Post on 03-Aug-2020
transcript
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Face processing and detection using Artificial Neural Networks
and Image Processing
Michel PAINDAVOINE, Fan YANG
paindav@u-bourgogne.fr
fanyang@u-bourgogne.fr
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Outline1. - Introduction to neural networks
Neural networks learningPerceptron and Adaline networks
5. - Autoassociative memory Principal Components AnalysisWavelet Transform and Face recognition
9. - Multi-Layer Perceptron Back-Propagation learning rule
Face identification
12. - Radial Basis Function neural networkUnsupervised training techniqueFace detection and identification in video sequences
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1. Introduction to neural networks
Schematic of a biological neuron and an artificial neuron
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Hebbian learning rule : If two neurons i and j are active simultaneously, their interconnection must be strengthened.
aaw jiij η=∆
1.1 Perceptron
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1.2 Adaptive linear element : Adaline network
∑=
=I
iiijj xwo
0
Widrow-Hoff learning (delta) rule : Minimize the summed square error function by gradient descent method in order to adjust the weight.
xotw ijjij )( −=∆ η
tj : target response of the jth neuron
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1.3 An example of pattern recognition
We want to recognize the follow numbers patterns 0 - 9 :
The purpose is to associate each pattern with its class corresponding to :
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1.3 An example of pattern recognition
The matrix of weights is initiated with values chosen randomly. The number pattern 0,1, …9 are presented to input units and the responses of the output units are calculated with :
)()(14
0xwfafo i
iijjj ∑==
=
Initially, the total error E of incorrect classification is : Error = 54%
The Widrow-Hoff learning rule is applied to modify the weights.
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1.3 An example of pattern recognition
After 51 iteratios, the final matrix of weight is obtained.
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1.3 An example of pattern recognition
A perfect pattern of number 8 is correctly categorized
A nearly perfect pattern of number 8 is correctly categorized
A imperfect pattern of number 8 is not correctly categorized
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2. Auto-associative memory Single layer network made of fully interconnected linear units,
Content addressable memory,
Able to retrieve a whole pattern of information given one part of this information.
An auto-associative memory composed of 5 fully interconnected units.
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2.1 Auto-associative memory and Face recognition
The linear auto-associator is applied to images : transform each digitized image into a vector by concatening the column of the matrix of the pixel values of the image.
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2.1 Auto-associative memory and Face recognition
Illustration of a content addressable memory for faces : the auto-associative memory is able to reconstruct a face from an incomplete input (top).
Illustration of a content addressable memory for faces : the auto-associative memory is able to reconstruct a face from an noise degraded input (left).
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2.2 Wavelet transform and Face recognition
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2.2 Wavelet transform and Face recognition
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2.2 Wavelet transform and Face recognition
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2.2 Wavelet transform and Face recognition
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2.3 Auto-associative memory and PCA
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2.3 Auto-associative memory and PCA
XWWW TTt
Tt
Tt XT )( )()()1( −+=+ η
UW Tt
Tt U Φ ++ = )1()1( ][ )( )1(
)1( Λ−Φ+
+ −= ηI t
t I
H.ABDI developed a simple method of implementing the Widrow-Hoff algorithm by using the eigen-decomposition of the synapse matrix W
This decomposition give rise to Principal Components Analysis (PCA).
X is the stimuli matrix of auto-associator, U is the matrix of eigenvectors (Principal components) of XXT,
Λ is the matrix of eigenvalues of XXT.
UW TU=∞)(
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2.4 Non linear separable problems
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3. Multi-layer neural networks
Can overcome many restrictions : solve non linear separable problems
Universal approximator
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3.1 Generalized Widrow-Hoff rule : Back-propagation learning rule
hz ljlj δη=∆ )(')( aot jjjj f−=δ
xw ilil δη=∆
Principle : Back-propagate the error signal from the output layer to hidden layers
)('1
az llj
J
jjl f∑
=
= δδ
From input layer to hidden layer : connection matrix W :
From hidden layer to output layer : connection matrix Z :
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3.1 Generalized Widrow-Hoff rule : Back-propagation learning rule
e xxf −+=
11)(The sigmoid (logistic) function :
)](1)[()(' xfxfxf −=Interesting property :
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3.2 Face identification using the MLP
PCA
Datacompress
MLP Identity
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3.2 Face identification using the MLP
??? Non recognized
Guylaine, Christine, …
Daniel, Bernard, Elbay, …
Patterns for network training
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Input x Hidden nodes
Output)(xf i
js
Iii ......1=Jjj ......1=
jip
J classesInput vector of N
dimension
4. Radial Basis Function (RBF) network
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1x
2x
3x
Nx
nx),( iic σ
2
2
2)(
)( i
xd
i exf σ−
=
4.1 Principle of RBF neural network
Hidden nodes :
iC≡0 1 2 3 41−2−3−4−
2.0
4.0
6.0
8.0
1
2.1
iσ
( )xfi
x
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4.1 Principle of RBF neural network
)(1 xf
)(2 xf
)(3 xf
)(xf I
)(xf i
jp1
jp2
jp3
jip
jIp
∑=
⋅=I
iiij xfpS
j1
)(
2.0
4.0
6.0
8.0
0
5 10 15 205−10−15−20− 0
Output units :
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4.1 Principle of RBF neural networkUn-supervised training technique : Clustering
kc
lcic
iσkc
kσ kσiclciσ
kckσ
lckσ
kc
lckσ
ic kcic
lc
ickσ
kσ
kclc kσ
ic
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Face detection (or localization) :
Faces identification :
Where ?!
Who ?!
1x 2x
1y
2y
Mr. Y
~~~~~
~~~~~
4.2 Faces detection and identification using RBF
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face
or
non face?
non face !
Face !Mr. X
?person recognized
or non recognized ?
Classic process
Face images Processing
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Used process
person recognized or
non recognized ?
Mr. X
?
?
Proposed method(based on mapping Algo./Archi. Approach)
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Extraction of input vectors
Detection and identification by
RBF network
1=e3
2=e9
4=e27
8=e
Pre-processing
Face detection and identification process :
4.2 Faces detection and identification using RBF
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4.3 Experiments and Results
Variation of the input vector lengths
87,5%551701796801 pix./8 on row1 pix./2 on col.
87,1%601701796801 pix./16 on each row
93,3%012017961601 pix./8 on each row
95,8%07617963201 pix./4 on each row
92,2%014017961280Original window (40x32)
Correct results
Incorrect reco.Non reco. Nb. facesNumber
componentsSub sampling
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Variation of used mesured distances
96,4%0641796320d1(x)
95,8%0761796320d2(x)
Correctresults
Incorrectreco.
Non reco.Nb. facesNumber componentsDistance
∑=
−=N
nnn cxxd
11 )(( )∑
=−=
N
nnn cxxd
1
22 )(
4.3 Experiments and Results
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Variation of RBF kernel activation functions
92%01181796320Heaviside
96,4%0321796320Gaussian
Correct results
Incorrectreco.
Non reco.Nb. facesNumber
componentsFonction
4.3 Experiments and Results
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4.3 Faces detection and identification using RBF
Experimental results for one scale :
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6. Conclusion/Perspectives
Neural networks :
are efficient tools for pattern recognition
facilitate hardware implementations by massive parallel
Features extraction to few neural networks
Image processing