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## Pattern Recognition

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### Pattern Recognition Speaker: Wen-Fu Wang Advisor: Jian-Jiun Ding E-mail: r96942061_at_ntu.edu.tw Graduate Institute of Communication Engineering National Taiwan ... – PowerPoint PPT presentation

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Title: Pattern Recognition

1
Pattern Recognition
• Speaker Wen-Fu Wang
• 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
• 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
• 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
• 1.Fast
• 2.Convenient
• 3.Displacement
• 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
• 1. The way always combine with other
• methods, then it got high accuracy
• 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
• 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
• 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
• 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
• 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
• 1.This method may use to a more
• complex structure
• 2.It is a good method for character set
• 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
• 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
• 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
• 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