Shape Classification Based on Skeleton Path Similarity

1
Shape Classification Based on Skeleton Path
Similarity

• Xingwei Yang, Xiang Bai, Deguang Yu, and Longin
  Jan Latecki

2
Shape similarity

• The goal of the shape similarity is using the
  information of the shape to recognize it like
  humans perception.

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Two main kinds of methods

• Contour
• Advantage it is easy to implement and similar to
  humans perception.
• Disadvantage it will meet problems on the
  articulated shapes.

• Skeleton
• Advantage it is not sensitive to the distortion
  of the articulated shape compared to contour.
• Disadvantage it is sensitive to the noise of
  contour.

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The main content of this talk

• 1. obtaining the skeleton which is insensitive to
  the contour noise.
• 2. introducing a skeleton representation.
• 3. Implementing the skeleton into Bayesian
  classifier to recognize shapes.
• 4. show results and discuss

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Skeleton Pruning by Contour Partitioning with
DiscreteCurve Evolution

• 1.1 The need for skeleton pruning

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Skeleton Pruning by Contour Partitioning with
DiscreteCurve Evolution

• 1.2 using Discrete Curve Evolution to simplify
  the contour
• where line segments s1, s2 are the polygon sides
  incident to a common vertex v, ß(s1, s2) is the
  turn angle at the common vertex v, l is the
  length function.

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Skeleton Pruning by Contour Partitioning with
DiscreteCurve Evolution
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Skeleton Pruning by Contour Partitioning with
DiscreteCurve Evolution

• 1.3 More results

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Skeleton representation

• The endpoint in the skeleton graph is called an
  end node, and the junction point in the skeleton
  graph is called a junction node. The shortest
  path between a pair of end nodes on a skeleton
  graph is called a skeleton path. We show a few
  example skeleton paths

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Skeleton representation
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Skeleton representation

• The shortest paths between every pair of skeleton
  endpoints are represented as sequences of radii
  of the maximal disks at corresponding skeleton
  points. In our paper, the skeleton path is
  sampled to 50 points.

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Implementing the skeleton into Bayesian classifier

• The shape dissimilarity between two skeleton
  paths is called a path distance. The path
  distance pd between sp and sp is
• ri is radius of the i th point on the skeleton
  path

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Implementing the skeleton into Bayesian classifier

• Given a shape ?' that should be classified by
  Bayesian Classifier, we build the skeleton graph
  G(?') of ?' and input G(?') as the query. For a
  skeleton graph G(?'), if the number of end nodes
  is n, the corresponding number of paths is n(n-1)
  . Then, the Bayesian Classifier computes the
  posterior probability of all classes for each
  path sp'?G(?'). By accumulating the posterior
  probability of all of the paths of G(?'), the
  system automatically yields the ranking of class
  hypothesis.

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Implementing the skeleton into Bayesian classifier

• If two different paths have small pd value, the
  value of probability should be large. Otherwise,
  it should be small. Therefore, we use Gaussian
  distribution to compute the probability p

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Implementing the skeleton into Bayesian classifier

• The class-conditional probability for observing
  sp' given that ?' belongs to class ci is
• We assume that all paths within a class path set
  are equiprobable, therefore
• ci is one of the M classes.

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Implementing the skeleton into Bayesian classifier

• The posterior probability of a class given that
  path sp'?G(?') is determined by Bayes rule

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Implementing the skeleton into Bayesian classifier

• Similar to the above assumption, p(ci)1/M. The
  probability of sp' is equal to

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Implementing the skeleton into Bayesian classifier

• By summing the posterior probabilities of a class
  over the set of paths in the input shape, we
  obtain the probability that the input shape
  belongs to a given class. Obviously, the biggest
  one, Cm, is the class that input shape belongs to

19
Experiments

• The table is composed of 14 rows and 9 columns.
  The first column of the table represents the
  class of each row. For each row, there are four
  experimental results which belong to the same
  class. Each experimental result has two elements.
  The first one is the query shape and the second
  one is the classification result of our system.
  If the result is correct, it should be the equal
  to the first column of the row. The red numbers
  mark the wrong classes assigned to query objects.
  Since there is only one error in 56
  classification results, the classification
  accuracy in percentage by this measure is 98.2.

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Experiments
21
Experiments

• The results of the proposed method

22
Experiments

• The results of Super and Suns method