AN SVDBASED GRAY SCALE IMAGE QUALITY MEASURE FOR LOCAL AND GLOBAL ASSESSMENT

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• AN SVD-BASED GRAY SCALE IMAGE QUALITY MEASURE FOR
  LOCAL AND GLOBAL ASSESSMENT
• A. Shnayderman, A. Gusev, A. M. Eskicioglu
  Department of Computer and Information
  ScienceBrooklyn College of the City University
  of New York2900 Bedford Avenue, Brooklyn, NY
  11210
• IEEE Transactions on Image Processing, February
  2006.

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IMAGE QUALITY MEASURES

• Image quality measures can be classified into two
  groups
• Subjective
• Objective
• Subjective evaluation is cumbersome because the
  human observers can be influenced by several
  factors
• Environmental conditions
• Motivation and mood
• Objective measures include bivariate measures
• MSE
• Lp-norm
• Measures mimicking the HVS
• Graphical measures

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INCORPORATING A MODEL OF THE HVS INTO A OBJECTIVE
MEASURE

• Fuhrmann et al discourage the use of metrics
  based on the spatial properties of the HVS as
  they require precise knowledge of the viewing
  conditions.
• Franti argues that the distortion measure should
  be independent of a number of factors
• The compression method
• Basic image processing operations
• The viewing distance
• According to Wang and Bovik, the viewing
  conditions play an important role in human
  perception of image quality. However
• They are not fixed in most cases
• The specific data is generally not available to
  the image analysis system.

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WHAT IS AN IDEAL IMAGE QUALITY MEASURE?

• An ideal image quality measure should be able to
  describe the
• amount of distortion
• type of distortion
• distribution of error
• Such a measure is expected to provide accurate
  predictions of quality not only at distortion
  ranges near the visual threshold but also when
  distortions are significantly above the visual
  threshold.
• Undoubtedly, there is a need for an objective
  measure that provides more information than a
  single numerical value.
• Assessment of image quality is an open problem
  today.

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OPINION ABOUT LOCAL MEASUREMENT

• Lukas Budrikis (1982) It was found that
  further improvements in quality prediction were
  possible only if local rather than global
  averaging procedures were used.
• Karunasekera Kingsbury (1995) Alternatively,
  a matrix of error measurements over subregions of
  the image may be more useful in some
  applications.
• Westen, Lagendijk Biemond (1995) Another
  possibility is to combine the responses at each
  position, which leads to an image with values
  that represent a local visibility of distortions.
  In coding applications, such a local measure of
  image quality is probably more useful than a
  global one.
• Eude Mayache (1998) A multidimensional
  quality measure, with each dimension being
  related to a properly identified artifact, is an
  attractive solution for the evaluation of the
  image quality.

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SVD

• Singular Value Decomposition (SVD)
• Every real matrix can be decomposed into a
  product of 3 matrices.
• A USVT
• U and V are orthogonal matrices
• S diag (s1, s2, ...)
• si singular values of A
• columns of U left singular vectors of A
• columns of V right singular vectors of A
• SVD is one of the most useful tools of linear
  algebra with several applications to multimedia.
• Image compression
• Watermarking
• Other signal processing applications

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A NEW SVD-BASED MEASURE
si
sj
Original image
Distorted image

• Graphical measure
• Divide both images into 8x8 blocks.
• For each block, compute Di
  , where n is the block size, are the
  singular values of the original block, and
  are the singular values of the distorted block.
  If the image size is kxk, we have (k/n)x(k/n)
  blocks.
• Set of Dis is a distortion map
• Numerical measure
• MSVD
  , Dmid mid point of the sorted Di

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DISTORTION TYPES AND LEVELS
Level
Type
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SUBJECTIVE EVALUATION

• 15 observers
• Undergraduate/graduate students
• Professors
• Some observers were very familiar with image
  processing.
• Some observers had CS background
• High quality print-outs of the original image and
  distorted images.
• Images were ranked in two ways
• Within a given distortion type (i.e, ranking of
  the 5 distorted images)
• Across six distortion types (i.e., ranking of the
  6 distorted images for each distortion level)
• No viewing distance was imposed.
• 50 points in the scale
• 1 for the best image
• 50 for the worst image

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TEST IMAGES
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8X8 BLOCKS OF LENA WITH LARGEST AND SMALLEST SV
RATIOS
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SCATTER PLOTS OF FOUR MEASURES
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OVERALL PERFORMANCE OF FOUR MEASURES
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PERFORMANCE WITHIN EACH DISTORTION TYPE
Table 3. (a) CC-based performance within
each distortion type
(b) RMSE-based performance within each
distortion type
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PERFORMANCE ACROSS EACH DISTORTION LEVEL
Table 4. (a) CC-based performance across
each distortion level
(b) RMSE-based
performance across each distortion level
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SENSITIVITY OF M-SVD TO BLOCK SIZE
Smaller block size results in more detailed
distortion maps leading to higher correlation
with subjective evaluation. Similarly, larger
block size results in coarser distortion maps
leading to lower correlation with subjective
evaluation.
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PERFORMANCE OF GRAPHICAL MEASURE JPEG LEVEL 5
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PERFORMANCE OF GRAPHICAL MEASURE JPEG 2000
LEVEL 5
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PERFORMANCE OF GRAPHICAL MEASURE GAUSSIAN BLUR
LEVEL 5
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PERFORMANCE OF GRAPHICAL MEASURE GAUSSIAN NOISE
LEVEL 5
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PERFORMANCE OF GRAPHICAL MEASURE SHARPENING
LEVEL 5
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PERFORMANCE OF GRAPHICAL MEASURE DC-SHIFTING
LEVEL 5
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OBSERVATIONS ABOUT THE DISTORTION MAPS

• JPEG As the distortion level is increased, the
  image becomes blocky (which is the major artifact
  for Discrete Cosine Transform (DCT)-based JPEG
  compression). This artifact becomes visible in
  the maps starting from compression ratio 301,
  especially on Lenas shoulder and the wall.
• JPEG2000 As this new compression standard is
  based on the wavelet transform, the images become
  blurry along the edges, and in high frequency
  areas. As we increase the compression ratio, the
  maps display how the image loses its fidelity.
  When compared with JPEG, this technology is
  superior especially at higher compression ratios.
  
• Gaussian blur This type of distortion
  substantially affects the edges and high
  frequency areas, resulting in seriously blurred
  images. As the radius of blurring is increased,
  we see high peaks in the maps along the edges,
  and high frequency areas.
• Gaussian noise The effect is a uniformly
  distributed noise across the image which is
  depicted in the maps as the amount of noise goes
  up. The noise is visible in high frequency, low
  frequency, and textured areas.
• Sharpening This type of filter makes the
  textured and high frequency areas sharper and
  crispier. The maps show the distortion in the
  affected areas. In contrast, sharpening does not
  introduce noticeable noise in the low frequency
  areas.
• DC-shifting If a constant value is added to all
  the pixel values, the image becomes uniformly
  lighter, and if a constant value is subtracted
  from all the pixel values, the image becomes
  uniformly darker. Because of the range of pixel
  values of Lena (24-245), we subtracted values
  that resulted in darker areas along the edges
  with a sharp contrast. As smaller pixel values
  led to smaller singular values, our measure
  computed smaller differences along those edges,
  resulting in grooves in the maps. In the other
  areas, the distribution of distortion is uniform.

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CONCLUSIONS

• A new image quality measure is presented M-SVD.
• Numerical measure
• A derivation from the graphical measure, which is
  expressed as a Minkowski metric.
• Computes a global estimate of the distortion in
  the image.
• Its overall performance is better than that of
  the UQI and MSSIM.
• No analysis required to compute a weighted sum in
  predicting the overall error.
• Reliable prediction of visual quality not only
  near the visual threshold but also well above the
  visual threshold.
• Graphical measure
• Consistently displays the type of distortion, the
  amount of distortion, and the distribution of
  error.
• A wide range of distortion types
• Compression (2 types), blur, noise, sharpening,
  and shifting
• Neither the graphical measure nor the numerical
  measure requires a simplified model of the HVS.
• The SVD is of order O(n3).
• If the image size is large, the computations are
  slower.
• If the image is divided into smaller blocks, and
  SVD is applied to each block, the total
  processing time is much lower.