Chapter 12 Object Recognition - SJTUbcmi.sjtu.edu.cn/~luhongtao/dip/res/Chapter12.pdf · Patterns...
Transcript of Chapter 12 Object Recognition - SJTUbcmi.sjtu.edu.cn/~luhongtao/dip/res/Chapter12.pdf · Patterns...
Digital Image Processing, 2nd ed.Digital Image Processing, 2nd ed.www.imageprocessingbook.com
© 2002 R. C. Gonzalez & R. E. Woods
Chapter 12Object Recognition
Chapter 12Object Recognition
Digital Image Processing, 2nd ed.Digital Image Processing, 2nd ed.www.imageprocessingbook.com
© 2002 R. C. Gonzalez & R. E. Woods
Patterns and Pattern Classes
• A pattern is an arrangement of descriptors, such as those discussed in Chapter 11.
• The name feature is used often in the pattern recognition literature to denote a descriptor.
• A pattern class is a family of patterns that share some common properties.
Digital Image Processing, 2nd ed.Digital Image Processing, 2nd ed.www.imageprocessingbook.com
© 2002 R. C. Gonzalez & R. E. Woods
Chapter 12Object Recognition
Chapter 12Object Recognition
Digital Image Processing, 2nd ed.Digital Image Processing, 2nd ed.www.imageprocessingbook.com
© 2002 R. C. Gonzalez & R. E. Woods
Chapter 12Object Recognition
Chapter 12Object Recognition
Digital Image Processing, 2nd ed.Digital Image Processing, 2nd ed.www.imageprocessingbook.com
© 2002 R. C. Gonzalez & R. E. Woods
Chapter 12Object Recognition
Chapter 12Object Recognition
Digital Image Processing, 2nd ed.Digital Image Processing, 2nd ed.www.imageprocessingbook.com
© 2002 R. C. Gonzalez & R. E. Woods
Chapter 12Object Recognition
Chapter 12Object Recognition
Digital Image Processing, 2nd ed.Digital Image Processing, 2nd ed.www.imageprocessingbook.com
© 2002 R. C. Gonzalez & R. E. Woods
Recognition Based on Decision-Theoretic Methods
• In other words, an unknown pattern x is said to belong to the ith pattern class if, upon substitution of x into all decision functions,
yields the largest numerical value.
( )( ) ( ) ijWjxdxd
xxxx
ji
Tn
≠=>=
;,...,2,1 ,,, classespattern for W ,,,Let W2121 ωωω KK
( )xdi
Digital Image Processing, 2nd ed.Digital Image Processing, 2nd ed.www.imageprocessingbook.com
© 2002 R. C. Gonzalez & R. E. Woods
MatchingMinimum distance classifier
• Suppose that we define the prototype of each pattern class to be the mean vector of the patterns of that class:
• We then assign x to class ωi if Di(x) is the smallest distance.
WjxN
mjx
jj
j ,,2,1 1K== ∑
∈ω
( ) jj mxxD −=
Digital Image Processing, 2nd ed.Digital Image Processing, 2nd ed.www.imageprocessingbook.com
© 2002 R. C. Gonzalez & R. E. Woods
Minimum distance classifier
• It is not difficult to show (Problem 12.2) that selecting the smallest distance is equivalent to evaluating the functions
• assign x to class ωi if di(x) is the largest numerical value.
• This formulation agrees with the concept of a decision function, as defined in Eq. (12.2-1).
( ) Wjmmmxxd jTjj
Tj ,...,2,1
21
=−=
Digital Image Processing, 2nd ed.Digital Image Processing, 2nd ed.www.imageprocessingbook.com
© 2002 R. C. Gonzalez & R. E. Woods
Chapter 12Object Recognition
Chapter 12Object Recognition
Digital Image Processing, 2nd ed.Digital Image Processing, 2nd ed.www.imageprocessingbook.com
© 2002 R. C. Gonzalez & R. E. Woods
Chapter 12Object Recognition
Chapter 12Object Recognition
Digital Image Processing, 2nd ed.Digital Image Processing, 2nd ed.www.imageprocessingbook.com
© 2002 R. C. Gonzalez & R. E. Woods
Matching by correlation
• correlation coefficient, which is defined as( ) ( ) ( )∑∑ ++=
s ttysxwtsfyxc ,,,
( )( ) ( )[ ] ( )[ ]
( ) ( )[ ] ( )[ ] 21
22,,,
,,,,
⎭⎬⎫
⎩⎨⎧
−++−
−++−=
∑∑∑∑
∑∑
s ts t
s t
wtysxwtsftsf
wtysxwtsftsfyxγ
Digital Image Processing, 2nd ed.Digital Image Processing, 2nd ed.www.imageprocessingbook.com
© 2002 R. C. Gonzalez & R. E. Woods
Chapter 12Object Recognition
Chapter 12Object Recognition
Digital Image Processing, 2nd ed.Digital Image Processing, 2nd ed.www.imageprocessingbook.com
© 2002 R. C. Gonzalez & R. E. Woods
Chapter 12Object Recognition
Chapter 12Object Recognition
Digital Image Processing, 2nd ed.Digital Image Processing, 2nd ed.www.imageprocessingbook.com
© 2002 R. C. Gonzalez & R. E. Woods
Optimum Statistical Classifiers
• the equation often called the conditional average risk or loss in decision-theory terminology.
• The classifier that minimizes the total average loss is called the Bayes classifier.
• Thus the Bayes classifier assigns an unknown pattern x to class ωi ifin other words, x is assigned to class ωi if
( ) ( )∑=
=W
kkkjj xpLxr
1/ω
( ) ( ) ijWjforxrxr ji ≠=< ;,...,2,1
( ) ( ) ( ) ( )q
W
qqqjk
W
kkki PxpLPxpL ωωωω ∑∑
==
<11
//
Digital Image Processing, 2nd ed.Digital Image Processing, 2nd ed.www.imageprocessingbook.com
© 2002 R. C. Gonzalez & R. E. Woods
Bayes classifier for Gaussian pattern classes
( ) ( ) ( )( )
( ) 2,1 2
1/2
2
2 ===−
−
jPePxpxd j
mx
jjjj
j
j
ωσπ
ωω σ
( )( )
( ) ( )jjT
j mxCmx
n
jnj e
Cxp
−−− −
=1
21
222
1/π
ω { }xEm jj =
( )( ){ }Tjjjj mxmxEC −−= ∑
∈
−=jx
Tjj
T
jj mmxx
NC
ω
1
Bayes decision function for class ( ) ( ) ( )jjjj Pxpxd ωωω / is =
( ) ( ) jTjj
Tjj mCmmCxPxd 11
21ln −− −+= ω
Digital Image Processing, 2nd ed.Digital Image Processing, 2nd ed.www.imageprocessingbook.com
© 2002 R. C. Gonzalez & R. E. Woods
Chapter 12Object Recognition
Chapter 12Object Recognition
Digital Image Processing, 2nd ed.Digital Image Processing, 2nd ed.www.imageprocessingbook.com
© 2002 R. C. Gonzalez & R. E. Woods
Chapter 12Object Recognition
Chapter 12Object Recognition
Digital Image Processing, 2nd ed.Digital Image Processing, 2nd ed.www.imageprocessingbook.com
© 2002 R. C. Gonzalez & R. E. Woods
Chapter 12Object Recognition
Chapter 12Object Recognition
Digital Image Processing, 2nd ed.Digital Image Processing, 2nd ed.www.imageprocessingbook.com
© 2002 R. C. Gonzalez & R. E. Woods
Chapter 12Object Recognition
Chapter 12Object Recognition
Digital Image Processing, 2nd ed.Digital Image Processing, 2nd ed.www.imageprocessingbook.com
© 2002 R. C. Gonzalez & R. E. Woods
Neural Network
( ) ( ) ( )( )kwww
wJkwkw=
⎥⎦⎤
⎢⎣⎡∂
∂−=+ α1
Digital Image Processing, 2nd ed.Digital Image Processing, 2nd ed.www.imageprocessingbook.com
© 2002 R. C. Gonzalez & R. E. Woods
Chapter 12Object Recognition
Chapter 12Object Recognition
Digital Image Processing, 2nd ed.Digital Image Processing, 2nd ed.www.imageprocessingbook.com
© 2002 R. C. Gonzalez & R. E. Woods
Chapter 12Object Recognition
Chapter 12Object Recognition
Digital Image Processing, 2nd ed.Digital Image Processing, 2nd ed.www.imageprocessingbook.com
© 2002 R. C. Gonzalez & R. E. Woods
Chapter 12Object Recognition
Chapter 12Object Recognition
Digital Image Processing, 2nd ed.Digital Image Processing, 2nd ed.www.imageprocessingbook.com
© 2002 R. C. Gonzalez & R. E. Woods
Chapter 12Object Recognition
Chapter 12Object Recognition
Digital Image Processing, 2nd ed.Digital Image Processing, 2nd ed.www.imageprocessingbook.com
© 2002 R. C. Gonzalez & R. E. Woods
Chapter 12Object Recognition
Chapter 12Object Recognition
Digital Image Processing, 2nd ed.Digital Image Processing, 2nd ed.www.imageprocessingbook.com
© 2002 R. C. Gonzalez & R. E. Woods
Chapter 12Object Recognition
Chapter 12Object Recognition
Digital Image Processing, 2nd ed.Digital Image Processing, 2nd ed.www.imageprocessingbook.com
© 2002 R. C. Gonzalez & R. E. Woods
Chapter 12Object Recognition
Chapter 12Object Recognition
Digital Image Processing, 2nd ed.Digital Image Processing, 2nd ed.www.imageprocessingbook.com
© 2002 R. C. Gonzalez & R. E. Woods
Chapter 12Object Recognition
Chapter 12Object Recognition
Digital Image Processing, 2nd ed.Digital Image Processing, 2nd ed.www.imageprocessingbook.com
© 2002 R. C. Gonzalez & R. E. Woods
Chapter 12Object Recognition
Chapter 12Object Recognition
Digital Image Processing, 2nd ed.Digital Image Processing, 2nd ed.www.imageprocessingbook.com
© 2002 R. C. Gonzalez & R. E. Woods
Chapter 12Object Recognition
Chapter 12Object Recognition
Digital Image Processing, 2nd ed.Digital Image Processing, 2nd ed.www.imageprocessingbook.com
© 2002 R. C. Gonzalez & R. E. Woods
Structural Method
Digital Image Processing, 2nd ed.Digital Image Processing, 2nd ed.www.imageprocessingbook.com
© 2002 R. C. Gonzalez & R. E. Woods
Chapter 12Object Recognition
Chapter 12Object Recognition
Digital Image Processing, 2nd ed.Digital Image Processing, 2nd ed.www.imageprocessingbook.com
© 2002 R. C. Gonzalez & R. E. Woods
String Matching
Digital Image Processing, 2nd ed.Digital Image Processing, 2nd ed.www.imageprocessingbook.com
© 2002 R. C. Gonzalez & R. E. Woods
Chapter 12Object Recognition
Chapter 12Object Recognition
Digital Image Processing, 2nd ed.Digital Image Processing, 2nd ed.www.imageprocessingbook.com
© 2002 R. C. Gonzalez & R. E. Woods
Chapter 12Object Recognition
Chapter 12Object Recognition
Digital Image Processing, 2nd ed.Digital Image Processing, 2nd ed.www.imageprocessingbook.com
© 2002 R. C. Gonzalez & R. E. Woods
Chapter 12Object Recognition
Chapter 12Object Recognition
Digital Image Processing, 2nd ed.Digital Image Processing, 2nd ed.www.imageprocessingbook.com
© 2002 R. C. Gonzalez & R. E. Woods
Automatic as string recognizers
Digital Image Processing, 2nd ed.Digital Image Processing, 2nd ed.www.imageprocessingbook.com
© 2002 R. C. Gonzalez & R. E. Woods
Chapter 12Object Recognition
Chapter 12Object Recognition
Digital Image Processing, 2nd ed.Digital Image Processing, 2nd ed.www.imageprocessingbook.com
© 2002 R. C. Gonzalez & R. E. Woods
Syntactic Recognition of Trees
Digital Image Processing, 2nd ed.Digital Image Processing, 2nd ed.www.imageprocessingbook.com
© 2002 R. C. Gonzalez & R. E. Woods
Chapter 12Object Recognition
Chapter 12Object Recognition
Digital Image Processing, 2nd ed.Digital Image Processing, 2nd ed.www.imageprocessingbook.com
© 2002 R. C. Gonzalez & R. E. Woods
Chapter 12Object Recognition
Chapter 12Object Recognition
Digital Image Processing, 2nd ed.Digital Image Processing, 2nd ed.www.imageprocessingbook.com
© 2002 R. C. Gonzalez & R. E. Woods
Chapter 12Object Recognition
Chapter 12Object Recognition
Digital Image Processing, 2nd ed.Digital Image Processing, 2nd ed.www.imageprocessingbook.com
© 2002 R. C. Gonzalez & R. E. Woods
Chapter 12Object Recognition
Chapter 12Object Recognition
Digital Image Processing, 2nd ed.Digital Image Processing, 2nd ed.www.imageprocessingbook.com
© 2002 R. C. Gonzalez & R. E. Woods
Chapter 12Object Recognition
Chapter 12Object Recognition
Digital Image Processing, 2nd ed.Digital Image Processing, 2nd ed.www.imageprocessingbook.com
© 2002 R. C. Gonzalez & R. E. Woods
Chapter 12Object Recognition
Chapter 12Object Recognition
Digital Image Processing, 2nd ed.Digital Image Processing, 2nd ed.www.imageprocessingbook.com
© 2002 R. C. Gonzalez & R. E. Woods
Chapter 12Object Recognition
Chapter 12Object Recognition