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Face Recognition Using Fuzzy Fisherface Classifier
Presenters:Nilesh PadwalVivek K.Rajat Rastogi
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Contents
Fuzzy Fisherface AppproachAlgorithmFlowchartYale DatabaseORL DatabaseComparison of Recognition RatesConclusionReferences
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Fuzzy Fisherface Approach
More sophisticated usage of class assignment of patterns (faces)
Classification results affect the within-class and between-class scatter matrices
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The Computations Of Membership Degrees
Compute the membership grade to class for pattern ,
0.51 0.49( / ) if same as the label of the pattern
0.49( / ) if same as the label of the patternij
ij
n k i jth
n k i jth
+ =⎧⎪⎨ ≠⎪⎩
i jth
where is number of the neighbors of theijnjth data that belong to ith class
ijµ
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AlgorithmResults of FKNN are used in computations of mean value and scatter covariance matrices,Mean vector of each class
The between class and within class fuzzy scatter matrices are respectively,
~1
1
N
i j jj
i N
i jj
Xm
µ
µ
=
=
=∑
∑
~ ~
1
~ ~
1 1
( )( )
( )( )i
k i
cT
i iFB ii
c cT
i iFW k k FWi x C i
S N m m m m
S x m x m S
=
= ∈ =
= − −
= − − =
∑
∑ ∑ ∑
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AlgorithmThe optimal fuzzy projection WF-FLD and feature vector transformed by fuzzy fisherfacemethod are given by
~
arg max
( )
TFB
F FLD TWFB
T T Ti F FLD i F FLD i
W S WW
W S W
v W X W E z z
−
− −
=
= = −
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Flowchart
courtesy:Source [1]
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Yale DatabaseTotal Images- 165, total Classes- 15 (11 Images For Each Class) One Image for each configuration: Center-light, glasses/no glasses, happy, normal, left/right light, sad, sleepy, surprised, wink.
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Yale Database
Mugshots were acquired using digicam,Each image was digitized and presented by a 243 X 320 pixel array
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ORL DatabaseTotal Images: 400, total classes: 40 (10 Images for each class)Mugshots were acquired using DigiCam, varying facial detailsEach image was digitized and presented by a 112 X 92 pixel array
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Comparison of Mean Recognition Rates (Yale)
93.8791.9470.85Case 3
(5-training,6-testing)
96.2496.0471.66Case 2
(7-training,4-testing)
94.293.472.44Case 1
(6-training,5-testing)
Fuzzy Fisherface(Fuzzy+PCA+LDA) (%)
Fisherface(PCA+LDA)(%)
Eigenface (PCA)(%)
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Comparison of Mean For Recognition Rates (ORL)
93.5093.3886.94Case 3
(4-training,6-testing)
95.594.7591.13Case 2
(5-training,5-testing)
97.1295.5990.94Case 1
(6-training,4-testing)
Fuzzy Fisherface(Fuzzy+PCA+LDA)
(%)
Fisherface(PCA+LDA)(%)
Eigenface (PCA)(%)
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Comparison of Recognition Rate For Yale Database
0
20
40
60
80
100
Case 1 Case 2 Case 3
EigenfaceFisherfaceFuzzy-Fisherface
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Comparison of Recognition Rate For ORL Database
80828486889092949698
Case 1 Case 2 Case 3
EigenfaceFisherfaceFuzzy-Fisherface
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Confusion Matrix (Yale)Case 2(7/4)
Fisherface Fuzzy Fisherface
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Comparison
Fisherface
Fuzzy Fisherface
Eigenface
Input Image Matched Image
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Comparison
Fisherface
Fuzzy Fisherface
Eigenface
Input Image Matched Image
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Comparison
Fisherface
Fuzzy Fisherface
Eigenface
Input Image Matched Image
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ConclusionFuzzy fisherface approach outperforms the other two methods for the datasets considered.
Sensitive to variations in illumination and facial expression reduced substantially.
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ReferencesKeun-Chang Kwak, Witold Pedrycz : Face Recognition Using Fuzzy Fisherface Classifier, Journal of Pattern Recognition 38(2005),1717-1732Turk, M., Pentland, A.: Eignefaces for Recognition. Journal of Cognitive Neuroscience, Vol.3, (1991) 72-86Turk, M., Pentland, A.: Face Recognition Using Eignefaces. In Proc. IEEE Conf. On Computer Vision and Pattern Recognition. (1991) 586-591Belhumeur, P., Hespanha, J., Kriegman, D.: Eigenfacesvs. Fisherfaces: Face Recognition using class specific linear projection. In Proc. ECCV, (1996) 45-58Yale Face Database, http://cvc.yale.edu/projects/yalefaces/yalefaces.htmlORL Face Database, http://www.uk.research.att.com/facedatabase.html
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Thank You