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Pattern Recognition

Pattern Recognition. Speaker: Wen-Fu Wang Advisor: Jian-Jiun Ding E-mail: r96942061@ntu.edu.tw Graduate Institute of Communication Engineering National Taiwan University, Taipei, Taiwan, ROC. Outline. Introduction Minimum Distance Classifier Matching by Correlation

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Pattern Recognition

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  1. Pattern Recognition • Speaker: Wen-Fu Wang • Advisor: Jian-Jiun Ding • E-mail: r96942061@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. Sensor Feature generation Feature selection Classifier design System evaluation 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 j=1,2,…,W(1) j=1,2,…,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 j=1,2,…,W(3) j=1,2,…,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 x=0,1,2,…,M-1,y=0,1,2,…,N-1(5)

  12. Origin K J o M 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 (n=1) involving two pattern classes (W=2) 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. 1 2 3 1 0 4 0 2 7 5 6 3 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. Order6 Order4 Chain code: 0321 Difference : 3333 Shape no. : 3333 Chain code: 003221 Difference : 303303 Shape no. : 033033 Order8 Chain code: 00332211 Difference : 30303030 Shape no. : 03030303 Chain code:03032211 Difference :33133030 Shape no. :03033133 Chain code: 00032221 Difference : 30033003 Shape no. : 00330033 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. b b b b b b 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 c e b a d

  38. Syntactic Recognition of Tree Grammars • For example c e b a d

  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] 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

  45. 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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