the Fourier

transform is zero (or pi) or a linear function of frequency if the input is shifted. In either

case, the phase of the bispectrum will be zero. This is expected because all the

information resides in the Fourier magnitude for such inputs. The magnitude of the DFT

of the input for positive frequencies may then be used to compute higher order spectral

invariants (referred to as indirect HOS invariants) [11]. Because virus images can exhibit

symmetry in projections, the indirect method is used in this work. An added advantage of

using the indirect method is that the DFT magnitude sequence is band-limited, and scale

invariance is better satisfied for these indirect features. Preliminary experimental and

analytical evaluations of texture and contour in Chapter 4 also justify and support the use

of the indirect method in obtaining the bispectral features in the application to viruses.


0 2 4 6 8 10 12 140

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h(k)

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G(k

)

(a) (d)

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Imag

inar

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(b) (e)

0 2 4 6 8 10 12 140

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Frequency, w

| H(w

) |

0 2 4 6 8 10 12 140

1

2

3

4

5

Frequency, w

| G(w

) |

(c) (f)

Figure 5.1: Illustration of the inability of the power spectrum to retain phase information. Figure 5.1(a) Non minimum phase of input sequence, h(k), Figure 5.1(b) Zeros of the non-minimum phase, Figure 5.1(c) Power spectrum of the non-minimum phase sequence. The zeros outside the unit circle in Figure 5.1(b) are inversed conjugate to produce a minimum phase sequence. Figure 5.1(d) 1-D plot of the minimum phase sequence, Figure 5.1(e) Zeros of the minimum phase sequence, Figure 5.1(f) Power spectrum of the minimum phase sequence.


20 40 60

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0.5

f2

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Figure 5.2: The left top and bottom figures show the imaginary and real parts of the bispectrum of Figure 5.1(a) and the right top and bottom figures show the imaginary and real parts of the bispectrum of Figure 5.1(d). The differences observed in the plots show the ability of bispectrum to retain the phase information.

5.2.1 Illustration of the Indirect Method in obtaining Bispectral

Features using Synthetic Images

The indirect method in obtaining the bispectral invariant parameters is outlined in

Chapter 3. The steps can be summarized using the flow chart in Figure 5.3. Using Radon

transform projections, the 2-D image is reduced to 1-D image [11], rotation invariance is

achieved by taking radial spectra of these features. The radial spectra of the bispectral

invariants, ),( θωaP where θω is a frequency in cycles per 180 degrees is a set of features

that are invariant to rotation, translation and scaling.


The steps of computing these invariant features are clearly illustrated using synthetic

images of n-fold symmetries as shown in Figures 5.4, 5.5 and 5.6. Figures 5.4(c) and

5.4(d) show the Radon transform projections at 45 degree angle of images with a 5 fold

symmetry and 7 fold symmetry binary object, respectively. Figure 5.5 shows the real and

imaginary parts of the bispectrum of these projections. Figure 5.6 shows the radial

spectrum of the bispectral features, )2/1(P . Note that the 5 fold symmetry image

produces a peak showing a dominant symmetry at 5 cycles per 180 degree, whereas the 7

fold symmetry image produces a peak at 7 cycles per 180 degrees.

To illustrate how robustness can be achieved by averaging these features, the 7 fold

symmetry image is used and white Gaussian noise is added to the image with SNR equal

to 0dB. With only one image used, the plot of the radial spectrum of the bispectral

features, as shown in Figure 5.7(a) does not reveal a dominant symmetry at 7 cycles per

180 degrees. In Figure 5.7(b), the individual spectra are accumulated over 75 of the 7 fold

symmetry images with similar signal to noise ratio (SNR = 0dB). Ensemble averaging

images produce spectra (see top line in Figure 5.7(b)) that eventually converge to a form

revealing a visible peak at 7 cycles per 180 degrees. This is applicable to EM images

where due to the low signal to noise ratio, individual viral particles are difficult to discern

visually and present a challenge to feature extraction. Averaging of these features

improves the classification performance.


Figure 5.3: Flow chart of computation of invariant parameters. ),( θaP is invariant to scaling and translation and ),( θωaP is invariant to scaling, translation and rotation. The algorithm was tested on a 5 fold symmetry and a 7 fold symmetry image and results are presented in Figures 5.4, 5.5 and 5.6.

n

x(n)(θ)

Input

Zero pad and FFT

Triple Product X(f1)X(f2)X*(f1+f2)

Integrate along line of slope a

Parameter P(a,θ)

| DFT|

Parameter P(a,ωθ)

| DFT|

Obtain the DFT magnitude, retain positive frequencies spectrum only


Figure 5.4: Figure 5.4(c) and 5.4(d) show the Radon transform projection at 45 degree angle of the 7 fold symmetry image, Figure 5.4(a) and the 5 fold symmetry image, Figure 5.4(b).

7 fold symmetry 5 fold symmetry 5.4(a) 5.4(b)

5.4(c) 5.4(d)

5.5(a) 5.5(b)


Figure 5.5: Figure 5.5(a) and Figure 5.5(c) show the real and imaginary parts of the bispectrum of the Radon transform projection at 45 degree angle of Figure 5.4(a). Figure 5.5(b) and Figure 5.5(d) show the real and imaginary parts of the bispectrum of Figure 5.4(b). The bispectrum is a triple product of Fourier coefficients and is a complex valued function of two frequencies, f1 and f2, where f1 and f2 are frequencies normalized by one half of the sampling frequency. Different shaped projections result in different bispectra. Invariant features are extracted by integrating along radial lines and taking the phase. The scale shown at the colorbar above is the log of the absolute value of the real and imaginary parts of the bispectrum. The above plots show that features, )a(P close to

21a = may capture differences as well.

Figure 5.6: Figure 5.6(a) and 5.6(b) show plot of ))(2/1( θωP as a function of θω , (where θω is a frequency in cycles per 180 degrees) of Figure 5.4(a) and Figure 5.4(b).

))(2/1( θωP is invariant to scaling, translation and rotation. Note that Figure 5.6(a) shows a dominant symmetry at 7 cycles per 180 degrees whereas Figure 5.6(b) shows a dominant symmetry at 5 cycles per 180 degrees.

5.6(b) 5.6(a)

5.5(c) 5.5(d)


Figure 5.7: Figure 5.7(a) shows the radial spectrum of the bispectral features,

))(2/1( θωP as a function of θω , (where θω is a frequency in cycles per 180 degrees) of a 7 fold symmetry. White Gaussian noise has been added and SNR = 0dB to the image. In Figure 5.7(b), the individual spectra are accumulated over 75 such images. Note that Figure 5.7(a) does not demonstrate a dominant symmetry at 7 cycles per 180 degrees due to the low signal to noise ratio. As an ensemble of images is taken and the spectra are accumulated, it eventually converges to a shape. A peak at 7 cycles per 180 degrees can be seen in Figure 5.7(b). Robustness to noise can thus be achieved by averaging these features.

Next, a 3-D reconstructed Adenovirus displayed on greyscale image in 2-D is compared

with a 5 fold symmetry image. In Figure 5.8, plots of ))(( θωaP are compared, where

a =1/2 and θω = 1, 2……. 16 cycles per 180 degrees. ))(( θωaP which is invariant to

translation, rotation and scaling captures information from the contour and texture

properties of the virus image that is useful for verification.

3-D reconstructions of virus particles are normally taken from a large set of electron

cryomicroscopy (cryo-EM) images. Comparing with conventional EM, where the

specimens are metal stained and dried for observation, in cryo-EM, the unstained

particles are preserved in a flash-frozen aqueous environment. The drying process in

5.7(a) 5.7(b)


conventional EM (example negative staining) tends to flatten the structure onto the

support plane, causing distortions to the 3D structure. In other words, what is seen in the

electron micrographs might not be a faithful representation of the virus. Consequently,

the 3D reconstruction image is not used here to build the reference feature vectors for

classification. A large set of negative stained EM images was used, which will produce a

more accurate classification result when the testing set is of a similar preparation method.

Figure 5.8: Comparison between a 5 fold symmetry image and a 3D reconstructed virus image using plots of radial spectra of the bispectral features, P(1/2). These features which are invariant to translation, rotation and scaling contain information from the contour and texture that are useful for verification.

5 fold symmetry 3D reconstructed Adenovirus

5.3 Gastroenteric Viruses 91 5.3 Gastroenteric Viruses Acute gastroenteritis is one of the most common diseases that affect humans, and is a

significant cause of morbidity and mortality worldwide [64], causing 3-5 million deaths

per year. The majority of these occur in developing countries [65] and children under 5

years of age [64]. Viruses, apart from bacteria and other parasites, have been known to be

the important causes of gastroenteritis. Four major categories of viruses are now

recognized as clinically important to this problem. These are Rotavirus, Astrovirus,

Adenovirus and Calicivirus [64, 66]. Many studies have been conducted to determine

which gastroenteric viruses are more prevalent with respect to geography, sex, seasonal

pattern and age distribution [67-72]. Research shows that Rotavirus is responsible for the

majority of these deaths and 20-52% of all acute gastroenteric episodes [73-75]. Accurate

understanding of the relative prevalence of these agents would help design strategies to

control the disease.

Generally there are 3 diagnostic methods for gastroenteritis viruses in stool samples;

(immune) transmission electron microscopy (TEM), antigen ELISA and polymerase

chain reaction (PCR) [76]. The diagnostic significance, advantages and disadvantages of

these methods have been compared in Section 1.1 and 2.4.

92 5.4 Image Analysis 5.4 Image Analysis Gastroenteric viruses are normally shed in high concentrations, often reaching particle

concentrations of 1011ml-1 which makes it suitable to diagnose these viruses using EM.

The difficulty arises in distinguishing these viruses with one another because they are all

nearly circular in shape with little visual differences (Figure 5.9 and Figure 5.10), and

produce the same pathological symptoms in the patients. This can be overcome by

having an automated verification system. We considered the problem of detecting

Rotavirus against the other gastroenteric viruses such as Calicivirus, Adenovirus and

Astrovirus. Rotavirus was chosen as the target virus due to prevalence of this virus in

causing acute gastroenteritis. Although size alone can distinguish these viruses, this study

is conducted under the assumption that the magnification level and true particle size is

unknown. Classification of these viruses are based upon contour and texture. In Section

5.8, another experiment is conducted with viruses of similar size. The viruses chosen are

Astrovirus, Hepatitis A virus (HAV) and Poliovirus.

The following steps comprise the image analysis:

Segmentation: Segmentation is performed to separate individual viral particles from the

image. Viral particles in the images are segmented out into subimages (64 by 64 pixel),

and the images are aligned using the centroid of each subimage. This alignment need not

be perfect because the features extracted are translation invariant. Then a circular mask is

applied to each particle to eliminate the peripheral region that may contain neighbouring

virus cells. A circular mask will not corrupt the type of periodicity of the bispectral

5.4 Image Analysis 93

features as exhibited by the virus image within it. The features extract asymmetry

information from the virus image and a perfectly circular mask will not introduce any

asymmetry as a result of masking. Examples of segmented image of each type of virus

are shown in Figure 5.10.

(a) (b)

(c) (d)

Figure 5.9: A sample image of each type of virus used for testing. These images are different in magnification and resolution. (a) Adenovirus (b) Astrovirus (c) Rotavirus (d) Calicivirus

94 5.4 Image Analysis

(a) (b) (c) (d)

Figure 5.10: A single virus of each type. (a) Adenovirus (b) Astrovirus (c) Rotavirus (d) Calicivirus. These subimages are extracted from portions shown by square boxes in figure 5.9 and a circular mask is applied to each. Note that although there are small differences in texture, it is difficult to tell them apart by visual examination. Pseudo colouring could be used to emphasize the differences in texture but the difficulty arises when there is some variation in texture within the same virus type, on images that are obtained from various sources of different background, scale, contrast and noise.

Extraction of cell features: Each subimage (Figure 5.10) is subjected to the steps shown

in Figure 5.3. Radon transform projections at 32 angles are computed from each

subimage to yield one-dimensional functions. Ten bispectral features, ))(( θaP (where

1,.....,102,101a = and ),.....,322,32)rad( πππθ = are computed from each projection.

A total of 320 features can thus be extracted from each subimage. These features are not

rotation invariant. A discrete Fourier transform (DFT) is then computed on the features

considered as sequences with the angle of rotation as the index, to yield a new set of

features, ))(( θωaP , where θω is a frequency in cycles per 180 degrees. The resulting

features are invariant to rotation, translation and scaling, and are therefore robust to small

changes in the sizes of viral particles and their orientation. They are sensitive to

asymmetries in the shape of the virus, and because of their robustness to orientation and

size they can be combined for a population of virus particles, to pick up useful shape

5.4 Image analysis 95

differences that are not visually evident from electron micrograph images of single

particles.

Feature Selection: In general, the dimension of the feature vector (i.e., the number of

features) may be very large at the feature generation stage. Given a number of available

features, the main task of the feature selection (or reduction) process is to select

information rich features providing a large interclass distance and a small intraclass

variance in the feature vector space. In this work, the dimensionality is reduced by

computing the largest distance separation, F between the target virus and the background

virus, given by

)/()( 2

221

221 σσµµ +−=F (5.1)

where 1µ and 2µ are the mean of the target virus and the background virus and 1σ and

2σ are the standard deviation of the target virus and background virus computed over

some subset of the training set. These 150 features are then arranged according to the

ones that produced the largest distance separation between the target and background

virus. Then the dimensionality of the features used for training are varied in the interval

of 50 to 150 at an increment of 10 to produce an optimal result.

The steps of creating an automated recognition system outlined in Chapter 3 did not

include the process of reducing the dimensionality of features. Numerous techniques are

found in the literature and will be reviewed briefly here. Two means of reducing the

dimensionality are through selection of a subset of features and by extracting the

96 5.5 GMM Modeling principal components of variation from the vector. One of the commonly used feature

transformation techniques, the principal component analysis (PCA) [77], did not perform

well on these images. The ineffectiveness of using PCA might be due to the various

clusters or modes that exist from the data (images) obtained from multiple sources that

might not be linearly separable when projected on their first principal component.

Although, PCA chooses the components that best represent the data, it does not

necessarily choose the components that would be best for discriminating one class of data

from another.

The feature selection approach, described above was used here because it has several

advantages over the feature transformation approach. Feature selection retains the

integrity of each of the features within the set, allowing easier examination and

interpretation of classification results. Another advantage of the feature selection

approach is that features that are not selected need not be computed at all for future

unknown observations, which in some cases can save considerable computation time.

5.5 GMM Modeling Gaussian Mixture Models (GMMs) were trained for feature distributions from the viral

particles. GMM was chosen to model the feature density functions from the target virus

and background virus because of the range of modes or clusters produced by the images

with different scale, background and contrast that were used in training each virus type.

Figure 5.11 shows the cluster plot of 2 randomly chosen bispectral features of three

5.5 GMM Modeling 97

different set of images of Rotavirus. They differ in scale, background and contrast. Each

feature is an average from a subpopulation of 10 viral particles. As can be seen, the plot

that represents the probability distribution of the features shows quite compact and

isolated clusters in feature space.

As determined in Section 3.4.2, each type of virus is represented by a GMM describing

its features, with its mean vectors, covariance matrix and the mixture weights as

parameters. One of the critical factors in training a GMM is selecting the order of the

mixture. There are no good theoretical means to guide these selections, so they are best

experimentally determined for a given task. An experimental examination of these factors

is discussed in the following section.

5.5.1 Experimental Evaluation of Model Order and Dimensionality of

Training Observations

Determining the number of components in a mixture needed to model the features

adequately is an important, but challenging problem. There is no theoretical way to

estimate the number of mixture components a priori. Choosing too few mixture

components can produce a model that does not accurately model the distinguishing

characteristics of the feature distribution. Choosing too many components can reduce

performance when there are a large number of model parameters relative to the available

training data, and also can result in excessive computational complexity both in training

and classification. The following experiments examine the performance of the GMM to

98 5.5 GMM Modeling model feature distribution from the virus particles for different model orders using a fixed

and variable amount of training data.

To investigate the virus recognition performance of the GMM, a different combination of

number of mixtures, M and dimensionality of training observations, D were used in the

experiments. First the number of training observations is fixed while varying the number

of mixtures. As mentioned earlier, the number of training observations is incremented at

the interval of 10 starting from 50 to 150 features.

In all cases, a diagonal covariance form of the GMM was used with a covariance matrix

for each component. The input data were pre-processed with a k-means algorithm that

performs an unsupervised learning to find centres of clusters that reflect the distribution

of the data, followed by iterations of the Expectation Maximization (E-M) algorithm. The

iteration was stopped when the change in log likelihood of the error function at the

solution between two steps of the E-M algorithm of the target and background virus was

below a preset threshold and considered insignificant.

Using different combinations of training sets, 5000 trials where each trial consists of

feature averaging of 15 particles were used for training. The features used for training and

testing were randomly chosen and there was no overlapping between the training and test

set. Table 5.1 presents the test results in terms of percentage of efficiency, which is

calculated from miss and false alarm probabilities of Rotavirus against the other viruses.

The result is an average over 1000 trials. It is found that at a higher dimension of features,

the GMM model becomes unstable and sensitive to the selection of mixture components.

5.5 GMM Modeling 99 Consequently, the results of more than 130 features are not presented in Table 5.1. The

highest efficiency, 97.4% is achieved when D=110 and M=10. This combination will be

used in the following section to train the features.

(Features, Mixture)

(D,M)

Miss (%) False alarm (%), FA Efficiency (%)

((100-Miss) + (100-FA))/2

(130, 10) 1.1 3.2 93.1

(130, 20) 2.1 3.4 94.1

(130, 30) 0.6 4.8 95.2

(120, 10) 1.0 5.3 92.1

(120, 20) 1.2 3.8 92.5

(120, 30) 5.1 3.5 95.7

(120, 40) 3.0 7.6 94.7

(110, 10) 0.9 4.3 97.4

(110, 20) 2.6 5.4 96.0

(110, 30) 1.3 6.7 96.0

(110, 40) 2.2 6.9 95.5

(110, 50) 4.3 6.4 94.7

(100, 10) 1.4 8.5 95.1

(100, 20) 2.3 8.3 94.7

(100, 30) 1.9 7.1 95.5

(100, 40) 1.2 9.0 94.9

(100, 50) 1.2 11.8 93.5

(90, 10) 1.5 9.0 94.8

(90, 20) 1.1 10.1 94.4

(90, 30) 2.4 11.4 93.1

(90, 40) 2.2 8.0 94.9

(90, 50) 1.8 12.7 92.8

(80, 10) 2.0 7.9 95.1

(80, 20) 2.6 13.6 91.9

(80, 30) 1.5 24.1 87.2

(80, 40) 1.7 18.9 89.7

100 5.6 GMM Verification (60, 5) 1.4 13.9 92.4

(60, 10) 1.3 15.7 91.5

(60, 15) 2.1 14.6 91.7

(60, 20) 1.6 19.5 89.5

(60, 25) 1.5 22.4 88.1

(60, 30) 1.8 31.0 83.6

(50, 5) 3.2 24.7 86.1

(50, 10) 2.2 24.9 86.5

(50, 15) 2.6 26.9 85.3

(50, 20) 1.2 29.5 84.7

Table 5.1: Efficiency (%) of different combinations of number of mixtures, M and dimensionality of training observations, D used to examine the performance of GMM.

5.6 GMM Verification The test set is scored against both the target model (Rotavirus) and the background model

(Calicivirus, Astrovirus and Adenovirus). In the experiment of viruses of similar size, the

target model is Astrovirus and the background models are HAV and Poliovirus. In the

first verification test, the decision score ),( NXS λ is a log likelihood ratio of a

subpopulation of N particles, where N is the number of particles used to compute a

feature vector by averaging, given by

)|('log)|('log),( NiNiN XfXfXST βλλ −== (5.2)

5.7 Experiments 101 In the second verification test, each decision score, ),(' NXS λ is an average of M sets

where each set consist of a subpopulation of N particles, as can be shown in the formula:

)|('log)|('log),('1

NiNi

M

iN XfXfXST βλλ −== ∑

=

(5.3)

where Nλ is the target model, iX is the test set comprised of a subpopulation of N

particles, )|(' NiXf λ is the likelihood of the target virus, and )|(' NiXf β is the average

likelihood of the three background virus, with each of the background virus is weighted

equally.

If T

5.7 Experiments Two types of experiments were conducted. In the first experiment, the training and

testing were carried out on a population of virus images pooled from all the EM images

of that type obtained from various sources (referred to as a pooled population). A pooled

population is useful when a single image does not provide enough viral particle

subimages for statistically reliable training or testing. Although the population is pooled,

viral particle subimages used for training are different from those used for testing.

> 0, then the virus is identified as the target virus < 0, then the virus is identified as non-target virus

102 5.7 Experiments

In the second experiment, the testing and training is done on populations derived from

separate images. The images used in the training set were different from those in the test

set. All viral particles in a given population are selected from the same image (referred to

as a single image population). The feature vector in each case is obtained by averaging

features from a set of N number of particles as shown in Figure 5.7. The first verification

test was performed on both the single image population and the pooled population, while

the second verification test was only performed on the pooled population. Figure 5.12

illustrates the selection of viral particles from EM images used for testing and training in

the pooled population and the single image population cases.

Figure 5.11: Cluster plot of features from three different sets of Rotavirus images with different backgrounds, contrast and scale. Each point is an average feature from a subpopulation of 10 viral particles. The plot shows quite compact and isolated clusters or modes in feature space.

5.7 Experiments 103

Figure 5.12: Illustration of selection of viral particles from different sets of EM images used for testing and training in pooled population and single image population. In the single image population, the testing and training is done on populations derived from separate images. In a pooled population, the virus images pooled from all the EM images of that type obtained from various sources.

Single image population Pooled population Training Testing Training Testing

U

U

U

EM image 1 EM image 3 EM image 4 EM image 2

104 5.7 Experiments 5.7.1 Experiment on a Pooled Population Different sets of digitised electron microscope images obtained from various sources of

these gastroenteric viruses were used for testing and training. Ten images of Rotavirus of

different scale, background, contrast and appearance of contour were chosen. A total of

12 images of Adenovirus, Astrovirus and Calicivirus were used as the background virus.

For each virus type, the training set consists of 5000 trials where each trial is a feature

average of N particles. The remaining particles were used to select the test set. Twenty

particles of each of the three background viruses were chosen randomly to form 60

particles for a test set of the background virus.

A subpopulation of N particles was chosen from the test sets (a pooled population) of the

target virus and the background virus. In the first verification test of the pooled

population, each decision score is produced by a subpopulation of N particles, where N is

the number of particles used to compute a feature vector by averaging (referred to as a

subpopulation test). In the second verification test, likelihood scores of M sets where each

set consists of a subpopulation of N particles, were averaged to produce a decision score

(referred to as the averaged score subpopulation test).

The verification tests were performed on subpopulations of N viral particles where N = 5,

8, 10, 13 and 15. For each subpopulation size, 100 tests (scores) with randomly selected

subpopulations from the test set were conducted and the results are presented in Detection

Error Tradeoff (DET) curves. In the second verification test, M was set to 2.

5.7 Experiments 105

Results of the subpopulation test are presented in Figures 5.13 and 5.14. From Figure

5.13, it can be seen that as the test ensemble for feature averaging is increased from 5 to

15 particles, the equal error rate (EER) drops quite significantly from 15% to 2.5%

(Figure 5.14). The test was stopped at 15 particles because there was no improvement in

the EER as the subpopulation size for feature averaging was increased, from 13 particles

to 15 particles.

Legend

Figure 5.13: DET curve using the bispectral features from subpopulations of 5, 8, 10, 13 and 15 viral particles on a pooled population. As the test ensemble size for feature averaging is increased, the EER drops. EER is the point on the DET curve where the false alarm probability is equal to the miss probability. Refer to Figure 5.14 for EER values of each subpopulation size.

106 5.7 Experiments

Figure 5.14: Plot of EER versus ensemble size shows that as the test ensemble for feature averaging increases, the EER drops for N= 15 to 2.5%.

The EER drops even lower when the number of sets of subpopulations used for

comparing probability densities modeled by GMMs increases. Results of an averaged

score subpopulation test with M=2 and N=15 particles is presented in Figure 5.15. 5000

tests (scores) with randomly selected subpopulations from the test set were conducted.

From the DET curve, the EER drops from 2% to less than 0.2% as M goes from 1 to 2.

If two test populations are thrown at the GMM, and log-likelihood scores are obtained,

they could be used in different ways. In output fusion, decisions are combined. Each

score could be used to obtain a decision and the decisions may be combined. For

example, a decision to accept may be made only if both individual decisions are to

accept. In this case, false acceptance rate will be the product of individual false

acceptance rates. However, the false rejection rate will be the sum of the individual rates.

02468

10121416

5 8 10 13 15Ensemble size

EER

(%)

, N

5.7 Experiments 107

The false acceptance will go from 2% to 0.04%, but at the expense of false rejection

which goes from 2% to approximately 4% at the same threshold (assuming an equal error

rate of 2% at that threshold).

Alternately, a decision to reject may be made only if both individual decisions are to

reject [78]. In this case, the false rejection rate will go to approximately 0.04%, but false

acceptance to 4% at that threshold (Figure 5.15).

By contrast, in input fusion, features or scores are combined. Individual scores may be

weighted and combined depending upon the confidence one has in each score. There will

exist some optimal weighting of the scores for which the performance is best. When there

is no prior knowledge of confidence or the two tests are equal in all respects, the scores

may simply be averaged (50% weight for each of the two scores). This is done here. It

turns out that averaged scores yield better performance than output fusion in this case.

5.7.2 Experiment on a Single Image Population In the second experiment, only images that have more than 20 viral particles per image

were chosen because the testing and training were conducted on subpopulations of

particles that are drawn from the same image. Nine images of rotavirus of different scale,

background, contrast and appearance of contours were chosen, and 5 of these were used

for training and the rest for testing. For the background virus, a total of 11 images were

used; 5 images of Adenovirus, 4 images of Astrovirus and 3 images of Calicivirus.

108 5.7 Experiments

Out of these images, 3 Adenovirus images were used for training and two each of

Astrovirus and Calicivirus; and the rest were used for testing. Similar to experiment on a

pooled population, 5000 trials where each trial is an average feature of N viral particles

were used for training. There is no overlap in training and test set.

Legend

Figure 5.15: DET curve using the bispectral features from subpopulation of N=15 viral particles on a pooled population. The solid curve shows an average of 2 sets of subpopulation of 15 viral particles, while the dotted curve shows the case for M = 1 (M, N, refer to equations 5.2, 5.3). The EER drops to less than 0.2%. The darker solid curve shows an output fusion of two test populations. In this case, false acceptance rate will be the product of individual false acceptance rates, and the false rejection rate will be the sum of the individual ones. This shows that the averaged scores yield better performance than output fusion in this case.

______ ---------- M = 1 ______

M = 2

Output fusion

5.7 Experiments 109 The verification test was performed on subpopulations of viral particles of sizes N = 5, 8,

10, 13, 15 and 18. One hundred tests (scores) were performed for each subpopulation size

(Figures 5.16 and 5.17). The figures show that as the test ensemble for feature averaging

is increased from 5 to 18 particles, the equal error rate (EER) drops from 20% to 2%. The

test was stopped at 18 particles (Figure 5.17) because there was no improvement in EER

as the subpopulation size increased from 15 to 18 particles.

Legend

Figure 5.16: DET curve using the bispectral features from subpopulations of 5, 8, 10, 13, 15 and 18 viral particles on a single image population. The EER drops as the feature averaging of the subpopulation size increases. Refer to Figure 5.17 for EER values of each subpopulation size.

110 5.8 Virus of Similar Size

Figure 5.17: Plot of EER versus ensemble size shows that as the test ensemble for feature averaging increases, the EER drops for 18 particles to 2%

5.8 Virus of Similar Size

An experiment was conducted to determine the ability to distinguish particles similar true

size. Two types of viruses with similar size; Astrovirus of diameter 28-30nm and viruses

of Parvoviridae family, Hepatitis A virus (HAV) and Poliovirus of diameter 22-30nm

were chosen. Six images of Astrovirus and 7 images of HAV and Poliovirus were used

for training and testing. Figure 5.18 shows the electron micrograph of Astrovirus and

HAV of the same magnification level. Astrovirus was used as the target virus and HAV

and Poliovirus were used as the background virus.

0%

5%

10%

15%

20%

25%

5 8 10 13 15 18Ensemble size

EER

(%)

, N

5.8 Virus of Similar Size 111

(a) (b)

Figure 5.18: A sample image of (a) Astrovirus and (b) Hepatitis A virus. The magnifications of these images are the same. The verification test of a pooled population was performed on subpopulations of viral

particles, where N= 5, 10, 15, 20. The results in subpopulations of 500 tests show that as

the subpopulations is increased to 20 viral particles, the EER drops to 5% (Figure 5.19).

The EER drops further as M is increased from 1 to 2 of a subpopulation of 20 particles to

less than 2%.

112 5.9 Evaluation with SVM Classifier

Legend

M=1, N=5

M=1, N=10

M=1, N=15

M=1, N=20

M=2, N=20

M=1, N=5

M=1, N=10

M=1, N=15

M=1, N=20

M=2, N=20

Figure 5.19: DET curve using the bispectral features from subpopulation of N = 5, 10, 15, 20 particles, M =1 and subpopulation of N = 20, M=2 on a pooled population. The EER drops to less than 2% when features of 2 sets of subpopulation of 20 particles were averaged. 5.9 Evaluation with SVM Classifier 5.9.1 Introduction

The higher order spectral features resulting from the virus particles also were trained

using Support Vector Machines (SVMs). SVM was chosen and compared with the GMM

classifier. Among other classifiers such as Bayes to neural networks, SVMs appear to be

a good candidate because of their ability to generalize in high-dimensional spaces, such

as spaces spanned by texture patterns. The appeal of SVMs is based on their strong

5.9 Evaluation with SVM Classifier 113 connection to the underlying statistical learning theory. That is, as outlined in Section

3.4.3, a SVM is an approximate implementation of the structural risk minimization

(SRM) method [56]. For several pattern classification applications, SVMs have been

shown to provide better generalization performance than traditional techniques, such as

neural networks [79, 80].

5.9.2 Experimental Procedure

Similar to GMM verification, the test set is scored against both the target virus

(Rotavirus) and the background virus (Calicivirus, Astrovirus and Adenovirus). For

SVM, which is a binary classification, the decision score, ),( NXS λ in equation 5.2 is an

average of three scores. Each score is obtained by subtracting the log likelihood of the

target virus with one of the background virus when tested with a test set comprised of a

subpopulation of N particles (equation 5.2).

Bispectral features from the resulting virus particles are extracted using techniques

outlined in Section 5.4. The virus particles used for testing and training are chosen using

the pooled population method (first paragraph of Section 5.7.1). For definition of pooled

population, please refer to Section 5.7. In all cases, the Gaussian RBF kernel was used,

which is given by:

( ) ⎟⎟⎠

⎞⎜⎜⎝

⎛ −=

β

2||exp, yxyxk (5.4)

114 5.9 Evaluation with SVM Classifier

___ N=5, GMM ___ N=10, GMM ___ N=15, GMM * N=5, SVM * N=10, SVM * N=15, SVM

A β of 0.1 was used, which was found to perform better in verification of rotavirus for the

bispectral features. The number of features used for training and testing also were varied

to obtain the optimal result (see Chapter 6).

5.9.3 Results and Discussion

The verification tests were performed on subpopulations of N viral particles where N = 5,

10, and 15. For each subpopulation size, 100 tests (scores) with randomly selected

subpopulations from the test set were conducted and the results were presented in

Detection Error Tradeoff (DET) curves (Figure 5.20). It can be seen that there is not

much difference in the equal error rate (EER) in all the subpopulations.

Legend

Figure 5.20 DET curve using the bispectral features from subpopulations of 5, 10 and 15 viral particles on a pooled population using SVM and GMM classifier.

5.10 3D virus reconstruction 115 5.10 3D Virus Reconstruction

In the last decade, there has been a burst of activity in the use of EM for the elucidation

of virus activity. This has resulted from two advances in techniques; cryo-EM has

allowed the preservation of fragile specimens in the EM, and the development of efficient

algorithms for processing micrographs to produce 3D structures of icosahedral particles.

The 3D structures are normally reconstructed from its 2D projections. One of the most

commonly used and well-known algorithms to reconstruct 3D virus is the weighted back

projection method (WBP) [81], which is based on superposing 3D functions ("back-

projection bodies") obtained by translating the 2D projections along the directions of

projection.

The 2D projections are obtained through several thousand experimental particles using

the untilted and tilted images (for random conical tilt) of the same micrograph. In the

random conical tilt reconstruction method [82], the actual reconstruction is done from the

tilted particles, but the alignment and classification comes from the untitled images. In

this method is it necessary that the untitled images with the same orientation (the particles

are showing the same face to the viewer, but the only difference between them is that

they can be rotated by some angle in the plane of the image) are aligned and classified to

obtain their class averages. With these clearer class images, the 3-D density is then

reconstructed by using the back projection method as mentioned earlier. The benefit of

using higher order spectral features is that alignment is not necessary because of the

invariant properties.

116 5.11 Summary However, the differences between 2D projections of the same virus when the angle is

different (random conical tilt) can affect the higher order spectral method. In this case, it

is necessary to divide these images into clusters, and build the class averages from there.

Thus, the ‘extra’ step of alignment of the images before averaging can be eliminated by

using higher order spectra due to the rotation and shift invariant properties, allowing

computational savings. Experimentally this has not been carried out, but is one of the

possible avenues for future research.

5.11 Summary The chapter shows that higher order spectral features that are invariant to translation,

rotation and scaling are effective in identifying viruses from digitized electron

micrographs. As mentioned in Chapter 3, the system can be made fully automated by

automatically segmenting the individual virus particles.

Verification tests were conducted on 4 major types of viruses that cause gastroenteritis;

Adenovirus, Astrovirus, Rotavirus and Calicivirus, where Rotavirus was chosen as the

target virus and the rest as the background virus. Results are presented for tests with

various subpopulation sizes, N, used for averaging feature values and varying number of

subpopulations, M, used for averaging likelihoods. EER of around 2% is achieved for

N=15, M=1. EER drops to less than 0.2% for M=2.

Tests also were conducted on viruses of similar true size. Astrovirus was scored against

HAV and Poliovirus. Results show that the EER drops to less than 2% for N=20, M=2.

5.11 Summary 117

Support Vector Machine (SVM) was compared with Gaussian Mixture Model (GMM) to

classify the viruses. Experimental evaluation shows that there are no substantial

differences in the EER when trained and tested with subpopulations of 5, 10 and 15

particles using these classifiers separately to verify Rotavirus. In the next chapter,

Rotavirus, Adenovirus and Calicivirus are used separately as the target virus in a

comparative study of higher order spectral features and Gabor features.

Chapter 6 Relative Performance Evaluation

6.1 Introduction

The previous chapter investigates the use of radial spectra of higher order spectral

features in virus recognition. The aim of this chapter is to provide a comparative study of

higher order spectral and Gabor features in virus recognition. Gabor filtering is one

prominent filtering method, and has been shown to provide an excellent basis for

identifying textured images, and thus has been used in many applications. A few

comparisons between Gabor filtering with other filtering methods, as well as with other

feature extraction techniques have been presented.

120 6.1 Introduction Randen and Husoy [83] did a comparative study of the filtering methods, reviewing

Wavelets, Gabor filters and Wedge filters, and concluded that no single approach

performs best or very close to the best for all images because different images yield

different results. Pichler [84] compares wavelet transforms with adaptive Gabor filtering

feature extraction, and reported superior results using the Gabor technique. However, the

computational requirements are much larger for the wavelet transform, and in certain

applications accuracy may be compromised for a faster algorithm. Filtering features also

have been compared to the co-occurrence features in some other studies, with different

conclusions. Strand and Taxt [85] concluded that the co-occurrence features were

performing best, while Laws [86] and Clausi and Jernigan [87] drew the opposite

conclusion. Different setups, different test images, and different filtering methods may be

the reasons for the contradicting results.

Comparison of Gabor features with higher order spectral features has been investigated

using a set of images from the Brodatz album by Elunai [88]. In this study, experiments

show that higher order spectral invariant features produce better classification results for

more texture pairs than the Gabor features.

6.2 Gabor Filter 121 6.2 Gabor Filter

As outlined in Chapter 3, a 2D Gabor function, ),( yxg can be expressed as

)(2exp),(),( VyUxjyxgyxh +−′′= π (6.1)

where

⎥⎥

⎦

⎤

⎢⎢

⎣

⎡

⎟⎟

⎠

⎞

⎜⎜

⎝

⎛

⎟⎟⎠

⎞⎜⎜⎝

⎛+⎟⎟

⎠

⎞⎜⎜⎝

⎛−=

22

5.0exp2

1),(yxyx

yxyxgσσσπσ

(6.2)

and ))cos()sin(),sin()cos((),( θθθθ yxyxyx +−+=′′ are the coordinates viewed by

system of rotated axis. The axis is rotated by a specified angle θ anticlockwise from the

positive x-axis. The frequencies in the orthogonal directions, U and V, can be combined

into the resultant frequency )( 22 VUf += cycles per image. For a square image of

dimension N x N, the response frequencies θf used in the experiment for each orientation

θ are obtained from octave frequencies given by:

]sin*max[cos0

θθθf

f = (6.3)

Thus, using (6.1) and (6.2) it is possible to design Gabor filters with arbitary

frequency, 0f , orientation, θ and bandwidth, b which is the product of xfσ . In this

experiment, 30 different orientations from 0° to 360° in steps of 12°, and five frequencies

per degree using (6.3) for 0f = 1, 2, 3, 4 and 5 cycles per image were used. b was adopted

122 6.3 Discriminant Analysis Testing and Results as 0.56, which is a commonly used bandwidth in feature extraction. These features are

rotation variant, so a DFT coding step is required to obtain rotation invariance. This

method of extracting rotation invariant features is used by [89].

6.3 Discriminant Analysis Testing and Results In Chapter 5, two types of experiments were carried out; pooled population and single

image population (refer to Section 5.7 for definition). In this segment of work, only an

experiment of the pooled population will be conducted. The experimental evaluation is

carried out using a set of negative stained EM images of Rotavirus, Adenovirus,

Calicivirus and Astrovirus. Rotavirus, Adenovirus and Calicivirus are used separately as

the target virus. Similar to the experimental procedure outlined in Section 5.4, the images

are segmented into individual viral particles and Gabor features were extracted from each

viral particle. The Gabor features that were extracted using the method and parameters

outlined in Section 6.2 are invariant to translation and rotation.

The experimental procedure outlined above was repeated using bispectral features. 150

features were extracted using the steps outlined in Figure 5.3. Radon transform

projections at 30 angles were computed to yield a one dimensional function. Five

bispectral features, ),( θaP (where 1,.....,5/2,5/1=a and ),.....,30/2,30/)( πππθ =rad

were computed from each such projection. The training and test samples used were

similar to the ones used in the Gabor features.

6.3 Discriminant Analysis Testing and Results 123

To evaluate and compare the quality of both the feature sets, discriminant testing is

performed. The Fisher linear discriminant (FLD) is used to measure and compare the

separability of Gabor and HOS features. The FLD is used since it is a recognized

nonparametric method to analyze the class separation in the feature space. The FLD is

determined by calculating the Fisher criterion

( ) ωωωωτωτ w

TB

T SS== (6.4)

where BS and wS are the between-class and within-class scatter matrices.

The average feature sets of Gabor and HOS and the ratio of this average are presented in

Table 6.1. The average feature sets of Gabor of Rotavirus, Adenovirus and Calicivirus

used separately as target virus is less than that obtained by the HOS feature sets. Clearly,

the higher order spectra feature sets have stronger separability than the Gabor feature

sets.

Features Target virus

Average feature of

Gabor ( )gabavg _τ

Average feature of HOS ( )hosavg _τ

Ratio

( )hosavggabavg __ ττ Rotavirus

2753

5318

0.52

Adenovirus

664

1310 0.51

Calicivirus

671

1208

0.55

Table 6.1 Comparison of the feature space separability of Gabor and HOS features using FLD.

124 6.4 Training and Classification using SVM 6.4 Training and Classification using SVM

Support Vector Machine (SVM) was used to train and classify populations of viral

particles. The features used are obtained using the experimental procedure outlined in

Section 6.3. When designing and training a SVM, selection of the kernel function and the

constraint parameter C are important. Traditionally, this has been done by trial-and-error

for kernel selection and exhaustive search for C. More recently, an algorithm for

automatically selecting the kernel parameters to minimize an upper bound on the

generalization error was given [90]. In either case, the SVM must be optimized for a large

number of different choices of parameters.

To make the comparison of Gabor and higher order spectral features in virus recognition

more effective, the constraint parameter C and number of features N that were used for

training and testing were varied. In this work, a trial-and-error method was used focusing

on SVMs with the RBF kernel. RBF widths, C of 0.001, 0.1 and 10 were considered. For

determining the optimal values of C and N in all cases, the same number of training sets

was used, with samples for training up to 40%, i.e. 400 samples, and the remaining 60%

for testing. The features used for training and testing were randomly chosen and there

was no overlapping between them. The recognition performance will be affected by the

selection of training data, and thus each experiment is conducted 1000 times and the

reported results given are an average. Each trial consists of feature averaging of 10

different particles.

6.4 Training and Classification using SVM 125 6.4.1 Results and Discussion

The comparison classification results of Gabor and higher order spectral features are

shown in Figure 6.1. The result presented in percentage of efficiency is calculated from

the miss and false alarm probabilities. The highest efficiency, 83% is obtained by using

higher order spectral features with kernel width of 0.1 and 75 features when Rotavirus is

the target virus. The experimental evaluation also is carried out using Adenovirus and

Calicivirus as the target virus. In both cases, higher order spectral features perform much

better than Gabor features, with 100% efficiency in the verification of adenovirus using

higher order spectral features compared with 69% using Gabor features. In the

verification of Calicivirus, higher order spectral features achieved an efficiency of 87%

while Gabor features only produced 62%.

126 6.5 Summary

30 40 50 60 70

50

60

70

80

90

100

No of features

Effic

ienc

y (%

)gabor,kernel = 0.001

gabor,kernel = 0.1

gabor,kernel = 10

HOS, kernel = 0.001

HOS, kernel = 0.1

HOS, kernel = 10

Figure 6.1: The plot of efficiency versus number of features for a subpopulation of 10 viral particles trained using SVM classifier. A choice of 3 kernel widths were used, 0.001, 0.1 and 10 to train the features. The efficiency is calculated from the miss and false alarm probabilities.

6.5 Summary

In this chapter, Gabor features were compared with higher order spectral features in virus

recognition. Experimental evaluation of both the feature sets were performed using

negative stained EM images of four types of viruses; rotavirus, adenovirus, astrovirus and

calicivirus, whose morphologies are quite similar. To evaluate and compare the quality

of both the feature sets, Fisher linear discriminant (FLD) was used to measure and

compare the feature space separability of Gabor and HOS features. The HOS feature sets

demonstrated to produce higher feature space separation compared to Gabor feature sets.

6.5 Summary 127

A SVM was used to train the features. The optimal result is gained by trying different

combinations of kernel widths and number of features in training and testing

observations.The result shows that the highest efficiency, 83% is achieved by using

higher order spectral features of the RBF kernel width of 0.1 in the verification of

Rotavirus. In the verification of Calicivirus and Adenovirus, higher order spectral

features are superior to Gabor features (Table 6.2).

Rotavirus

Calicivirus

Adenovirus

HOS features

83%

87%

100%

Gabor features

79%

62%

69%

Table 6.2: Efficiency (%) of higher order spectral features and Gabor features in the

verification of Rotavirus, Calicivirus and Adenovirus.

Chapter 7 Conclusion and Further Work

7.1 Conclusion

This thesis has made an original and substantial contribution to science. The methodology

developed is able to detect and classify different types of viruses, that are difficult to

distinguish visually from two-dimensional images obtained from an electron microscope.

It is based on radial spectra of higher order spectral invariant features that capture

information about variation in texture and contour and differences in symmetries of

different types of viruses. This method takes advantage of the large numbers of particles

available in these images using invariant properties of the higher order spectral features

and statistical techniques of feature averaging and soft decision fusion to improve

classification accuracy.

130 7.1 Conclusion

Experimental evaluations were carried out on negative stained EM images of

gastroenteritis viruses. A high statistical reliability and low misclassification rates were

achieved using this methodology. An Equal Error Rate of less than 0.2% was achieved in

verifying Rotavirus by input fusion, where the features are combined from 15 images,

and soft decisions (likelihoods) are averaged from 2 such sets of 15 images. Even though

only 6 types of viruses were used in this scope of work, preliminary studies of texture and

contour (Chapter 4) have shown the ability of higher order spectral features in

distinguishing a large number of images of different textures and contours. An average

misclassification of 1.37% was obtained over forty different textures chosen from the

Brodatz album.

Gabor features were compared with higher order spectral features to verify Rotavirus,

Calicivirus and Adenovirus. Overall results show a superiority of higher order spectral

features over Gabor features in this application. An efficiency of 83% was achieved in the

verification of Rotavirus using HOS versus 79% using Gabor. In the verification of

Calicivirus and Adenovirus, efficiencies of 87% and 100% were achieved using HOS

compared with only 62% and 69% using Gabor. The results presented used a feature

averaging of 10 particles and SVM as the classifier. Higher efficiency can be achieved by

increasing the number of particles for feature averaging or averaging the likelihood

scores (as shown in Chapter 5).

This methodology can be incorporated with the existing automated virus segmentation

methods to make it fully automated. With the simple and fast negative stain preparation

7.2 Further Work 131 and automated pattern recognition, electron microscopy permits a rapid detection and

identification of infectious agents. This will further encourage a broad application of EM

such as investigation of potential bioterrorist events [91-93] and identification of an

outbreak.

7.2 Further Work

Continuing on from the research presented in this thesis, a number of possible avenues

for further research have been identified, including:

(i) Chapter 3 discussed some of the segmentation methods of negative stained EM

virus images. These segmentation methods can be applied and incorporated with our

system to have a fully automated virus recognition system.

(ii) Chapter 5 showed the comparison of higher order spectral (bispectral) and Gabor

features in virus recognition, with results showing a higher degree of accuracy using

bispectral features in this application. There are a great number of other techniques that

remain untested. Thus, there exists much potential to improve on the results presented in

this thesis by testing other texture-based approaches. In this scope of work, input fusion,

where the likelihood scores were averaged from M sets, each set consists of feature

averaging of N images were used. There are different kinds of fusion strategies that are

available. Thus, the combination of these features in an intelligent manner also is a

132 7.2 Further Work topic worthy of future consideration although this investigation can be computationally

quite demanding.

(iv) A multiple classifier system that is based on a combination of outputs of a set of

different classifiers has been shown as a method to develop high performance

classification systems. The dimensionality of the data that can be reduced either through

selection of a subset of features, or by extracting from the vector the principal

components of variation also leads to an increase in classification accuracies. Numerous

examples of these techniques are found in the literature. Thus, further investigation on

combining classifiers and feature selection methods is another avenue for possible future

research.

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Appendix A A Study of Texture and Contour A.1 Experimental Results of the Relative Importance of Phase and Magnitude in Texture

D101 D92D101 D92

D78 D101D78 D101

(a) (b)

Figure A.1(a): Subfigures of (a)-(b) Results when images of 2 homogeneous textures used as input textures after subjected to steps in Figure 4.2. The top images of each subfigure are the input and the bottom images are the output.

144 Appendix A

D101 D56D101 D56 D46 D34D46 D34

(c) (d)

D34D20 D34D20 D20 D6D20 D6

(e) (g) Figure A.1(a): Subfigures of (c)-(g) Results when images of 2 homogeneous textures used as input textures after subjected to steps in Figure 4.2. The top images of each subfigure are the input and the bottom images are the output.

Appendix A 145

D6D3 D6D3 D6 D11D6 D11

(g) (h)

D11 D82D11 D82 D11 D101D11 D101

(i) (j) Figure A.1(a): Subfigures of (g)-(j) Results when images of 2 homogeneous textures used as input textures after subjected to steps in Figure 4.2. The top images of each subfigure are the input and the bottom images are the output.

146 Appendix A

D34 D78D34 D78 D11 D78D11 D78

(k) (l) Figure A.1(a): Subfigures of (k)-(l) Results when images of 2 homogeneous textures used as input textures after subjected to steps in Figure 4.2. The top images of each subfigure are the input and the bottom images are the output.

D42D31 D42D31 D97 D107D97 D107

(a) (b) Figure A.1(b): Subfigures (a)-(b) Results when images of 2 inhomogeneous textures used as input textures after subjected to steps in Figure 4.2. The top images of each subfigure are the input and the bottom images are the output.

Appendix A 147

D62 D42D62 D42 D62 D91D62 D91

(c) (d)

D88 D91D88 D91 D13 D45D13 D45

(e) (f) Figure A.1(b): Subfigures (c)-(f) Results when images of 2 inhomogeneous textures used as input textures after subjected to steps in Figure 4.2. The top images of each subfigure are the input and the bottom images are the output.

148 Appendix A

D88 D7D88 D7 D44 D40D44 D40

(g) (h)

D42D90 D42D90 D42 D45D42 D45

(i) (j) Figure A.1(b): Subfigures (g)-(j) Results when images of 2 inhomogeneous textures used as input textures after subjected to steps in Figure 4.2. The top images of each subfigure are the input and the bottom images are the output.

Appendix A 149

D30 D88D30 D88 D41 D62D41 D62

(k) (l) Figure A.1(b): Subfigures (k)-(l) Results when images of 2 inhomogeneous textures used as input textures after subjected to steps in Figure 4.2. The top images of each subfigure are the input and the bottom images are the output.

D62D55 D62D55 D42D46 D42D46

(a) (b) Figure A.1(c): Subfigures (a)-(b) Results when images of a homogenous and inhomogeneous texture used as input textures after subjected to steps in Figure 4.2. The top images of each subfigure are the input and the bottom images are the output.

150 Appendix A

D20 D61D20 D61

D45D101 D45D101

(c) (d)

D43 D56D43 D56 D46 D45D46 D45

(e) (f) Figure A.1(c): Subfigures (c)-(f) Results when images of a homogenous and inhomogeneous texture used as input textures after subjected to steps in Figure 4.2. The top images of each subfigure are the input and the bottom images are the output.

Appendix A 151

D11 D42D11 D42

D11 D40D11 D40

(g) (h)

D56 D62D56 D62 D16 D108D16 D108

(i) (j) Figure A.1(c): Subfigures (g)-(j) Results when images of a homogenous and inhomogeneous texture used as input textures after subjected to steps in Figure 4.2. The top images of each subfigure are the input and the bottom images are the output.

152 Appendix A

D21 D30D21 D30 D61 D52D61 D52

(k) (l) Figure A.1(c): Subfigures (k)-(l) Results when images of a homogenous and inhomogeneous texture used as input textures after subjected to steps in Figure 4.2. The top images of each subfigure are the input and the bottom images are the output.

Appendix A 153 A2. Classification Results of a Large Database of Different Textures and Contours using Higher Order Spectral Features

D1 D2 D3 D5 D6 D8 D9 D11 D16 D17 D19 D20 D21 D22 D24 D28

D2 1.87

D3 0.35 0.27

D5 0.79 3.54 0.08

D6 0.02 0.06 0.33 0

D8 0 0.97 0 0.68 0

D9 1.00 0.54 1.93 0.04 1.06 0

D11 6.22 1.68 0.93 0.27 0 0.20 1.25

D16 0 0 0.04 0 1.02 0.04 2.25 0.04

D17 0 0 0 0 1.47 0.02 0.41 0 0.33

D19 4.60 3.27 1.70 0.64 0.22 0.12 1.25 3.79 0.77 0.20

D20 0.68 2.35 0.16 2.00 0.02 0.10 0.66 0.25 0 0 1.97

D21 0.06 0 0.02 0 0 0 0.79 0 0.04 0.68 0.02 0

D22 0.81 0.37 2.33 0.33 0.08 0 0.93 1.66 0.12 0 2.72 1.29 0

D24 0.02 0.16 0.56 0 1.64 0.04 2.52 0.18 2.95 1.06 0.29 0 2.39 0.47

D28 3.64 7.06 0.31 2.31 0 0.41 0.29 2.10 0 0 7.72 2.50 0 0.56 0

D29 0.6 0.52 1.91 0 2.02 0.04 4.06 0.52 2.02 0.81 1.83 0.02 1.41 0.85 3.64 0.02

D32 0.27 0.02 2.6 0 3.20 0.02 3.58 0.16 1.62 0.39 0.70 0.04 0.52 1.18 5.25 0

D34 1..31 0.54 1.14 0.02 0.43 0 5.10 2.10 0.85 0.08 3.95 0.16 0.22 2.70 2.20 0.50

D36 0.29 0.66 5.75 0.12 0.27 0 1.45 0.43 0.08 0.02 2.27 0.10 0 3.62 0.10 0.27

D38 0.93 0.14 0.41 0.06 0.18 0.25 2.68 0.93 1.31 0.45 0.47 0 0.10 0.04 1.33 0

D52 0.20 0.25 3.77 0.02 0.58 0 1.56 0.66 0.41 0.16 0.47 0.29 0.16 2.45 3.16 0.12

D53 0.04 0 0 0 0 0.02 1.14 0 0.25 0.93 0.14 0 3.16 0.02 1.70 0

D55 0.35 0.22 0.41 0 2.29 0 2.64 0.25 1.64 0.52 0.39 0 0.27 0.18 3.29 0

D57 0 0.29 1.06 0 1.77 0 2.10 0.08 1.54 0.47 0.39 0.02 0.02 0.47 4.93 0.06

D68 2.8 0.52 0.81 0.06 0.22 0.08 2.68 2.75 0.54 0.16 2..35 0.14 0.02 0.43 1.83 0.06

D77 0 0 0 0 0.04 0.02 0.02 0 0.02 0.37 0 0 1.41 0 0.39 0

D78 0.27 0.04 0.37 0 1.66 0.10 2.16 0.02 1.91 1.00 0.06 0.08 1.43 0.08 4.04 0

D80 0.06 0.18 0.41 0 1.70 0.02 4.25 0.02 2.12 0.47 0.31 0.04 1.39 0.58 7.31 0

D82 0.14 0.08 0.37 0 2.45 0 3.97 0.14 2.00 2.33 0.27 0.20 0.75 0.45 6.68 0

D83 0.41 0.29 0.66 0 0.68 0.10 3.5 0.12 1.06 0.31 1.14 0.60 0.62 0.37 1.50 0.10

D84 1.00 0.85 6.27 0.12 1.62 0 4.70 1.83 1.25 0.25 1.12 0.95 0.16 3.54 3.16 0.62

D85 0.06 0.02 0.12 0 0 0.04 1.58 0.02 0.83 0.02 0.16 0 0.12 0.66 4.87 0

D92 2.70 1..35 2.58 0.41 0.29 0 3.66 2.60 0.43 0 4.54 1.66 0.33 3.25 1.18 2.00

D93 0.04 0.18 0.66 0 1.83 0 2.89 0.22 3.33 1.14 0.29 0.02 1.43 0.43 6.41 0

D101 0.79 5.12 0.35 3.58 0.06 0.45 0.39 1.79 0.14 0 2.06 1.52 0.10 0.33 0.06 6.08

D103 0.08 0.18 3.08 0 1.54 0 3.02 0.52 0.62 0.16 0.68 0.16 0.14 1.33 3.08 0.18

D104 0.14 0.12 6.43 0.02 0.72 0 1.72 0.81 1.08 0.08 0.43 0.02 0.10 2.02 2.87 0.04

D110 2.39 0.45 3.10 0.02 0.18 0.10 6.16 1.77 0.29 0 3.50 0.37 0.10 3.06 1.33 0.22

D111 2.12 3.60 0.22 1.54 0 0.16 0.14 2.12 0 0 7.83 2.31 0 0.97 0.02 6.06

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154 Appendix A

D32 D34 D52 D53 D55 D57 D68 D77 D78 D80 D82 D83 D85 D92 D93 D101

D34 3.79

D52 0.54 2.31

D53 1.65 0.77

D55 2.08 2.50 0.02

D57 1.31 0.18 1.37 0.22

D68 1.79 0.75 2.25 0.22 3.54

D77 1.29 2.10 0.93 0.10 0.50 0.68

D78 1.93 3.31 0.02 1.08 0.16 0.45 0

D80 0.41 0.04 1.08 0.54 1.95 0.68 1.72 0.06

D82 2.27 0.68 0.85 1.50 4.33 2.77 0.93 0.20 3.37

D83 4.87 0.83 2.91 0.64 4.87 2.29 1.37 0.04 1.91 4.45

D84 3.37 2.18 0.72 0.29 0.75 0.37 2.43 0.16 0.97 4.47 2.06

D85 3.33 1.08 4.58 0.25 2.20 2.56 2.10 0.25 1.16 2.35 4.43 1.56

D92 4.62 6.89 0.18 0.75 2.18 2.18 0.10 0.06 1.45 3.93 2.10 2.14 0.68

D93 2.64 0.35 2.27 0.31 0.60 0.87 3.75 0 0.97 0.93 0.85 2.54 5.45 0.25

D101 3.22 9.35 1.54 1.00 4.91 3.20 1.00 0 3.33 7.83 3.89 2.00 2.75 5.20 0.66

D103 5.35 1.33 0.12 0.04 0.12 0.06 0.27 0.04 0.18 0.14 0.31 0.20 0.33 0.08 0.72 0.08

D104 0.25 0.64 7.72 0.27 1.18 5.00 0.70 0.02 1.00 2.12 3.27 0.77 4.27 0.50 2.02 0.31

D110 2.93 3.56 4.18 0.04 1.83 4.29 0.66 0.08 1.06 1.66 1.06 1.41 5.75 0.58 1.12 0.41

D111 1.45 2.43 3.27 0.08 0.58 1.72 4.39 0 0.39 0.72 1.35 2.54 6.52 0.16 5.72 4.00

Table A.2: Misclassification in percentage of a large database of different textures and contours images that were chosen from the Brodatz album using higher order spectral features. The overall performance over forty textures shows an average misclassification of 1.37%.

Appendix A 155 A.3 Classification Results of Images of the Same Texture but Different Contours using Higher Order Spectral Features

Circular 5 fold sym 6 fold sym Circular 5 fold sym 6.19 6 fold sym 4.25 9.35 7 fold sym 3.44 8.04 7.63

(a)

Circular 5 fold sym 6 fold sym Circular 5 fold sym 5.21 6 fold sym 2.54 5.42 7 fold sym 5.75 4.96 3.73

(b)

Table A.3: Misclassification rate (%) of four different contours of (a) D8 and (b) D17 texture images using higher order spectral features.

156 Appendix A A.4 Classification Results of Images with Various Level of Noise using Higher Order Spectral Features

D5 D8 D17 D5 D8 31.0 D17 28.8 25.6 D21 32.9 31.5 30.4

(a)

D5 D8 D17 D5 D8 8.58 D17 0.16 1.2 D21 0.21 1.2 10.2

(b)

D5 D8 D17 D5 D8 7.8 D17 0.21 1.25 D21 0.17 1.25 11.2

(c)

D5 D8 D17 D5 D8 5.5 D17 0.39 1.0 D21 0.48 0.98 13.2

(d)

Table A.4: Misclassification rate (%) of four textures with added white Gaussian noise of SNR equal to (a) -80 dB (b) -10 dB (c) 0 dB (d) 10dB using higher order spectral features.

Appendix A 157 A.5 Classification Results with Averaging of Features and Input Fusion of Noisy Images using Higher Order Spectral Features

D5 D8 D17 D5 D8 5.33 D17 1.04 0.83 D21 1.25 0.5 12.8

(a)

D5 D8 D17 D5 D8 0.104 D17 0 0 D21 0 0 1.98

(b)

D5 D8 D17 D5 D8 0 D17 0 0 D21 0 0 0

(c)

Table A.5: Misclassification rate (%) when M = (a) 2 (b) 5 and (c) 10 sets and N=5 images were used for classification using higher order spectral features. Gaussian noise of SNR = -30 dB was added to the image.

Glossary Antigen: Any agent that initiates antibody formation and/or induces a state of active

immununological hypersensitivity and that can react with the immunoglobulins that are

formed.

Capsid: A protein shell comprising the main structural unit of a virus particle.

Capsomers: The individual protein units that form the capsid of a virus

Envelope: A lipid membrane enveloping a virus particle.

Nucleocapsid: The core of a virus particle consisting of the genome plus a complex of

proteins.

Virions: Structurally mature, extracellular virus particles.

Protomer: Set of DNA sequences necessary for initiation of transcription by a DNA-

dependent RNA polymerase.

Pleomorphic: The variation in size

virus recognition in electron microscope images using...

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