# Robust Face Detection and Recognition by a3087a8a7400e297

VIEWS: 49 PAGES: 14

• pg 1
```									Robust Face Detection and Recognition
Based on Dimensionality-Increasing
Techniques

Chengjun Liu
Computer Science Department
New Jersey Institute of Technology
Liu@cs.njit.edu
http://www.cs.njit.edu/~liu

1
TSWG:Robust Face Detection and Recognition
Overview
■ Face Detection
BDF – Bayesian Discriminating Features Method
BDF-SVM in Video using Motion, BDF, SVM
■ Face Recognition
Kernel Methods with Fractional Power Polynomial (FPP) Models
Face Recognition Grand Challenge (FRGC) Performance

2
TSWG:Robust Face Detection and Recognition
Bayesian Discriminating Features Method
■ DFA – Discriminating Feature Analysis
Input Image
1-D Harr Wavelet Representation
The Amplitude Projections
■ Face and Nonface Class Modeling

M 2        Y − M f − ∑ iM1 zi2
2

∑ +   zi                    =

+
1  i =1 λi            ρ                   
ln  p (Y | ω f )  = − 
                                                             
2  M                                    
 ln  ∏ λi  + ( N − M )ln ρ + Nln(2π ) 
  i =1                                

3
TSWG:Robust Face Detection and Recognition
Bayesian Discriminating Features Method
■ Bayesian Face Detection

ω f
                     if (δ f < θ ) and (δ f + τ < δ n )
Y∈
ω n
                     otherwise

− ∑ iM1 zi2
2
M
z 2          Y−Mf                            M 
δf =∑                                               + ln  ∏ λi  + ( N − M )ln ρ
=
i
+
i =1    λi                  ρ                        i =1 

Y − M n − ∑ iM1 ui2
2
M
ui2                                          M (n) 
δn = ∑                +                =
+ ln  ∏ λi  + ( N − M )lnε
i =1    λi( n )                  ε                    i =1  

P (ω n )
τ = 2ln
P (ω f )

4
TSWG:Robust Face Detection and Recognition
BDF-SVM Face Detection in Video
■ BDF-SVM – FaceDT in Video using Motion, Color, DFA
SVM – Support Vector Machine

Statistical Learning Theory (SLT) and Structural Risk Minimization (SRM)
5
TSWG:Robust Face Detection and Recognition
BDF-SVM Face Detection in Video
■ BDF-SVM – FaceDT in Video using Motion, Color, DFA
SVM – Support Vector Machine
e.g.: Kernel Function: k ( x, y ) = ( x ⋅ y + 1)
d

 x1 
 M 
        
 x1 
 x1            2 
x              x1 
Rn → F : x =  2  → Φ( x) =  M 
M              2 
               xn 
 xn            x1 x2 
        
   M 
x x 
 n −1 n 
Nonlinear Mapping from Input Space to Feature Space
6
TSWG:Robust Face Detection and Recognition
BDF-SVM Face Detection in Video
■ BDF-SVM – FaceDT in Video using Motion, Color, DFA
SVM – Support Vector Machine

The Optimal (Maximal Margin) Hyperplane in Feature Space
7
TSWG:Robust Face Detection and Recognition
Kernel Methods with FPP Models
■ FPP – Kernel Methods with Fractional Power Polynomial
Models
Kernel Methods
Motivations – Cover’s Theorem on the separability of patterns:
Nonlinearly separable patterns in an input space are linearly separable
with high probability if the input space is transformed nonlinearly to a
high dimensional feature space.
 x1 
 M 
        
 x1 
 x1            2 
x              x1 
Rn → F : x =  2  → Φ( x) =  M 
M              2 
 
xn            xn 
                x1 x2 
        
   M 
x x 
 n −1 n 
8
TSWG:Robust Face Detection and Recognition
Kernel Methods with FPP Models
■ FPP – Kernel Methods with FPP Models
Kernel Methods
Kernel Functions – Mercer Condition
Kernel Function
k (x,y) = (Φ(x) ⋅ Φ(y))

Gram Matrix: Given a finite data set X = { X 1 , X 2 ,..., X M } in the
input space and a function k : X × X → R (or C ) , the M x M
matrix K with elements Kij = k ( X i , X j ) is called Gram matrix of
k with respect to X 1 , X 2 ,..., X M .

Mercer Condition: A sufficient and necessary condition for a
symmetric function to be a kernel function is that its Gram matrix
is positive semi-definite.

9
TSWG:Robust Face Detection and Recognition
Kernel Methods with FPP Models
■ FPP – Kernel Methods with FPP Models
Kernel Methods
Kernel Functions – 3 classes of commonly used
Polynomial Kernel Functions

k (x,y) = (x ⋅ y) d

Gaussian (RBF) Kernel Functions
 x−y      2

k (x,y) = exp  −            
   2σ 2       
              
Sigmoid Kernel Functions

(
k (x,y) = tanh κ (x ⋅ y)d + ϑ    )
where d ∈ N , σ > 0, κ > 0, and ϑ < 0
10
TSWG:Robust Face Detection and Recognition
Kernel Methods with FPP Models
■ Experiments – Frontal Faces
Face recognition performance of the kernel PCA method with three FPP
models using the Mahalanobis measure

11
TSWG:Robust Face Detection and Recognition
Kernel Methods with FPP Models
■ Experiments – Frontal Faces
Face recognition performance of the Gabor wavelet based kernel PCA
method with a fractional power polynomial model using the Mahalanobis
measure (99.5% using 246 features for Md_Gabor_0.6)

12
TSWG:Robust Face Detection and Recognition
Kernel Methods with FPP Models
■ Experiments – FaceID across Pose
Face recognition performance of the Gabor wavelet based kernel PCA
method with FPP models using the Mahalanobis measure (95.3% using 64
features for Md_Gabor_0.7)

13
TSWG:Robust Face Detection and Recognition
Face Recognition Grand Challenge (FRGC)
■ Face Recognition Grand Challenge (FRGC) Performance
366 FRGC training images
152 FRGC gallery images
608 FRGC probe images

14
TSWG:Robust Face Detection and Recognition

```
To top