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Algorithm for Combined Wavelet Quasi-Superresolution Igor Vujović*, Ivica Kuzmanić*, Mirjana Vujović** *University of Split, Maritime Faculty, Zrinjsko-Frankopanska 38, Split, Croatia ** Private Occupational Health Practice, Trg Kralja Tomislava 9, Ploče, Croatia

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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.

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INTRODUCTION 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.

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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

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SIZE OF WAVELET FILTER 2x2 and 3x3 windows on regulary sampled images

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INFLUENCE OF THE NEIGHBORING COEFICIENTS How to decribe these influences to each pixel?

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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.

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TABLE I Location of Low-resolution matrix Elements on High-resolution Grid and Expression of Approximations (for every coefficient) LR (1,1)ALR (1,2) CDE LR (2,1)HLR (2,2)

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

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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; end ii=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 coeficients end; end

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IMAGE QUALITY To 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 for Daubechies wavelet of the second order (Matlab designation ‘db2’).

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RESULTS zoomed part of the HR image Original image HR image zoomed part of the original

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RESULTS Original zoomed part of the original zoomed part of the processed HR image

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RESULTS Proposed algorithm Zoomed original Less grains Less pointed steps

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RESULTS

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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)...

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CONCLUSIONS It 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.

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