12'1 Patterns and pattern classes

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Chapter 12 Object Recognition

• 12.1 Patterns and pattern classes
• Definition of a pattern classa family of
  patterns that share some common properties
• Feature and descriptor
• Pattern arrangements used in practice are
  vectors, strings and trees
• Pattern vectors
• The nature of a pattern vector x depends on the
  approach
• Used to describe the physical pattern itself
• Discriminant analysis of iris flowers
• The classic feature selection problem the
  degrees of class separabiilty depends on the
  choice of descriptors selected for application

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• Noisy object and its corresponding signature
• Select the descriptors on which to base each
  component of a pattern vector
• Pattern characteristics are described by
  structural properties
• For example fingerprint recognition based on
  minutiae
• Pattern classes are based on quantitative
  information size and location
• Features based on spatial relationships abrupt
  ending, branching, merging, and disconnected
  segments
• Strings pattern problem a staircase pattern
• This pattern could be sampled and expresses in
  terms of a pattern vector
• The basic structure would be lost in the method
  of description
• Resol define the elements and b and let the
  pattern be the string of symbols w.abababab
• String descriptions generate patterns of objects

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• Other entities whose structure is based on the
  relatively simple connectivity of primitives,
  usually associated with boundary shape
• Hierarchical ordering leads to tree structures
• For example a satellite image
• based on the structural relationship composed
  of

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12.2 Recognition base on Decision- theoretic
methods

• Decision functionsthe property of class belong
  to wi
• di(x) gt dj(x) j1,2,,W j?i
• Decision boundary separating class wi from wj
• di(x)- dj(x)0
• 12.2.1 Matching
• Represent each class by a proto-type pattern
  vector
• Minimum distance classifier
• Define the prototype class to be the mean vector
  of the patterns of that class
• Determine the class membership of an unknown
  pattern vector x is to assign it to class of its
  closet prototype
• Use Euclidean distance to determine closeness
  computing the distance measures

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• Assign x to class wi if Di(x) is the smallest
  distance the best match
• Selecting the smallest distance is equivalent to
  evaluating the functions
• the decision boundary between class wi and class
  wj for a minimum distance classifier is
• Matching by correlation
• The correlation between f(x,y) and w(x,y) is
• Disadvantage sensitive to changes in the
  amplitude of f and w
• Resol performing matching via the correlation
  coefficient
• Obtaining normalization for changes in size and
  rotation can be difficult
• Add a significant computation
• 12.2.2 Optimum statistical classifiers
• A probabilistic approach to recognition
• Become important because of the randomness which
  pattern classes normally are generated

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• Foundation
• The probability that a particular pattern x comes
  from class wi
• The average loss incurred in assigning x to class
  wj
• Rewrite the average loss as
• Drop 1/p(x), the average loss reduces to
• The Bayes classifier the classifier that
  minimize the total average loss
• Assign an unknown pattern x to wj if rj(x) lt
  rj(x)
• Loss of unity for incorrect decision and a loss
  of zero for correct decision
• A pattern vector z is assigned to the class whose
  decision function yields the largest numerical
  value

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• Bayes classifier for Gaussian pattern classes
• The Bayes decision function have the form
• If the two classes are equally likely to occur
• P(W1)P(W2)1/2
• The Gaussian density of the vectors in the j-th
  pattern class has the form (12.2-19)
• Mean and co-variance matrix (12.2-22,, 12.2-23)
• If all the covariance matrices are equal, then
  CjC, we obtain (12.2-27) linear decision
  functions (hyper-plane)
• If CI, p(wj)1/W, for j1,2,,W, then dj(x)
  (12.2-28)

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