advanced image processing iirs-2008

8/10/2019 Advanced Image Processing IIRS-2008

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ADVANCED IMAGE

PROCESSING

Sanjay K. GHOSH

Professor of Civil Engg

IIT ROORKEE

email: [email protected]@yahoo.co.in

IMAGE PROCESSING AND

ANALYSIS

Act of examining images for the purpose of identi fying

objects and judging their signi f icance

Image analyst studies the remotely sensed data and

attempts through logical process

detection,

identification classification

measurement

Evaluate the significance of physical and cultural

objects, their patterns and spatial relationship.


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Representation of Data. Photograph

Image

The data is in digital form

where the area is

subdivided into equal size

picture elements or pixels.

The information is

collected in narrow

wavelength range referredas a BAND

FCC OF ROORKEE AREA IRS LISS III DATA


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IKONOS DATA OF ROORKEE DATA

PROCESSING & ANALYSIS

INTERPRETATION

Visual - Human based

Digital - Computer assisted


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COMPARISON

VISUAL ANALYSIS

Single band or as FCC

Subjective

Slow

Analyst Bias

DIGITAL ANALYSIS

Multi Image

Objective

Fast with many options

Free of Analyst bias

Elements of Image Interpretation

Primary Elements

Black and White Tone

Color

Stereoscopic Parallax

Spatial Arrangement of Tone& Color

Size

Shape

Texture

Pattern

Based on Analysis of

Primary Elements

Height

Shadow

Contextual ElementsSite

Association


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DIGITAL IMAGE PROCESSING

Image classification and analysis

digitally identify and

classify pixels

supervised

unsupervised


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Image Classification and Analysis

Spectral pattern recognition

Digital image classification uses the spectral

information represented by the digital numbers in one

or more spectral bands, and attempts to classify each

individual pixel based on this spectral information

The resulting classified image is comprised of a mosaic of

pixels, each of which belong to a particular theme, and is

essentially a thematic "map" of the original image.

Common classification procedures

Supervised classification

Unsupervised classification


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Supervised classification

Training areasthe analyst identifieshomogeneous representativesamples of the differentsurface cover types

To determine the numerical"signatures

Once the computer hasdetermined the signatures foreach class, each pixel in theimage is compared to these

signatures and labeled as theclass it most closely"resembles" digitally

Unsupervised classification

reverse of supervised

classification

Spectral classes are grouped

first

Then matched to information

classes the analyst specifies how

many groups or clusters

It is iterative in nature

not completely without

human intervention


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Comparison

PROBLEM OF MIXED PIXEL With coarse resolution data, the occurrence of mixed pixels

had been intense, and it was thought that this aspect will

reduce with increase in spatial resolution.

However, this problem has remained same in magnitude

with increase in spatial resolution.

With coarse resolution, the chances of two or more classes

contributing to a mixed pixel were high but the number of

such pixels was small. With improved spatial resolution, the number of classes

within a pixel has reduced but the number of mixed pixels

has increased.

In a way, the problem of mixed pixels remained, may be its

direction of impact has changed.


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PROBLEM OF MIXED PIXEL Consider a simple land area consisting of two classes,

namely, water and land (Fig.1).

Two pixels belong to only one class, i.e., pixel 1 haswater and pixel 4 has land, and these are called as pure

pixels.

Pixels 2 and 3 has varying composition of land andwater, and are called mixed pixels.

A mixed pixel displays a composite spectral responsethat may be dissimilar to the spectral response of eachof its component classes, and therefore, the pixel maynot be allocated to any of its constituent classes.

Therefore, an error is likely to occur in theclassification of the image.

Convention statistical based image classification (alsoknown as hard classification) which assumes that the

pixels contain pure information, would identify thepixel to one and only one class.

Thus pixel 2 may be classified as water and pixel 3 asland (Fig.1b).

Depending upon the proportion of mixed information,it may result into a loss of pertinent information

present in a pixel and subsequently in an image.

Pixel 2

Pixel 3 Pixel 4

Land

Water

0 1

(a) Actual land cover (b) Hard classification

(i) Water (ii) Land

(c) Fraction Image

Land

Land Water

Water

Pixel 2

Pixel 3 Pixel 4

Pixel 1

Pixel 1 Pixel 2

Pixel 3 Pixel 4

Pixel 1 Pixel 2

Pixel 3 Pixel 4

Mixed pixels have to be accommodated in theclassification process in some way, by making useof sub-pixel or soft classification methods basedon certain heuristic and logical reason has to beadopted.

The output from these methods is a set of class

membership values for each pixel known as soft,fuzzy or sub-pixel classification outputs whichrepresent the probability fraction or proportionimages (Fig.1c).

These soft outputs strongly relate to actual extentsof the classes on ground.


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Soft classification methods

Spectral mixture analysis.

Fuzzy set theory.

Artificial neural network.

Linear Mixture Model (LMM) Widely used for the decomposition of the class proportion of

mixed pixels.

The method assumes that the spectral response of a pixel is alinear sum of the mean spectral responses of the various landcover classes weighted by their relative proportion on theground

The model can be mathematically expressed as

whereMij is the end member spectra representing the meanclass spectral response ofjth land cover class in the ithband,

fj are the proportions ofjth land cover class in a pixel,

ei is the error term for ithband, which expresses the difference

between the observed spectral response and the model derivedspectral response of the pixel.

=

+=c

jiijji eMfx

1


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Linear Mixture Model (LMM)

It may be noted that class proportions of a mixed

pixel are not negative and that the sum of all theclass proportions is equal to one, and can beexpressed as

Andfj 0 for allj land cover classes.

The end member spectra matrix M represents thespectral responses of classes, and may be calculated

by taking the average spectral response of that classhaving pure pixels, or estimated from laboratory andfield measurements of the classes, or by performing

principal component analysis.

=

=c

j

jf1

1

When applied to remote sensing of semi-vegetated areasthe linear mixture model approach assumes that end-members can be frequently be recognized from the imageitself ('image end-members').

Disregarding theoretical considerations, such as the factthat the model assumes a single-scattering approach, it isthe difficulty in locating end-member spectra that presentthe main difficulty to the user.

Logic indicates that an end- member proportion can not benegative and, if the model is properly specified, that thesum of the proportions of end-members at a given pointmust be less than or equal to unity.


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It is possible to build these constraints into the linearmixture model so that the result derived for every

individual pixel satisfy these logical requirements. It is, however, more practical to consider the

unconstrained model which simply computes, from alibrary of end member spectra, the end-member

proportions at a given point.

If the model fits perfectly then there should be no end-member proportions less than zero or greater thanunity, and the sum of the proportions at a given point.

If the model fits perfectly then there should be no end-member proportion less than zero or greater than

unity, and the sum of the proportions should notexceed 1.0.

Furthermore a root mean squared error may not showany systematic pattern.

Only by using and unconstrained model is it possibleto check that these conditions are met.

One constraint imposed by linear unmixing is that thenumber of end-members cannot exceed the number ofspectral bands available.

Even so, the selection of end-members which iscrucial to the successful application of the linearmixing model in fraught with difficulties.


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Fuzzy c-Means (FCM) FCM is an iterative clustering method employed to

partition pixels of remote sensing images into differentclass membership values.

The key is to represent the similarity that a pixel shareswith each cluster with a function (membership function)whose value lies between zero and one.

Each pixel will have membership in every cluster.

Memberships close to unity signify a high degree ofsimilarity between the pixel and that cluster.

The net effect of such a function of clustering is toproduce fuzzy c-partitions of a given data.

A fuzzy c-partition of the data is the one whichcharacterizes the membership of each pixel in all theclusters by a membership function that ranges from zero toone.

Possibilistic c-Means (PCM) The main motivation behind the use of PCM relates to the

relaxation of the probabilistic constraint of FCM.

Formulation of PCM is based on a modified FCM objective

function whereby an additional term called as regularizing term

is included.

It is similar to FCM as PCM clustering is also an iterative

process where the class membership values are obtained by

minimizing the generalized least-square error objective function

where is a parameter that depends on the distribution of pixels

in the cluster j and is assumed to be proportional to the mean

value of the intra cluster distance

= = = =

+=N

i

c

j

c

j

mN

i

ijjAji

m

ijm ivxVUJ1 1 1 1

2

)()(),(

j


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Neural Network Based Methods Artificial neural networks have the capability to generalize

the relation between the evidence (e.g., remote sensingdata) and the conclusion (e.g., landcover classification)without developing any mathematical models.

Thus, unlike statistical parametric methods, they do notassume that the data follows a distribution.

The neural network contains interconnected layers eachcontaining a number of units, symbolizing the biologicalconcept of a neuron.

The interconnections carry weights, which are adjusted inan interactive learning process to provide neural networksolution.

The learning process may be supervised or unsuperviseddepending on whether training data are required or not.

Accordingly, a number of supervised an unsupervisedneural network algorithms have been developed.

Supervised Neural Network

Number of units in the input layer is equal the number of bandsused for the classification.

Unlike input layer, hidden and output layers process the data.The output layer produces the neural network results.

The number of units in the output layer is generally equal to thenumber of classes to be mapped.

Class 1

Band1

Band2

Band3

Band4

input Layer (i) Input Layer (s) Output Layer (j)

Remote Sensing Data Land Cover Classes

Class 2

Class 3

Class 4

Class 5

Wi

s

Ws

j

Typically, a supervisedneural network consists ofthree layers; an inputlayer, a hidden layer andan output layer.

The input layer receivesthe data (i.e., the multi-spectral remote sensingimage data).

=i

isiWxsnet sjWiOsO =


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Supervised Neural Network

Therefore, the number of units in the input and output

layers are fixed by the application designed. Selection of the number of hidden layers and their units is

a critical step for the successful operation of the neuralnetwork.

Using too few units in the hidden layer may result intoinaccurate classification as the network may not bepowerful enough to process the data.

On the other hand, by using a large number of hiddenunits, the computational time becomes large. It may alsoresult into the network being over-trained.

The optimum number of units in the hidden layer is oftendetermined by trial and error, though some empiricalrelations do exist.

Back Propagation Neural Network (BPNN) The BPNN is a generalized least squares algorithm that adjusts the

connection weights between units to minimize the mean square errorbetween the network output and the target output.

The target output is known from reference data.

Data provided to input unit are multiplied by the connection weightsand are summed to derive the net input to the unit in the hidden layer.

where, xi is a vector of magnitude of the ith input (i.e., spectralresponse of pixel),

Wis is matrix of the connection weights between ith input layer unit and

sth hidden layer unit.

Each unit in sth hidden layer computes a weighted sum of its inputs,and passes the sum via an activation function to the units in the jth

output layer through weight vectorWsj.

=i

isis Wxnet


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There is a range of activation functions to transform the data fromhidden layer unit to an output layer unit. These include pure linear,tangent, hyperbolic, sigmoid functions , etc.

Although, the use of these functions may lead to difference inaccuracy of classification. Generally, sigmoid function has beenwidely used, and may be defined as

where is the output from the sth hidden layer unit, and is a gainparameter that controls the connection weights between the hiddenlayer unit and the output layer unit .

Outputs from the hidden units are multiplied with the connectionweights, and are summed to produce the output of thejth unit in theoutput layer

where Oj is the network output for the jth output unit (i.e., the land

cover class) and Wsj is the weight of the connection betweensth hidden

layer unit andjth output layer unit.

]exp/[ snet

+= 11Os

sjsj WOO =

An error functionE, determined from a sample of target (known)outputs and network outputs, is minimized iteratively. Theprocess continues untilEconverges to some minimum value, andthe adjusted weights are obtained.

E=

where Tj is the target output vector, Oj is the network outputvector, and c is the number of classes.

The target vector is determined from the known class allocationsof the training pixels, which are coded in binary form. Forexample, a pixel belonging to class 3 shall be coded as 0 0 1 0 0 atthe five output units.

The collection of known class allocations of all pixels will formthe target vector.

=

c

j

jj OT

1

2)(50.0


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Target output coding for BPNN

0

0

1

0

0

Band 1

Band 2

Band 3

Band 4

Remote Sensing Data

Input Layer Input LayerOutput Layer

Class Allocation

Learning algorithms such as backpropagation have parameters

(e.g momentum and learning rate) that mush be selected. These

can significantly influence the performance of a network. What

values should be selected and should be they be varied in training.

Learning

parameters

There are a range of learning algorithms available.

Backpropagation is the most widely used but can be slow and

faster variants, which make assumptions about the error surface,

are popular. Which should be used.

Learning

algorithm

Determines the capacity of the network to learn and generalize. In

general, large network may learn more accurately but have poorer

generalization ability than a small network. Larger networks are

also slower to train. How many hidden units and layers should be

used?

Number

of hidden

unit & layers

CommentParameter

/ issue


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The initial weight settings of the pre-trained network can significantly

influence network performance. Typically, these are generally set

randomly, but within what range?

Initial weights

There is a need to ensure that the network has learnt to correctly

identify class membership from the training data but is not

overtraining and so has acceptable generalization ability. How is thisto be assessed? Should verification sets be used?

When/how to

terminate

training

The training error is generally negatively related to the number of

training iterations. The accuracy of generalizations may be non-

monotonically related to the intensity of training: typically the

accuracy of generalization increases as the network gradually learns

the underlying relationship with greater accuracy but will eventually

decline as the network becomes over trained. How many iterations of

the learning algorithm should be used?

Number of

training

iterations

There is usually one input unit associated with each discriminating

variable but other approaches may be used. Also the data input t o the

neural network generally have to be rescaled for the analysis,

typically to a 0 to 1 or -1 to 1 scale. What method should be used to

achieve this and what allowance should be made for data to extend

beyond the range observed in the training set?

Data input

and scaling

CLASSIFICATION ACCURACYASSESSMENT

The accuracy assessment is a critical step in any mapping process, andthus is an essential component that allows a degree of confidence tobe attached to maps for their effective use.

Traditionally, the accuracy of classification has been assessed usingerror matrix based measures.

Here, each pixel in the image is assumed pure, containing one classper pixel on the ground.

Thus, in essence, the continuum of variation found in the landscape isdivided into a finite set of classes such that pixels representing theseclasses became pure, and the error matrix based measures may beused.

However, these classes become less separable as the class mixtureincreases, and therefore, the error matrix based measures may beinappropriate.

Alternate accuracy measures are, therefore, sought to evaluate theaccuracy of soft classification which represents the class mixture in ameaningful way.


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CLASSIFICATION ACCURACY

ASSESSMENT Euclidean distance

L1 distance

the cross-entropy

correlation coefficients

fuzzy error matrix (FERM)

All these measures may be treated as indirect methods ofassessing the accuracy of soft classification because theaccuracy evaluation is interpretative rather than arepresentation of actual value as denoted by the traditionalerror matrix based measures.

Correlation Coefficient CC The correlation coefficient CCmay also be used to indicate the

accuracy on individual class basis estimated from a soft classificationoutput and a soft reference data.

The higher the correlation coefficient, the higher is the classificationaccuracy of a class.

where

is the covariance between the two distributions (i.e. the soft classifiedoutput and the soft reference data) and

are the standard deviations of both the distributions.

ijij

ijijCovCC

21

),( 21

=

),( ij2

ij

1

Cov

ijij 21 ,


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THANK

YOU

advanced image processing iirs-2008

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