Digital Image Processing Lecture 24: Object

RecognitionJune 13, 2005

Prof. Charlene TsaiProf. Charlene Tsai

*From Gonzalez Chapter 12

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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.

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Example

2

1xx

xPetal width

Petal length

1

2

3

Is the feature selection good enough?

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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

W ,...,, 21

x,...,x,x 21 wddd

i

ijWdd ji ;...,1,2,j xx

0xx xdxdxddd jiijji

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Common Approaches

Matching Minimum distance classifier Matching by correlation (skip)

Optimum statistical classifiers Bayes classifier for Gaussian pattern classes

Neural network

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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

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MDC

The prototype of each pattern class is the mean vector of that class:

The distance metric is the Euclidean distance:

WN jj

j ...,1,2,j x1

mix

WD jj ...,1,2,j m-xx

Euclidean norm

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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:

j

Wd jTjj

Tj ...,1,2,j mm

2

1mxx

0mmmm 2

1mmx

xxx

jiT

jijiT

jiij ddd

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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

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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 pactice.

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Quiz

Q1: Compute the decision functions of a minimum distance classifier for the pattern shown in the next page.

Q2: Compute and sketch the decision surfaces implemented by the decision functions in Q1.

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m1=(4.3,1.3)T

m2=(1.5,0.3)T

m1=(5.5,2.1)T