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

2. 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.

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

4. 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

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

6. 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

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

8. 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:

9. 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

10. 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.