Chapter 12 Object Recognition 12 1 Patterns and

Chapter 12 Object 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: 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 separability depends on the choice of descriptors selected for application

Chapter 12 Object Recognition

• 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=…. abab… – 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”

Chapter 12 Object Recognition

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; 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:

– 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

• 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) < 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

• 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)

Chapter 12 Object Recognition