Robust Face Detection and Recognition

							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.: Quadratic Classifier Linear Classifier
     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)




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                                       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




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                                TSWG:Robust Face Detection and Recognition