Object Recognition (2)

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Pattern Recognition

Speaker: Wen-Fu Wang Advisor: Jian-Jiun Ding E-mail: [email protected] Graduate Institute of Communication Engineering National Taiwan University, Taipei, Taiwan, ROC

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Outline

Introduction Minimum Distance Classifier Matching by Correlation Optimum statistical classifiers Matching Shape Numbers String Matching

3

Outline

Syntactic Recognition of Strings String Grammars

Syntactic recognition of Tree Grammars

Conclusions

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Introduction Basic pattern recognition flowchart

SensorFeature

generationFeature selection

Classifier design

System evaluation

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Introduction The approaches to pattern recognition developed

are divided into two principal areas: decision-theoretic and structural

The first category deals with patterns described using quantitative descriptors, such as length, area, and texture

The second category deals with patterns best described by qualitative descriptors, such as the relational descriptors.

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Minimum Distance Classifier Suppose that we define the prototype of each

pattern class to be the mean vector of the patterns of that class:

Using the Euclidean distance to determine closeness reduces the problem to computing the distance measures

1

j

j jx wj

m xN

j=1,2,…,W (1)

( )j jD x x m j=1,2,…,W (2)

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Minimum Distance Classifier

The smallest distance is equivalent to evaluating the functions

The decision boundary between classes and for a minimum distance classifier is

j=1,2,…,W (3)

j=1,2,…,W (4)

1( )2

T Tj j j jd x x m m m

( ) ( ) ( )ij i jd x d x d x 1( ) ( ) ( ) 02

T Ti j i j i jx m m m m m m

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Minimum Distance Classifier Decision boundary of minimum distance classifier

-0.5 0 0.5 1 1.5 2 2.5

0

0.5

1

1.5

2

x1

x 2¹Ï3.a¡G¤Gºû¥±¤ÀÃþ½d¨Ò

D

ClassC1ClassC2

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Minimum Distance Classifier Advantages: 1. Unusual direct-viewing 2. Can solve rotation the question 3. Intensity 4. Chooses the suitable characteristic, then solves mirror problem 5. We may choose the color are one kind of characteristic, the color question then solve.

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Minimum Distance Classifier Disadvantages: 1. It costs time for counting samples, but we must have a lot of samples for high accuracy, so it is more samples more accuracy! 2. Displacement 3. It is only two features, so that the accuracy is lower than other methods. 4. Scaling

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Matching by Correlation We consider it as the basis for finding

matches of a sub-image of size within an image of size , where we assume that and

( , ) ( , ) ( , )s t

c x y f s t w x s y t

J K( , )f x y M N

J M K N

for x=0,1,2,…,M-1,y=0,1,2,…,N-1 (5)

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Matching by Correlation Arrangement for obtaining the correlation of and at

point

M

K

J

Origin

o

f w

0 0( , )w x s y t 0 0( , )x y

( , )f x y

0 0( , )x y

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Matching by Correlation The correlation function has the disadvantage of being

sensitive to changes in the amplitude of and For example, doubling all values of doubles the value of An approach frequently used to overcome this difficulty is

to perform matching via the correlation coefficient

The correlation coefficient is scaled in the range-1 to 1, independent of scale changes in the amplitude of and

f wf

( , )c x y

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2 2

[ ( , ) ( , )][ ( , ) ]( , )

[ ( , ) ( , )] [ ( , ) ]

s t

s t s t

f s t f s t w x s y t wx y

f s t f s t w x s y t w

f w

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Matching by Correlation Advantages: 1.Fast 2.Convenient 3.Displacement Disadvantages: 1.Scaling 2.Rotation 3.Shape similarity 4.Intensity 5.Mirror problem 6.Color can not recognition

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Optimum statistical classifiers The probability that a particular

pattern x comes from class is denoted

If the pattern classifier decides that x came from when it actually came from , it incurs a loss, denoted

1

( ) ( )W

j kj kk

r x L p w x

iw( )ip w x

jw

iw ijL

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Optimum statistical classifiers From basic probability theory, we

know that

1

1( ) ( ) ( )( )

W

j kj k kk

r x L p x w P wp x

( ) ( ) ( ) ( )p A B p A p B A p B

1

( ) ( ) ( )W

j kj k kk

r x L p x w P w

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Optimum statistical classifiers Thus the Bayes classifier assigns an

unknown pattern x to class

1 1

( ) ( ) ( ) ( )W W

ki k k qj q qk q

L p x w P w L p x w P w

iw

1ij ijL

1

( ) (1 ) ( ) ( )W

j kj k kk

r x p x w P w

( ) ( ) ( )j jp x p x w p w

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Optimum statistical classifiers The Bayes classifier then assigns a

pattern x to class if,

or, equivalently, if

iw

( ) ( ) ( ) ( ) ( ) ( )i i j jp x p x w P w p x p x w P w

( ) ( ) ( ) ( )i i j jp x w P w p x w P w

( ) ( ) ( )j j jd x p x w P w

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Optimum statistical classifiers Bayes Classifier for Gaussian Pattern

Classes Let us consider a 1-D problem (n=1)

involving two pattern classes (W=2) governed by Gaussian densities

( ) ( ) ( )j j jd x p x w P w

2

2

( )

21 ( )2

j

j

x m

jj

e P w

1,2j

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Optimum statistical classifiers In the n-dimensional case, the

Gaussian density of the vectors in the jth pattern class has the form

11 ( ) ( )2

1 22

1( )(2 )

Tj j jx m C x m

j nj

p x w eC

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Optimum statistical classifiers Advantages: 1. The way always combine with other methods, then it got high accuracy

Disadvantages: 1.It costs time for counting samples 2.It has to combine other methods

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Matching Shape Numbers Direction numbers for 4-directional chain

code, and 8-directional chain code

0

1

2

3

0

1

2

3

4

56

7

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Matching Shape Numbers Digital boundary with resampling grid superimposed

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Matching Shape Numbers All shapes of order 4, 6,and 8

Order6

Order8

Chain code: 0321Difference : 3333Shape no. : 3333



Chain code:03032211Difference :33133030Shape no. :03033133


Order4

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Matching Shape Numbers Advantages: 1. Matching Shape Numbers suits the processing structure simple graph, specially becomes by the line combination 2. Can solve rotation the question 3. Matching Shape Numbers most emphatically to the graph outline, Shape similarity also may completely overcome 4. The Displacement question definitely may overcome, because of this method emphatically to the relative position but is not to the position

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Matching Shape Numbers Disadvantages : 1. It can not uses for a hollow structure 2. Scaling is a shortcoming which needs to change, perhaps coordinates the alternative means 3. Intensity 4. Mirror problem 5. The color is unable to recognize

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String Matching Suppose that two region boundaries,

a and b, are coded into strings denoted and ,respectively

Let represent the number of matches between the two strings, where a match occurs in the kth position if

max( , )a b

1 2... na a a 1 2.. mb b b

k ka b

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String Matching A simple measure of similarity

between and is the ratio

Hence R is infinite for a perfect match and 0 when none of the corresponding symbols in and match ( in this case)

max( , )R

a b

a b

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String Matching Simple staircase structure. Coded structure.

b b

b

b

b

b

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String Matching Advantages: 1.Matching Shape Numbers suits the processing structure simple graph, specially becomes by the line combination 2.Can solve rotation the question 3.Intensity 4.Mirror problem 5. Matching Shape Numbers most emphatically to the graph outline, Shape similarity also may completely overcome 6. The Displacement question definitely may overcome, because of this method emphatically to the relative position but is not to the position

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String Matching Disadvantages: 1.It can not uses for a hollow structure 2.Scaling 3.The color is unable to recognize

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Syntactic Recognition of Strings String Grammars When dealing with strings, we define a

grammar as the 4-tuple is a finite set of variables called non-

terminals, is a finite set of constants called

terminals, is a set of rewriting rules called

productions, in is called the starting symbol.

( , , , )G N P S N

P

S N

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Syntactic Recognition of Strings String Grammars Object represented by its skeleton primitives. structure generated by using a

regular string grammar

a cb

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Syntactic Recognition of Strings String Grammars Advantages: 1.This method may use to a more complex structure 2.It is a good method for character set Disadvantages: 1.Scaling 2.Rotation 3.The color is unable to recognize 4.Intensity 5.Mirror problem

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Syntactic Recognition of Tree Grammars

A tree grammar is defined as the 5-tuple and are sets of non-terminals and

terminals, respectively is the start symbol, which in general can be

a tree is a set of productions of the form ,

where and are trees is a ranking function that denotes the

number of direct descendants(offspring) of a node whose label is a terminal in the grammar

( , , , , )G N P r S

N

S

P i jT T

iT jTr

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Of particular relevance to our discussion are expansive tree grammars having productions of the form

where are not terminals and k is a terminal

1 2,, ..., nX X X

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An object Primitives used for representing the

skeleton by means of a tree grammar


a b c d e

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For example

a b c d e

1

(1)

S a

X

1

1

(2)

X b

X

1

2 3

(3)

X c

X X

2

2

(4)

X d

X

2(5)X a

3

3

(6)

X e

X

3(7)X a

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Advantages: 1. This method may use to a more complex structure 2. It is a good method for character set 3. The Displacement question definitely may overcome, because of this method emphatically to the relative position but is not to the position

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Disadvantages : 1. Scaling is a shortcoming which needs to change, perhaps coordinates the alternative means 2. Rotation 3. The color is unable to recognize 4. Intensity

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Conclusions The graph recognizes is covers the domain very

widespread science, in the past dozens of years, all kinds of method is unceasingly excavated, also acts according to all kinds of probability statistical model and the practical application model but unceasingly improves.

The graph recognizes applies to each different application domain, actually often also simultaneously entrusts with the entire wrap to recognize the system different appearance, which methods thus we certainly are unable to define to are "best" the graph recognize the method.

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Conclusions Summary the seven approach to pattern recognition,

each methods has advantages and disadvantages respectively. Therefore, we have to understand each method preciously. Then we choose the adaptable method for efficiency and accuracy.

The A method has obtained extremely good recognizing rate in some application and is unable to express the similar method applies mechanically in another application also can similarly obtain extremely good recognizing rate.

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Conclusions Below provides several possibilities

solutions the method 1. Scaling problem we may the reference area solve. 2. Neural networks solves for rotation problem. 3.The color question besides uses RBG to solve also may

use the spectrum to recognize differently. 4. Doing correlation with the reverse match filter for

Intensity mirror problem 5. We can use the measure of area for a hollow structure

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References [1] R. C. Gonzolez, R. E. Woods, "Digital Image

Processing, Second Edition", Prentice Hall 2002 [2] 蒙以正 , " 數位信號處理應用 Matlab", 旗標 2005 [3] S. Theodoridis, K. koutroumbas, "Pattern

Recognition", Academic Press 1999 [4] W. K. Pratt ,"Digital Image Processing, Third

Edition", John Wiley & Sons 2001 [5] R. C. Gonzolez, R. E. Woods, S. L. Eddins, "Digital

Image Processing Using MATLAB", Prentice Hall 2005 [6] 繆紹綱 , 數位影像處理活用 -Matlab, 全華 2000 [7] J. Schurmann, " A Unified View of Statistical and

Neural Approaches" Pattern Classification, Chap4, John Wiley & Sons, Inc., 1996

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References [8]K. Fukunaga, “Introduction to Statistical Pattern

Recognition”, Second Edition, Academic Press, Inc.,1990 [9] E. Gose, R. Johnsonbaugh, and Steve Jost, "Pattern

recognition and Image Analysis", Prentice Hall Inc., New Jersey, 1996

[10] Robert J. Schalkoff, "Pattern Recognition: Statical, Structural and Neural Approaches", Chap5, John Wiley & Sons, Inc., 1992

[11] J. S. Pan, F. R. Mclnnes, and M. A. Jack, "Fast Clustering Algorithm for Vector Quantization", Pattern Recognition 29, 511-518, 1996

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