Digital Image Processing Lecture 24: Object Recognition Prof. Charlene Tsai *From Gonzalez Chapter 12

Terminology A pattern (x,y,z): arrangement of descriptors (those discussed in previous 2 lectures) A feature: another name for a descriptor in pattern recognition A pattern class : a family of patterns that share some common properties.

Example Petal width Petal length Is the feature selection good enough?

Decision-Theoretic Methods Assuming W classes ( ), we want to find decision functions with the property that if pattern x belongs to class , then The decision boundary separating two classes is the set of x for which

Common Approaches Matching Optimum statistical classifiers Minimum distance classifier Matching by correlation (skip) Optimum statistical classifiers Bayes classifier for Gaussian pattern classes Neural network

Matching–Minimum Distance Classifier Techniques based on matching represent each class by a prototype pattern vector. An unknown pattern is assigned to the class to which it is closest in terms of a predefined metric. For MDC, the metric is the Euclidean distance

MDC The prototype of each pattern class is the mean vector of that class: The distance metric is the Euclidean distance: Euclidean norm

MDC Assign x to class if Dj(x) is the smallest. Smallest Dj(x) is equivalent to largest dj(x), the decision function: The decision boundary between classes i and j becomes:

MDC- Decision Boundary bisector of the line joining mi and mj. In 2D: bisector is a line In 3D: bisector is a plane m1=(4.3,1.3)T m2=(1.5,0.3)T

Comments Simplest matching method. A class is described by the mean vector Works well for Large mean separation, and Relatively small class spread Unfortunately, we don’t often encounter this scenario in practice.