Algorithm for Combined Wavelet QuasiSuperresolution

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Algorithm for Combined Wavelet Quasi-Superresoluti
on

• Igor Vujovic, Ivica Kuzmanic, Mirjana Vujovic
• University of Split, Maritime Faculty,
• Zrinjsko-Frankopanska 38, 21000 Split, Croatia
• Private Occupational Health Practice,
• Trg Kralja Tomislava 9, 20000 Ploce, Croatia
• ivujovic_at_pfst.hr

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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)
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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 i2m-1 for j2n-1
• difer1a(i,j)a1(i-1,j)-2a1(i,j)a1(i1,j)
  
• difer2a(i,j)a1(i,j-1)-2a1(i,j)a1(i,j1)
  
• difer3a(i,j)0.5a1(i1,j-1)-a1(i,j)0.5a
  1(i-1,j1)
• difer4a(i,j)0.5a1(i-1,j-1)-a1(i,j)0.5a
  1(i1,j1)
• etc... For other coefficients
• end end
• ii0
• for i222m-1 ii ii1 jj 0
• for j222n-1 jj jj1
• a1hr(i-1,j-1)a1(ii,jj)-difer4a(ii,jj)
  a1hr(i-1,j1)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,j1)a1(ii,jj)difer2a(ii,jj)
  a1hr(i1,j-1)a1(ii,jj)-difer3a(ii,jj)
• a1hr(i1,j)a1(ii,jj)difer1a(ii,jj)
  a1hr(i1,j1)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 t1256
• rmsrms(ha(t,1)-hpa(t,1))2
• end
• rmssqrt(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).

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RESULTS
HR image
Original image
zoomed part of the HR image
zoomed part of the original
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RESULTS
zoomed part of the processed HR image
Original
zoomed part of the original
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RESULTS
Less grains
Less pointed steps
Zoomed original
Proposed algorithm
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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.