Pattern Recognition

- Speaker Wen-Fu Wang
- Advisor Jian-Jiun Ding
- E-mail r96942061_at_ntu.edu.tw
- Graduate Institute of Communication Engineering
- National Taiwan University, Taipei, Taiwan, ROC

Outline

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

Outline

- Syntactic Recognition of Strings String Grammars
- Syntactic recognition of Tree Grammars
- Conclusions

Introduction

- Basic pattern recognition flowchart

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.

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

j1,2,,W (1)

j1,2,,W

(2)

Minimum Distance Classifier

- The smallest distance is equivalent to evaluating

the functions - The decision boundary between classes and for a

minimum distance classifier is

j1,2,,W (3)

j1,2,,W

(4)

Minimum Distance Classifier

- Decision boundary of minimum distance classifier

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.

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

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

for x0,1,2,,M-1,y0,1,2,,N-1

(5)

Matching by Correlation

- Arrangement for obtaining the correlation of

and at point

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

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

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

Optimum statistical classifiers

- From basic probability theory, we know that

Optimum statistical classifiers

- Thus the Bayes classifier assigns an unknown

pattern x to class

Optimum statistical classifiers

- The Bayes classifier then assigns a pattern x to

class if, - or, equivalently, if

Optimum statistical classifiers

- Bayes Classifier for Gaussian Pattern Classes
- Let us consider a 1-D problem (n1) involving two

pattern classes (W2) governed by Gaussian

densities

Optimum statistical classifiers

- In the n-dimensional case, the Gaussian density

of the vectors in the jth pattern class has the

form

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

Matching Shape Numbers

- Direction numbers for 4-directional chain code,

and 8-directional chain code

Matching Shape Numbers

- Digital boundary with resampling grid

superimposed

Matching Shape Numbers

- All shapes of order 4, 6,and 8

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

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

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

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)

String Matching

- Simple staircase structure.
- Coded structure.

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

String Matching

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

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.

Syntactic Recognition of Strings String Grammars

- Object represented by its skeleton
- primitives.
- structure generated by using a regular string

grammar

b

a

c

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

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

Syntactic Recognition of Tree Grammars

- Of particular relevance to our discussion are

expansive tree grammars having productions of the

form - where are not terminals and k is a

terminal

Syntactic Recognition of Tree Grammars

- An object
- Primitives used for representing the skeleton by

means of a tree grammar

b

c

e

a

d

Syntactic Recognition of Tree Grammars

- For example

c

a

b

d

e

Syntactic Recognition of Tree Grammars

- 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

Syntactic Recognition of Tree Grammars

- 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

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.

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.

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

References

- 1 R. C. Gonzolez, R. E. Woods, "Digital Image

Processing, Second Edition", Prentice Hall 2002 - 2 ???, "????????Matlab",?? 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 ???, ?????? ??-Matlab, ??2000
- 7 J. Schurmann, " A Unified View of Statistical

and Neural Approaches" Pattern Classification,

Chap4, John Wiley Sons, Inc., 1996

References

- 8K. 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