Algorithm for Combined Wavelet Quasi-Superresolution

Igor Vujović*, Ivica Kuzmanić*, Mirjana Vujović***University of Split, Maritime Faculty,

Zrinjsko-Frankopanska 38, 21000 Split, Croatia** Private Occupational Health Practice,

Trg Kralja Tomislava 9, 20000 Ploče, Croatiaivujovic@pfst.hr

INTRODUCTION

Superresolution is the process of obtaining high-resolution image from a set of low-resolution frames. Low-resolution frames are usually an attempt to compensate camera/object movements or vibrations, i.e. in surveillance of important premises.

The level of image detail is crucial for the performance of : • computer vision algorithms, • target recognition, detection and identification systems

(military applications),• license plate readers, • surveillance monitors, • medical imaging applications, etc.

INTRODUCTIONINTRODUCTION

Authors are involved in telemedicine for years.In our previous researches, we used wavelets for medical

imaging, in particular pulmonary X-ray. When got into contact with superresolution, it was interesting to see whether it was possible to use superresolution in medical imaging. But, patients go to X-ray examination once in two years. There is a lot of things that could happen to the patient in two years and that can change totally the X-ray! How long we should wait to obtain enough low-resolution images for superresolution?! Naturally, an idea arise: if it is possible to use the single image to obtain high-resolution image, the problem could be resolve in few moments depending on the computer used.

WAVELET EVOLUTION

• FGW – classical wavelet analysis, due to large amount of operations, it is not well for on-line applications

• Intuitive wavelets – weights to wavelet coefficients• Lifting steps increase speed of operation• SGW – lifting steps are the basis, improvement of

FGW• Need of improvement for nanostructures and for

edge detection• Solution: TGW – combination of morphology and

wavelets based on FGW and SGW wavelets

SIZE OF WAVELET FILTER

2x2 and 3x3 windows on regulary sampled images

INFLUENCE OF THE NEIGHBORING COEFICIENTS

How to decribe these influences to each pixel?

Wavelet Quasi-superresolution

In references, irregular sampling called interlaced sampling is used. It makes sense in cases of moving/vibrating environment. In a static image, implementation could be simplified by regular sampling, such as shown in Table 1. In advanced applications, statistics could be used as well as some sort of minimization. It could include vary of low-resolution pixels in high-resolution image. In our case, four different positions for the same low-resolution pixel can be used.

TABLE ILocation of Low-resolution matrix Elements

on High-resolution Grid and Expression of Approximations

(for every coefficient)

LR (1,1) A LR (1,2)

C D E

LR (2,1) H LR (2,2)

)2,1()1,1(2

1LRLRA

)1,2()1,1(2

1LRLRC

)1,2()2,1(

2

1)1,1(

2

1LRLRLRD

)2,2()2,1(2

1LRLRE

)2,2()1,2(2

1LRLRH

Algorithm for wavelet quasi-superresolution with approximation of coefficients and image morphology

MOTION FIELD IN WAVELET DOMAIN

for i=2:m-1; for j=2:n-1 difer1a(i,j)=a1(i-1,j)-2*a1(i,j)+a1(i+1,j); difer2a(i,j)=a1(i,j-1)-2*a1(i,j)+a1(i,j+1); difer3a(i,j)=0.5*a1(i+1,j-1)-a1(i,j)+0.5*a1(i-1,j+1); difer4a(i,j)=0.5*a1(i-1,j-1)-a1(i,j)+0.5*a1(i+1,j+1);

etc... For other coefficients end; endii=0;for i=2:2:2*m-1; ii = ii+1; jj = 0; for j=2:2:2*n-1; jj = jj+1; a1hr(i-1,j-1)=a1(ii,jj)-difer4a(ii,jj); a1hr(i-1,j+1)=a1(ii,jj)+difer3a(ii,jj); a1hr(i-1,j)=a1(ii,jj)-difer1a(ii,jj); a1hr(i,j-1)=a1(ii,jj)-difer2a(ii,jj); a1hr(i,j+1)=a1(ii,jj)+difer2a(ii,jj); a1hr(i+1,j-1)=a1(ii,jj)-difer3a(ii,jj); a1hr(i+1,j)=a1(ii,jj)+difer1a(ii,jj); a1hr(i+1,j+1)=a1(ii,jj)+difer4a(ii,jj);etc ... For other coeficientsend; end

IMAGE QUALITYTo see which image is better, we used histograms of the original and HR

image in percentages. Percentages are necessary because of different LR and HR number of pixels. The advantage is in having single number to compare. That is the reason for introduction of one number for such purposes. The number is obtained by calculating rms value of histogram differences:

for t=1:256; rms=rms+(ha%(t,1)-hpa%(t,1))^2; end; rms=sqrt(rms/256);In the above code ha% is histogram of the original image a in

percentages and hpa% histogram of the processed image in percentages. The final comparison image criterion is given as:

rms 0 where rms is given with above algorithm. I.e. for Figure “coins”, our histogram RMS gives value of 0.0299 for

Daubechies wavelet of the second order (Matlab designation ‘db2’).

RESULTS

zoomed part of the HR image

Original image HR image

zoomed part of the original

RESULTS

Original

zoomed part of the original

zoomed part of the processed HR image

RESULTS

Proposed algorithmZoomed original

Less grainsLess pointed steps

RESULTS

FURTHER RESEARCH• Further work should include comparison between different wavelets

in systematic fashion.• Motion field for subpixel resolution in wavelet domain in off-line

applications: - medical, - security, surveillance (postanalysis), - mapping, - calibration of computer vision applications...• Motion field for subpixel resolution in wavelet domain in on-line

applications: - computer/robot vision applications, - target recognition and tracking,- security, surveillance, - marine and military radars, - tele-manipulation (indoor, outdoor, under-water, space)...

CONCLUSIONSIt is also important to notice that interpolation filter in wavelet domene, as

well as combination of morphology, introduce characteristics of SGW at intinituive level. That could be interpreted as weight function in wavelet domene. It is modification of the FGW with one of crucial characteristics of the SGW. Simply said, it is the SGW on the first generation settings. Actualy, it is exact the opossite of current production of SGW, where we have lifting of FGW, which is FGW on SGW settings.

Assessment of image quality and comparison of the original and processed image are very subjective. We used histograms of the original and HR image in percentages and than took root mean square value. For every image a single scalar number is obtained. Image quality is better if that value is closer to zero.

Application of this algorithm can be found in both optical and SAR images. Latter is interesting in marine and naval applications and can be implemented in cost guard operations to save lives and environment.