Statistical Region Merging

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Statistical Region Merging

• R. Nock and F. Nielsen
• IEEE Transactions on pattern analysis and machine
  intelligence, Vol 26, Issue 11, p.p. 1452-1458,
  Nov. 2004

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Outline

• 1. Introduction
• 2. The model of image generation
• 3. Theoretical analysis and algorithms
• 4. Experimental results
• 5. Conclusion

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1. Introduction

• Segmentation is a tantalizing and central problem
  for image processing.
• A prominent trend in grouping focuses on graph
  theorem.
• The authors proposed a different strategy which
  belongs to region growing/merging techniques.
• Regions are sets of pixels with homogeneous
  properties and are iteratively grown by combining
  smaller regions.
• Region growing/merging techniques usually work
  with a statistical test to decide the merging of
  regions.
• A good region merging algorithm has to find a
  good balance between preserving the perceptual
  units and the risk of overmerging for the
  remaining region.

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1. Introduction

• A novel model of image generation and the
  segmentation approach are proposed.
• To reconstruct the true region from the observed
  region.
• With high probability, it suffers only the
  overmerging problem in segmentation.
• With high probability, it has small overmerging
  error.
• Fast and easily implementable.
• Can be used to images with many channels.
• Can handling noise and occlusions.

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2 The model of image generation

• 1. Introduction
• 2. The model of image generation
• 2.1 The model of image generation
• 3. Theoretical analysis and algorithms
• 4. Experimental results
• 5. Conclusion

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2.1 The model of image generation

• The observed image, I, contains I pixels, each
  containing RGB values and belonging to the set
  1,2,...,g

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2.1 The model of image generation

• The observed color channel is sampled from a
  family of Q distributions at each pixel of a
  perfect scene, I. (Range of the Q distributions
  are bounded by g/Q)

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2.1 The model of image generationAn example

• Example of some true image I (expectation) and
  the observed image I.

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2.1 The model of image generationhomogeneity
property

• In I, the optimal regions share a homogeneity
  property
• Inside a region, the statistical pixels have the
  same expectation for every color channel.
• Different regions have different expectations for
  at least one color channel.
• Inside a region, all distributions associated to
  each pixel can be different, as long as the
  homogeneity property is satisfied.

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3. Theoretical analysis and algorithms

• 1. Introduction
• 2. The model of image generation
• 3. Theoretical analysis and algorithms
• 3.1 Theoretical analysis
• Merging predicate
• Order in merging
• 3.2 Other properties of the proposed approach
• 3.3 Proposed algorithm SRM
• 4. Experimental results
• 5. Conclusion

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3.1 Theoretical analysis and algorithmsTheoretica
l analysis

• Two essential components in defining a region
  merging algorithm
• Merging predicate define how to merge to
  undetermined region.
• Order in merging define an order to be followed
  to check the merging predicate.

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3.1 Theoretical analysis and algorithmsMerging
predicate

• Theorem 1 (The independent bounded difference
  inequality). Let be a
  vector of n R.V.s. Suppose the real-valued
  function f satisfies
  whenever vectors x and x differ only in kth
  coordinate. Then, for any ,
• where is the expected value of the R.V.
  f(X)

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3.1 Theoretical analysis and algorithmsMerging
predicate

• From thm 1, we obtain the result on the deviation
  of observed differences between regions of I.
• Corollary 1. Consider a fixed couple (R,R) of
  regions of I. , the probability is no
  more than that

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3.1 Theoretical analysis and algorithmsMerging
predicate

• In the same statistical region,
  and with a high probability that
  does not exceed .
• Merging predicate merge R and R iff

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3.1 Theoretical analysis and algorithmsOrder in
merging

• Ideally, the order to test the merging of regions
  is
• when any test between two true regions occurs,
  that means that all tests inside each of the two
  true regions have previously occurred.

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3.2 Theoretical analysis and algorithmsOther
properties of the proposed approach

• The proposed approach is proved that only
  overmerging occurs, with high probability.
• The proposed approach has been shown to have an
  upperbound on the error incurred w.r.t. the
  optimal sementation, with high probability.
• The proposed approach is easily extended to
  numerical channels, such as RGB.

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3.3 Theoretical analysis and algorithmsProposed
algorithm SRM

• To choose a merging predicate and order in
  merging to approximate the ideal segmentation
  method.
• Merging predicate merge R and R iff
• Order in merging choose a real-valued function f
  and radix sort f(.,.) to approximate the order in
  merging. ( O(Ilog(g)) )

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4. Experimental results

• 1. Introduction
• 2. The model of image generation
• 3. Theoretical analysis and algorithms
• 4. Experimental results
• 4.1 Choice of f
• 4.2 Noise handling
• 4.3 Enhance the noise handling ability
• 4.4 Handling occlusions
• 4.5 Controlling the scale of the segmentation
• 5. Conclusion

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4.1 Experimental resultsChoice of f

• Choose , where and
  are the pixel channel values.
• The preordering can manage dramatic improvements
  over conventional scanning.

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4.1 Experimental resultsChoice of f

• A second choice of f is to use and in
  Sobel filters, where smoothing filter is
  performed by 1 2 1 and derivative filter is -1
  0 0 1.

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4.1 Experimental resultsChoice of f

• Comparison of the two choices of f

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4.2 Experimental resultsNoise handling

• Two noise types to be handled
• Transmission noise t(q) chosen uniformly in
  1,2,...,g
• Salt and pepper noise s(q) chosen uniformly in
  1,g

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4.3 Experimental results Enhance the noise
handling ability

• By integrating the moving average operators, the
  first kind of f is
  replaced by
• For the second kind of f, the smoothing filter is
  extended to be 1 2 ... ?1 ? ... 1, and the
  derivative filter is extended to be -? -?1 ...
  ?.

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4.3 Experimental results Enhance the noise
handling ability

• Noise handling ability of the extended SRM
  methods.

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4.4 Experimental results Handling occlusions

• First run SRM as already presented.
• In a second stage, run SRM again with the
  modification of to
  , and 4-connexity to clique
  connexity.
• Radix sorting with f has an overall time
  complexity O( (Ik2)logg) ).

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4.4 Experimental results Handling occlusions

• SRM with occlusion handling.

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4.5 Experimental results Controlling the scale
of the segmentation

• The objective of multiscale segmentation is to
  get a hierarchy of segmentations at different
  scales.
• In SRM, scale is controlled by tuning of
  parameter Q as Q increases, the regions found
  are getting smaller.

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5. Conclusion

• 1. Introduction
• 2. The model of image generation
• 3. Theoretical analysis and algorithms
• 4. Experimental results
• 5. Conclusion

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5. Conclusion

• A novel model of image generation is proposed,
  which captures the idea that grouping is an
  inference problem.
• A simple merging predicate and ordering in
  merging are provided.
• SRM suffers only overmerging problems and
  achieves low error in segmentation, both with
  high probability.
• SRM is very fast (segments a 512x512 image is in
  about one second on an Intel Pentium 4 2.4G
  processor)
• SRM is able to cope with significant noise
  corruption, handling occlusions, and perform
  scale-sensitive segmentations.