Pattern Recognition

1
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

2
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

4
Introduction

• Basic pattern recognition flowchart

5
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.

6
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)
7
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)
8
Minimum Distance Classifier

• Decision boundary of minimum distance classifier

9
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.

10
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

11
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)
12
Matching by Correlation

• Arrangement for obtaining the correlation of
  and at point

13
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

14
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

15
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

16
Optimum statistical classifiers

• From basic probability theory, we know that

17
Optimum statistical classifiers

• Thus the Bayes classifier assigns an unknown
  pattern x to class

18
Optimum statistical classifiers

• The Bayes classifier then assigns a pattern x to
  class if,
• or, equivalently, if

19
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

20
Optimum statistical classifiers

• In the n-dimensional case, the Gaussian density
  of the vectors in the jth pattern class has the
  form

21
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

22
Matching Shape Numbers

• Direction numbers for 4-directional chain code,
  and 8-directional chain code

23
Matching Shape Numbers

• Digital boundary with resampling grid
  superimposed

24
Matching Shape Numbers

• All shapes of order 4, 6,and 8

25
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

26
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

27
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

28
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)

29
String Matching

• Simple staircase structure.
• Coded structure.

30
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

31
String Matching

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

32
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.

33
Syntactic Recognition of Strings String Grammars

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

b
a
c
34
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

35
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

36
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

37
Syntactic Recognition of Tree Grammars

• An object
• Primitives used for representing the skeleton by
  means of a tree grammar

b
c
e
a
d

38
Syntactic Recognition of Tree Grammars

• For example

c
a
b
d
e



39
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

40
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

41
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.

42
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.
  

43
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

44
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

45
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