Chapter 12 Object Recognition Chapter 12 Object Recognition 12.1 Patterns and pattern classes Definition of a pattern class:a family of patterns that share

Chapter 12Object Recognition


12.1 Patterns and pattern classes• Definition of a pattern class:a family of patterns

that share some common properties• Feature and descriptor• Pattern arrangements used in practice are: vecto

rs, 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 separability 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 patte

rn 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 s

ymbols w=….abababab…

– String descriptions generate patterns of objects

• 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”







12.2 Recognition base on Decision- theoretic methods

• Decision functions:the property of class belong to wi

– di(x) > dj(x) j=1,2,…,W; ji

• 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 distanc

e measures: WjmxxD jj ,...,2,1 )(

– 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 c

lass 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) < 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

– The Gaussian density of the vectors in the j-th pattern class has the form

– Mean and co-variance matrix (12.2-22,, 12.2-23)

– If all the covariance matrices are equal, then Cj=C, we obtain (12.2-27) linear decision functions (hyper-plane)

– If C=I, p(wj)=1/W, for j=1,2,…,W, then dj(x) (12.2-28)

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Chapter 12 Object Recognition Chapter 12 Object Recognition 12.1 Patterns and pattern classes Definition of a pattern class:a family of patterns that share