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A f a c e r e c o g n i t i o n a l g o r i t h m b a s e d o n m o d u l a r P C A a p p r o a c h i s p r e s e n t e d i n t h i s p a p e r . T h e p r o p o s e d a l g o r i t h m w h e n c o m p a r e d w i t h c o n v e n t i o n a l P C A a l g o r i t h m h a s a n i m p r o v e d r e c o g n i t i o n r a t e f o r f a c e i m a g e s w i t h l a r g e v a r i a t i o n s i n l i g h t i n g d i r e c t i o n a n d f a c i a l e x p r e s s i o n . I n t h e p r o p o s e d t e c h n i q u e , t h e f a c e i m a g e s a r e d i v i d e d i n t o s m a l l e r s u b - i m a g e s a n d t h e P C A a p p r o a c h i s a p p l i e d t o e a c h o f t h e s e s u b - i m a g e s . S i n c e s o m e o f t h e l o c a l f a c i a l f e a t u r e s o f a n i n d i v i d u a l d o n o t v a r y e v e n w h e n t h e p o s e , l i g h t i n g d i r e c t i o n a n d f a c i a l e x p r e s s i o n v a r y , w e e x p e c t t h e p r o p o s e d m e t h o d t o b e a b l e t o c o p e w i t h t h e s e v a r i a t i o n s . T h e a c c u r a c y o f t h e c o n v e n t i o n a l P C A m e t h o d a n d m o d u l a r P C A m e t h o d a r e e v a l u a t e d u n d e r t h e c o n d i t i o n s o f v a r y i n g e x p r e s s i o n , i l l u m i n a t i o n a n d p o s e u s i n g s t a n d a r d f a c e d a t a b a s e s .
K e y w o r d s : P C A ; F a c e r e c o g n i t i o n ; M o d u l a r P C A ; P o s e i n v a r i a n c e ; I l l u m i n a t i o n i n v a r i a n c e
1 . I n t r o d u c t i o n
F a c e r e c o g n i t i o n i s a d i f f i c u l t p r o b l e m b e c a u s e o f t h e g e n e r a l l y s i m i l a r s h a p e o f f a c e s c o m b i n e d w i t h t h e n u m e r o u s v a r i a t i o n s b e t w e e n i m a g e s o f t h e s a m e f a c e . T h e i m a g e o f a f a c e c h a n g e s w i t h f a c i a l e x p r e s s i o n , a g e , v i e w p o i n t , i l l u m i n a t i o n c o n d i t i o n s , n o i s e e t c . T h e t a s k o f a f a c e r e c o g n i t i o n s y s t e m i s t o r e c o g n i z e a f a c e i n a m a n n e r t h a t i s a s i n d e p e n d e n t a s p o s s i b l e o f t h e s e i m a g e v a r i a t i o n s .
A u t o m a t i c r e c o g n i t i o n o f f a c e s i s c o n s i d e r e d a s o n e o f t h e f u n d a m e n t a l p r o b l e m s i n c o m p u t e r v i s i o n a n d p a t t e r n a n a l y s i s , a n d m a n y s c i e n t i s t s f r o m d i f f e r e n t a r e a s h a v e a d d r e s s e d i t . C h e l l a p p a e t a l . ( 1 9 9 5 ) p r e s e n t e d a s u r v e y o n s e v e r a l s t a t i s t i c a l - b a s e d , n e u r a l n e t w o r k - b a s e d a n d f e a t u r e - b a s e d m e t h o d s f o r f a c e r e c o g n i t i o n . C u r r e n t l y , o n e o f t h e m e t h o d s t h a t y i e l d s p r o m i s i n g r e s u l t s o n f r o n t a l f a c e r e c o g n i t i o n i s t h e p r i n c i p a l c o m p o n e n t a n a l y s i s ( P C A ) , w h i c h i s a s t a t i s t i c a l a p p r o a c h w h e r e f a c e i m a g e s a r e e x p r e s s e d a s a s u b s e t o f t h e i r e i g e n v e c t o r s , a n d h e n c e c a l l e d e i g e n f a c e s ( S i r o v i c h a n d K i r b y , 1 9 8 7 ; T u r k a n d P e n t l a n d , 1 9 9 1 ; M o g h a d d a m a n d P e n t l a n d , 1 9 9 7 ; M a r t i n e z , 2 0 0 0 ; G r a h a m a n d A l l i n s o n , 1 9 9 8 ) . P C A h a s a l s o b e e n u s e d f o r h a n d p r i n t r e c o g n i t i o n ( M u r a s e e t a l . , 1 9 8 1 ) , h u m a n - m a d e o b j e c t r e c o g n i t i o n ( M u r a s e a n d N a y a r , 1 9 9 5 ) , i n d u s t r i a l r o b o t i c s ( N a y a r e t a l . , 1 9 9 6 ) , a n d m o b i l e r o b o t i c s ( W e n g , 1 9 9 6 ) . B u t r e s u l t s s h o w t h a t t h e r e c o g n i t i o n r a t e i s n o t s a t i s f a c t o r y f o r p o s e v a r i a t i o n s e x c e e d i n g 3 0 a n d e x t r e m e c h a n g e s i n i l l u m i n a t i o n .
T h e m a i n o b j e c t i v e o f t h i s r e s e a r c h i s t o i m p r o v e t h e a c c u r a c y o f f a c e r e c o g n i t i o n s u b j e c t e d t o v a r y i n g f a c i a l e x p r e s s i o n , i l l u m i n a t i o n a n d h e a d p o s e . A s s t a t e d b e f o r e , P C A m e t h o d h a s b e e n a p o p u l a r t e c h n i q u e i n f a c i a l i m a g e r e c o g n i t i o n .
B u t t h i s t e c h n i q u e i s n o t h i g h l y a c c u r a t e w h e n t h e i l l u m i n a t i o n a n d p o s e o f t h e f a c i a l i m a g e s v a r y c o n s i d e r a b l y . I n t h i s r e s e a r c h w o r k a n a t t e m p t i s m a d e t o i m p r o v e t h e a c c u r a c y o f t h i s t e c h n i q u e u n d e r t h e c o n d i t i o n s o f v a r y i n g f a c i a l e x p r e s s i o n , i l l u m i n a t i o n a n d p o s e . W e p r o p o s e t h e m o d u l a r P C A m e t h o d , w h i c h i s a n e x t e n s i o n o f t h e c o n v e n t i o n a l P C A m e t h o d . I n t h e m o d u l a r P C A m e t h o d t h e f a c e i m a g e s a r e d i v i d e d i n t o s m a l l e r i m a g e s a n d t h e P C A m e t h o d i s a p p l i e d o n e a c h o f t h e m . W h e r e a s i n t h e t r a d i t i o n a l P C A m e t h o d t h e e n t i r e f a c e i m a g e i s c o n s i d e r e d , h e n c e l a r g e v a r i a t i o n i n p o s e o r i l l u m i n a t i o n w i l l a f f e c t t h e r e c o g n i t i o n r a t e p r o f o u n d l y . S i n c e i n t h e c a s e o f m o d u l a r P C A m e t h o d t h e o r i g i n a l f a c e i m a g e i s d i v i d e d i n t o s u b - i m a g e s t h e v a r i a t i o n s i n p o s e o r i l l u m i n a t i o n i n t h e i m a g e w i l l a f f e c t o n l y s o m e o f t h e s u b - i m a g e s , h e n c e w e e x p e c t t h i s m e t h o d t o h a v e b e t t e r r e c o g n i t i o n r a t e t h a n t h e c o n v e n t i o n a l P C A m e t h o d . A s i m i l a r m e t h o d c a l l e d m o d u l a r e i g e n s p a c e s w a s p r o p o s e d b y P e n t l a n d e t a l . ( 1 9 9 4 ) . I n t h i s m e t h o d P C A i s p e r f o r m e d o n t h e e y e s a n d n o s e o f t h e f a c e i m a g e .
T h i s p a p e r i s o r g a n i z e d a s f o l l o w s : S e c t i o n 2 d e s c r i b e s t h e c o n v e n t i o n a l P C A m e t h o d . S e c t i o n 3 e x p l a i n s t h e m o d u l a r P C A m e t h o d . S e c t i o n 4 d e s c r i b e s t h e f a c e d a t a b a s e s u s e d f o r t e s t i n g t h e f a c e r e c o g n i t i o n m e t h o d s . S e c t i o n 5 p r e s e n t s s i m u l a t i o n r e s u l t s o b t a i n e d b y a p p l y i n g t h e P C A m e t h o d a n d t h e p r o p o s e d m o d u l a r P C A m e t h o d t o t h e f a c e i m a g e s e t s w i t h l a r g e l i g h t a n d p o s e v a r i a t i o n s . F i n a l l y , a c o n c l u s i o n i s d r a w n i n S e c t i o n 6 .
2 . R e v i e w o f t h e P C A m e t h o d
T h e P C A m e t h o d h a s b e e n e x t e n s i v e l y a p p l i e d f o r t h e t a s k o f f a c e r e c o g n i t i o n . A p p r o x i m a t e r e c o n s t r u c t i o n o f f a c e s i n t h e e n s e m b l e w a s p e r - f o r m e d u s i n g a w e i g h t e d c o m b i n a t i o n o f e i g e n v e c t o r s ( e i g e n p i c t u r e s ) , o b t a i n e d f r o m t h a t e n s e m b l e ( S i r o v i c h a n d K i r b y , 1 9 8 7 ) . T h e w e i g h t s t h a t c h a r a c t e r i z e t h e e x p a n s i o n o f t h e g i v e n i m a g e i n t e r m s o f e i g e n p i c t u r e s a r e s e e n a s g l o b a l f a c i a l f e a t u r e s . I n a n e x t e n s i o n o f t h a t w o r k , K i r b y a n d S i r o v i c h ( 1 9 9 0 ) i n c l u d e d t h e i n h e r e n t s y m m e t r y o f f a c e s i n t h e e i g e n p i c t u r e s .
A l l t h e f a c e i m a g e s i n t h e f a c e d a t a b a s e a r e r e p r e s e n t e d a s v e r y l o n g v e c t o r s , i n s t e a d o f t h e u s u a l m a t r i x r e p r e s e n t a t i o n . T h i s m a k e s u p t h e e n t i r e i m a g e s p a c e w h e r e e a c h i m a g e i s a p o i n t S i n c e t h e f a c e s h a v e a s i m i l a r s t r u c t u r e ( e y e , n o s e a n d m o u t h , p o s i t i o n , e t c . ) , t h e v e c t o r s r e p r e s e n t i n g t h e m w i l l b e c o r r e l a t e d . W e w i l l s e e t h a t f a c e s o f t h e s a m e c l a s s w i l l g r o u p a t a c e r t a i n l o c a t i o n i n t h e i m a g e s p a c e . H e n c e t h e f a c e i m a g e s a r e r e p r e s e n t e d b y a s e t o f e i g e n v e c t o r s d e v e l o p e d f r o m a c o v a r i a n c e m a t r i x f o r m e d b y t h e t r a i n i n g o f f a c e i m a g e s . T h e i d e a b e h i n d e i g e n i m a g e s ( i n o u r c a s e e i g e n f a c e s ) i s t o f i n d a l o w e r d i m e n s i o n a l s p a c e i n w h i c h s h o r t e r v e c t o r s w i l l d e s c r i b e f a c e i m a g e s . F i g . 1 i l l u s t r a t e s t h i s i d e a g r a p h i c a l l y .
2 . 1 . C o m p u t i n g e i g e n f a c e s
C o n s i d e r t h e f a c e i m a g e s i n t h e f a c e d a t a b a s e t o b e o f s i z e L b y L . T h e s e i m a g e s c a n b e r e p r e s e n t e d a s a v e c t o r o f d i m e n s i o n L 2 , o r a p o i n t i n L 2 d i m e n s i o n a l s p a c e . A s e t o f i m a g e s t h e r e f o r e c o r r e s p o n d s t o a s e t o f p o i n t s i n t h i s h i g h d i m e n s i o n a l s p a c e . S i n c e f a c i a l i m a g e s a r e s i m i l a r i n s t r u c t u r e , t h e s e p o i n t s w i l l n o t b e r a n d o m l y d i s t r i b u t e d , a n d t h e r e f o r e c a n b e d e s c r i b e d b y a l o w e r d i m e n s i o n a l s u b s p a c e . P C A g i v e s t h e b a s i s v e c t o r s f o r t h i s s u b s p a c e ( w h i c h i s c a l l e d t h e f a c e s p a c e ) . E a c h b a s i s v e c t o r i s o f l e n g t h L 2 , a n d i s t h e e i g e n v e c t o r o f t h e c o v a r i a n c e m a t r i x c o r r e s p o n d i n g t o t h e o r i g i n a l f a c e i m a g e s .
L e t E M B E D E q u a t i o n . D S M T 4 b e t h e t r a i n i n g s e t o f f a c e i m a g e s . T h e a v e r a g e f a c e i s d e f i n e d b y
E M B E D E q u a t i o n . D S M T 4 1
E a c h f a c e d i f f e r s f r o m t h e a v e r a g e f a c e b y t h e v e c t o r E M B E D E q u a t i o n . D S M T 4 . T h e c o v a r i a n c e m a t r i x C i s o b t a i n e d a s
E M B E D E q u a t i o n . D S M T 4 2
T h e e i g e n v e c t o r s o f t h e c o v a r i a n c e m a t r i x a r e c o m p u t e d a n d t h e E M B E D E q u a t i o n . D S M T 4 s i g n i f i c a n t e i g e n v e c t o r s a r e c h o s e n a s t h o s e w i t h t h e l a r g e s t c o r r e s p o n d i n g e i g e n v a l u s . F r o m t h e s e e i g e n v e c t o r s , t h e w e i g h t s f o r e a c h i m a g e i n t h e t r a i n i n g s e t a r e c o m p u t e d a s
E M B E D E q u a t i o n . D S M T 4 3
W h e r e E M B E D E q u a t i o n . D S M T 4 s a r e t h e e i g e n v e c t o r s c o r r e s p o n d i n g t o t h e E M B E D E q u a t i o n . D S M T 4 l a r g e s t e i g e n v a l u e s o f C a n d K v a r i e s f r o m 1 t o E M B E D E q u a t i o n . D S M T 4 .
2 . 2 C l a s s i c a t i o n
A t e s t i m a g e I t e s t i s p r o j e c t e d i n t o f a c e s p a c e b y t h e f o l l o w i n g o p e r a t i o n :
E M B E D E q u a t i o n . D S M T 4 4
T h e w e i g h t s E M B E D E q u a t i o n . D S M T 4 f o r m a v e c t o r E M B E D E q u a t i o n . D S M T 4 , w h i c h d e s c r i b e s t h e c o n t r i b u t i o n o f e a c h e i g e n f a c e i n r e p r e s e n t i n g t h e i n p u t f a c e i m a g e . T h i s v e c t o r c a n t h e n b e u s e d t o f i t t h e t e s t i m a g e t o a p r e d e f i n e d f a c e c l a s s . A s i m p l e t e c h n i q u e i s t o c o m p u t e d i s t a n c e o f E M B E D E q u a t i o n . D S M T 4 f r o m E M B E D E q u a t i o n . D S M T 4 , w h e r e T p i s t h e m e a n w e i g h t v e c t o r o f t h e p t h c l a s s . T h e t e s t i m a g e c a n b e c l a s s i f i e d t o b e i n c l a s s p w h e n E M B E D E q u a t i o n . D S M T 4 , w h e r e E M B E D E q u a t i o n . D S M T 4 a n d E M B E D E q u a t i o n . D S M T 4 i s t h e t h r e s h o l d .
3 . M o d u l a r P C A m e t h o d
T h e P C A b a s e d f a c e r e c o g n i t i o n m e t h o d i s n o t v e r y e f f e c t i v e u n d e r t h e c o n d i t i o n s o f v a r y i n g p o s e a n d i l l u m i n a t i o n , s i n c e i t c o n s i d e r s t h e g l o b a l i n f o r m a t i o n o f e a c h f a c e i m a g e a n d r e p r e s e n t s t h e m w i t h a s e t o f w e i g h t s . U n d e r t h e s e c o n d i t i o n s t h e w e i g h t v e c t o r s w i l l v a r y c o n s i d e r a b l y f r o m t h e w e i g h t v e c t o r s o f t h e i m a g e s w i t h n o r m a l p o s e a n d i l l u m i n a t i o n , h e n c e i t i s d i f f i c u l t t o i d e n t i f y t h e m c o r r e c t l y . O n t h e o t h e r h a n d i f t h e f a c e i m a g e s w e r e d i v i d e d i n t o s m a l l e r r e g i o n s a n d t h e w e i g h t v e c t o r s a r e c o m p u t e d f o r e a c h o f t h e s e r e g i o n s , t h e n t h e w e i g h t s w i l l b e m o r e r e p r e s e n t a t i v e o f t h e l o c a l i n f o r m a t i o n o f t h e f a c e . W h e n t h e r e i s a v a r i a t i o n i n t h e p o s e o r i l l u m i n a t i o n , o n l y s o m e o f t h e f a c e r e g i o n s w i l l v a r y a n d r e s t o f t h e r e g i o n s w i l l r e m a i n t h e s a m e a s t h e f a c e r e g i o n s o f a n o r m a l i m a g e . H e n c e w e i g h t s o f t h e f a c e r e g i o n s n o t a f f e c t e d b y v a r y i n g p o s e a n d i l l u m i n a t i o n w i l l c l o s e l y m a t c h w i t h t h e w e i g h t s o f t h e s a m e i n d i v i d u a l ' s f a c e r e g i o n s u n d e r n o r m a l c o n d i t i o n s . T h e r e f o r e i t i s e x p e c t e d t h a t i m p r o v e d r e c o g n i t i o n r a t e s c a n b e o b t a i n e d b y f o l l o w i n g t h e m o d u l a r P C A a p p r o a c h . W e e x p e c t t h a t i f t h e f a c e i m a g e s a r e d i v i d e d i n t o v e r y s m a l l r e g i o n s t h e g l o b a l i n f o r m a t i o n o f t h e f a c e m a y b e l o s t a n d t h e a c c u r a c y o f t h i s m e t h o d m a y d e t e r i o r a t e .
I n t h i s m e t h o d , e a c h i m a g e i n t h e t r a i n i n g s e t i s d i v i d e d i n t o N s m a l l e r i m a g e s . H e n c e t h e s i z e o f e a c h s u b - i m a g e w i l l b e L 2 = N . T h e s e s u b - i m a g e s c a n b e r e p r e s e n t e d m a t h e m a t i c a l l y a s
E M B E D E q u a t i o n . D S M T 4 5
w h e r e i v a r i e s f r o m 1 t o M , M b e i n g t h e n u m b e r o f i m a g e s i n t h e t r a i n i n g s e t , j v a r i e s f r o m 1 t o N , N b e i n g t h e n u m b e r o f s u b - i m a g e s a n d m a n d n v a r y f r o m 1 t o E M B E D E q u a t i o n . D S M T 4 . F i g 2 s h o w s t h e r e s u l t o f d i v i d i n g a f a c e i m a g e i n t o f o u r s m a l l e r i m a g e s u s i n g E q . ( 5 ) f o r N = 4 .
T h e a v e r a g e i m a g e o f a l l t h e t r a i n i n g s u b - i m a g e s i s c o m p u t e d a s
E M B E D E q u a t i o n . D S M T 4 6
T h e n e x t s t e p i s t o n o r m a l i z e e a c h t r a i n i n g s u b - i m a g e b y s u b t r a c t i n g i t f r o m t h e m e a n a s
E M B E D E q u a t i o n . D S M T 4 7
F r o m t h e n o r m a l i z e d s u b - i m a g e s t h e c o v a r i a n c e m a t r i x i s c o m p u t e d a s
E M B E D E q u a t i o n . D S M T 4 8
N e x t w e f i n d t h e e i g e n v e c t o r s o f C t h a t a r e a s s o c i a t e d w i t h t h e E M B E D E q u a t i o n . D S M T 4 l a r g e s t e i g e n v a l u e s . W e r e p r e s e n t t h e e i g e n v e c t o r s a s E M B E D E q u a t i o n . D S M T 4 . T h e w e i g h t s a r e c o m p u t e d f r o m t h e e i g e n v e c t o r s a s s h o w n b e l o w :
E M B E D E q u a t i o n . D S M T 4 9
w h e r e K t a k e s t h e v a l u e s 1 , 2 , & , E M B E D E q u a t i o n . D S M T 4 , n v a r i e s f r o m 1 t o E M B E D E q u a t i o n . D S M T 4 , E M B E D E q u a t i o n . D S M T 4 b e i n g t h e n u m b e r o f i m a g e s p e r i n d i v i d u a l , a n d p v a r i e s f r o m 1 t o P , P b e i n g t h e n u m b e r o f i n d i v i d u a l s i n t h e t r a i n i n g s e t . W e i g h t s a r e a l s o c o m p u t e d f o r t h e t e s t s u b - i m a g e s u s i n g t h e e i g e n v e c t o r s a s s h o w n i n t h e n e x t e q u a t i o n :
E M B E D E q u a t i o n . D S M T 4 1 0
M e a n w e i g h t s e t o f e a c h c l a s s i n t h e t r a i n i n g s e t i s c o m p u t e d f r o m t h e w e i g h t s e t s o f t h e c l a s s a s s h o w n b e l o w :
E M B E D E q u a t i o n . D S M T 4 1 1
N e x t t h e m i n i m u m d i s t a n c e i s c o m p u t e d a s s h o w n b e l o w :
E M B E D E q u a t i o n . D S M T 4 1 2
E M B E D E q u a t i o n . D S M T 4 1 3
E M B E D E q u a t i o n . D S M T 4 f o r a p a r t i c u l a r v a l u e o f p , t h e c o r r e s p o n d i n g f a c e c l a s s i n t h e t r a i n i n g s e t i s t h e c l o s e s t o n e t o t h e t e s t i m a g e . H e n c e t h e t e s t i m a g e i s r e c o g n i z e d a s b e l o n g i n g t o t h e p t h f a c e c l a s s .
4 . I m a g e d a t a b a s e s
T h e p e r f o r m a n c e o f t h e c o n v e n t i o n a l P C A b a s e d a l g o r i t h m a n d t h e m o d u l a r P C A b a s e d a l g o r i t h m w e r e e v a l u a t e d w i t h t w o i m a g e d a t a - b a s e s , U M I S T a n d Y a l e . T h e U M I S T d a t a b a s e c o n s i s t s o f i m a g e s w i t h v a r y i n g p o s e a n d t h e Y a l e d a t a b a s e c o n s i s t s o f i m a g e s w i t h v a r y i n g i l l u m i n a t i o n a n d e x p r e s s i o n s . A l l t h e i m a g e s i n b o t h t h e d a t a b a s e s w e r e n o r m a l i z e d a n d c r o p p e d t o a s i z e o f 6 4 6 4 p i x e l s .
4 . 1 . U M I S T d a t a b a s e - p o s e v a r i a n t
F o r o u r t e s t s w e t o o k a p a r t i a l s e t o f f a c e i m a g e s c o n s i s t i n g o f 1 0 i m a g e s e a c h o f 2 0 d i f f e r e n t i n d i v i d u a l s f r o m t h e U M I S T f a c e d a t a b a s e . E a c h i m a g e o f a p e r s o n i s t a k e n a t a d i f f e r e n t p o s e , w i t h a n o r m a l e x p r e s s i o n . O u t o f t h e t e n i m a g e s o f a p e r s o n , o n l y e i g h t w e r e u s e d f o r t r a i n i n g a n d t h e r e m a i n i n g t w o w e r e u s e d t o t e s t t h e r e c o g n i t i o n r a t e . F i g . 3 a a n d b s h o w t h e s e t o f i m a g e s o f a p e r s o n u s e d f o r t r a i n i n g a n d t e s t i n g r e s p e c t i v e l y . T h e c h o i c e o f t h e t r a i n i n g a n d t e s t i n g i m a g e s w a s m a d e t o t e s t b o t h t h e a l g o r i t h m s w i t h h e a d p o s e a n g l e s t h a t l i e o u t s i d e t h e h e a d p o s e a n g l e s t h e y w e r e t r a i n e d w i t h . T h e P C A a n d m o d u l a r P C A m e t h o d s m a y p e r f o r m p o o r l y w i t h t h i s s e l e c t i o n o f t r a i n i n g a n d t e s t i n g i m a g e s , b u t o u r a i m i s t o c o m p a r e t h e i r p e r f o r m a n c e f o r t e s t i m a g e s w h o s e h e a d p o s e a n g l e s l i e o u t s i d e t h e h e a d p o s e a n g l e s o f t h e t r a i n i n g i m a g e s .
4 . 2 . Y a l e d a t a b a s e - e x p r e s s i o n a n d i l l u m i n a t i o n v a r i a n t
T h e Y a l e d a t a b a s e h a s 1 6 5 i m a g e s o f 1 5 a d u l t s , 1 1 i m a g e s p e r p e r s o n . T h e f a c e i m a g e s v a r y w i t h r e s p e c t t o f a c i a l e x p r e s s i o n a n d i l l u m i n a t i o n . T h e i m a g e s h a v e n o r m a l , s a d , h a p p y , s l e e p y , s u r p r i s e d , a n d w i n k i n g e x p r e s s i o n s . T h e r e a r e a l s o i m a g e s w h e r e t h e p o s i t i o n o f t h e l i g h t s o u r c e i s a t t h e c e n t e r , l e f t a n d r i g h t . I n a d d i t i o n t o t h e s e t h e r e a r e i m a g e s w i t h a n d w i t h o u t g l a s s e s . O u t o f t h e 1 1 i m a g e s o f a p e r s o n , o n l y e i g h t w e r e u s e d f o r t r a i n i n g a n d t h e r e m a i n i n g t h r e e w e r e u s e d t o t e s t t h e r e c o g n i t i o n r a t e s . F i g . 4 a a n d b s h o w t h e s e t o f i m a g e s o f a p e r s o n u s e d f o r t r a i n i n g a n d t e s t i n g r e s p e c t i v e l y . T h e c h o i c e o f t h e t r a i n i n g a n d t e s t i m a g e s w a s m a d e t o f a c i l i t a t e c o m p a r i s o n o f p e r f o r m a n c e o f b o t h t h e m e t h o d s f o r t e s t i m a g e s w i t h u n e v e n i l l u m i n a t i o n a n d p a r t i a l o c c l u s i o n .
W e a l s o c o n d u c t e d e x p e r i m e n t s b y l e a v i n g o u t o n e i m a g e f r o m e a c h i n d i v i d u a l ' s s e t o f 1 1 i m a g e s d u r i n g t r a i n i n g a n d t e s t i n g t h e r e c o g n i t i o n r a t e w i t h t h e i m a g e s l e f t o u t . T h i s w a s r e p e a t e d 1 1 t i m e s b y l e a v i n g o u t a d i f f e r e n t i m a g e e a c h t i m e . T h i s k i n d o f t e s t i n g i s r e f e r r e d t o a s l e a v e o u t o n e t e s t i n g i n t h e r e m a i n d e r o f t h e p a p e r .
5 . T e s t r e s u l t s
W e t e s t e d t h e p e r f o r m a n c e o f P C A a n d m o d u l a r P C A a l g o r i t h m s f o r v a r y i n g n u m b e r o f e i g e n v e c t o r s . C o n s i d e r i n g m o r e e i g e n v e c t o r s r e s u l t s i n i n c r e a s e d r e c o g n i t i o n r a t e s , h o w e v e r t h e i n c r e a s e i n c o m p u t a t i o n a l c o s t i s l i n e a r w i t h t h e n u m b e r o f e i g e n v e c t o r s . F i g . 5 s h o w s t h e r e c o g n i t i o n r a t e s o f P C A a n d m o d u l a r P C A f o r v a r y i n g n u m b e r o f e i g e n v e c t o r s . T h e r e s u l t s s h o w n i n F i g . 5 w e r e o b t a i n e d u s i n g t h e Y a l e f a c e d a t a b a s e b y l e a v i n g o u t o n e t e s t i n g . T h r e s h o l d w a s n o t u s e d f o r t h i s t e s t i n g ; h e n c e t h e r e a r e n o r e j e c t i o n s , o n l y c o r r e c t r e c o g n i t i o n o r f a l s e r e c o g n i t i o n . I t c a n a l s o b e o b s e r v e d f r o m F i g . 5 t h a t t h e r e c o g n i t i o n r a t e i s i n c r e a s i n g i n b o t h P C A a n d m o d u l a r P C A m e t h o d s a s w e i n c r e a s e t h e v a l u e o f E M B E D E q u a t i o n . D S M T 4 , a n d t h e r e i s n o t m u c h i m p r o v e m e n t f o r E M B E D E q u a t i o n . D S M T 4 . S i m i l a r r e s u l t s h a v e b e e n o b s e r v e d f o r v a l u e s N = 4 , 1 6 , 6 4 , 2 5 6 a n d 1 0 2 4 . T h e m o d u l a r P C A r e s u l t s h a v e a l s o b e e n c o m p a r e d w i t h t h e r e s u l t s o f m o d u l a r e i g e n s p a c e s d e s c r i b e d b y P e n t l a n d e t a l . ( 1 9 9 4 ) . I t h a s b e e n o b s e r v e d t h a t t h e m o d u l a r P C A a l g o r i t h m p r o - v i d e s b e t t e r r e c o g n i t i o n r a t e w i t h t h e a d d e d a d v a n t a g e t h a t i t d o e s n o t r e q u i r e t h e d e t e c t i o n o f s p e c i f i c f e a t u r e s l i k e e y e , n o s e a n d m o u t h .
T e s t s i n t h e r e m a i n d e r o f t h i s p a p e r w e r e c o n d u c t e d a t E M B E D E q u a t i o n . D S M T 4 = 2 0 , i . e . e i g e n v e c t o r s c o r r e s p o n d i n g t o t h e 2 0 m a x i m u m e i g e n v a l u e s o f t h e c o v a r i a n c e m a t r i x . T h e a i m o f o u r t e s t s w a s t o c o m p a r e t h e t w o a l g o r i t h m s w i t h v a r y i n g p o s e a n d i l l u m i n a t i o n f a c e i m a g e s a n d v a r y i n g E M B E D E q u a t i o n . D S M T 4 w o u l d h a v e t h e s a m e e f f e c t o n b o t h t h e a l g o r i t h m s a s s h o w n i n F i g . 5 , h e n c e o n l y t h e f i r s t 2 0 e i g e n v e c t o r s w e r e c o n s i d e r e d f o r t h e t e s t s .
W h e n t h e s i z e o f t h e s u b - i m a g e s i s l e s s t h a n o r e q u a l t o 4 * 4 E M B E D E q u a t i o n . D S M T 4 , t h e n u m b e r o f e i g e n v e c t o r s t h a t c a n b e o b t a i n e d f r o m t h e c o v a r i a n c e m a t r i x w i l l b e l e s s t h a n 2 0 , s i n c e t h e s i z e o f t h e c o v a r i a n c e m a t r i x i s l e s s t h a n o r e q u a l t o 1 6 1 6 . F o r t h e c a s e w h e r e E M B E D E q u a t i o n . D S M T 4 e i g e n v e c t o r s a r e c o n s i d e r e d . F o r e x a m p l e w h e n N = 2 5 6 , 1 6 e i g e n v e c t o r s a r e c o n s i d e r e d . F o r t h e c a s e w h e r e N = 4 0 9 6 , t h e a l g o r i t h m r e d u c e s t o c o m p a r i n g t h e p i x e l v a l u e s o f t e s t i m a g e a n d t r a i n i n g i m a g e s , p i x e l b y p i x e l .
W e a p p l i e d t h e P C A m e t h o d a n d t h e m o d u l a r P C A m e t h o d t o r e c o n s t r u c t t h e t e s t i m a g e s . I n t h e c a s e o f t h e P C A m e t h o d t h e i m a g e i s r e c o n s t r u c t e d a s
E M B E D E q u a t i o n . D S M T 4 1 4
T h e t e s t i m a g e i s r e c o n s t r u c t e d i n a s i m i l a r m a n n e r f o r t h e m o d u l a r P C A m e t h o d a n d i s g i v e n a s
E M B E D E q u a t i o n . D S M T 4 1 5
F i g s . 6 a n d 7 s h o w t h e r e c o n s t r u c t e d i m a g e s o f a f a c e i m a g e f r o m t h e t e s t s e t o f t h e U M I S T a n d Y a l e d a t a b a s e s u s i n g b o t h t h e m e t h o d s . I n t h e f i g u r e s , t h e r e c o n s t r u c t e d i m a g e s o b t a i n e d f o r t h e m o d u l a r P C A m e t h o d a r e c o n c a t e n a t e d t o f a c i l i t a t e v i s u a l c o m p a r i s o n w i t h t h e r e c o n s t r u c t e d i m a g e o b t a i n e d f o r P C A m e t h o d .
5 . 1 . R e s u l t s f o r p o s e v a r i a t i o n
I n t h i s e x p e r i m e n t w e c o m p a r e d t h e r e c o g n i t i o n r a t e , f a l s e r e c o g n i t i o n r a t e a n d f a l s e r e j e c t i o n r a t e o f t h e t w o m e t h o d s f o r l a r g e p o s e v a r i a t i o n s u s i n g t h e i m a g e s i n t h e U M I S T d a t a b a s e . T h e t r a i n i n g a n d t e s t i m a g e s w e r e c h o s e n a s d e s c r i b e d i n S e c t i o n 4 . 1 . F u r t h e r m o r e w e v a r y N f r o m 4 t o 4 0 9 6 t o o b s e r v e t h e e f f e c t o f N o n f a c e r e c o g n i t i o n . S i n c e t h e s i z e o f a l l t h e i m a g e s i n t h e d a t a b a s e i s 6 4 6 4 p i x e l s , t h e m a x i m u m v a l u e N c a n t a k e i s 4 0 9 6 , i . e . a s u b - i m a g e i s a s i n g l e p i x e l . F i g . 8 s h o w s t h e r e c o g n i t i o n r a t e , f a l s e r e c o g n i t i o n r a t e a n d f a l s e r e j e c t i o n r a t e f o r t h e m o d u l a r P C A m e t h o d w i t h v a r y i n g N . I n t h e c a s e o f P C A t h e r e c o g n i t i o n r a t e w a s 0 . 3 , f a l s e r e c o g n i t i o n r a t e w a s 0 . 6 2 5 a n d f a l s e r e j e c t i o n r a t e w a s 0 . 0 7 5 .
F r o m t h e r e s u l t s w e n o t e t h a t t h e m o d u l a r P C A m e t h o d h a s a s l i g h t l y b e t t e r r e c o g n i t i o n r a t e a n d f a l s e r e c o g n i t i o n r a t e a t N = 4 a n d 1 6 , b u t t h e c o n v e n t i o n a l P C A m e t h o d h a s a s l i g h t l y l e s s e r f a l s e r e j e c t i o n r a t e . H e n c e t h e p r o p o s e d m e t h o d d o e s n o t h a v e s i g n i f i c a n t i m p r o v e m e n t o v e r t h e P C A m e t h o d u n d e r t h e c o n d i t i o n o f v a r y i n g p o s e .
5 . 2 . R e s u l t s f o r e x p r e s s i o n a n d i l l u m i n a t i o n v a r i a t i o n
I n t h i s e x p e r i m e n t w e c o m p a r e d t h e r e c o g n i t i o n r a t e , f a l s e r e c o g n i t i o n r a t e a n d f a l s e r e j e c t i o n r a t e o f t h e t w o m e t h o d s f o r l a r g e e x p r e s s i o n a n d i l l u m i n a t i o n v a r i a t i o n s u s i n g t h e i m a g e s i n t h e Y a l e d a t a b a s e . T h e t r a i n i n g a n d t e s t i m a g e s w e r e c h o s e n a s d e s c r i b e d i n S e c t i o n 4 . 2 . A s b e f o r e w e v a r y t h e v a l u e o f N f r o m 4 t o 4 0 9 6 t o o b s e r v e t h e e f f e c t i t h a s o n f a c e r e c o g n i t i o n . F i g . 9 s h o w s t h e r e c o g n i t i o n r a t e , f a l s e r e c o g n i t i o n r a t e a n d f a l s e r e j e c t i o n r a t e f o r t h e m o d u l a r P C A m e t h o d w i t h v a r y i n g N . I n t h e c a s e o f P C A t h e r e c o g n i t i o n r a t e w a s 0 . 4 4 , f a l s e r e c o g n i t i o n r a t e w a s 0 . 3 1 a n d f a l s e r e j e c t i o n r a t e w a s 0 . 2 4 .
A s e c o n d s e t o f e x p e r i m e n t s w e r e p e r f o r m e d b y l e a v i n g o u t o n e t e s t i n g . T h e r e s u l t s o b t a i n e d f o r m o d u l a r P C A a r e s h o w n i n F i g . 1 0 . F o r P C A , r e c o g n i t i o n r a t e w a s 0 . 4 8 , f a l s e r e c o g n i t i o n r a t e w a s 0 . 3 6 a n d f a l s e r e j e c t i o n r a t e w a s 0 . 1 6 .
W e c a n o b s e r v e f r o m t h e r e s u l t s t h a t t h e m o d u l a r P C A m e t h o d c o m p l e t e l y o u t p e r f o r m s t h e P C A m e t h o d i n a l l a s p e c t s f o r N a t 4 , 1 6 a n d 6 4 . H o w e v e r , b e s t r e s u l t s w e r e o b t a i n e d f o r N a t 1 6 . R e c o n s t r u c t i o n o f o n e o f t h e t e s t i m a g e s w a s p e r f o r m e d u s i n g P C A a n d m o d u l a r P C A f o r N a t 1 6 . T h e r e s u l t s o f t h e r e c o n s t r u c t i o n a r e s h o w n i n F i g . 1 1 , t h e f i r s t i m a g e i s t h e r e c o n s t r u c t e d i m a g e o b t a i n e d u s i n g P C A m e t h o d , t h e s e c o n d i m a g e i s t h e o r i g i n a l i m a g e a n d t h e t h i r d i m a g e i s t h e c o n c a t e n a t i o n o f t h e r e c o n s t r u c t e d i m a g e s o b t a i n e d u s i n g t h e m o d u l a r P C A m e t h o d f o r N = 1 6 .
T h e P C A b a s e d m e t h o d w a s n o t v e r y e f f e c t i v e u n d e r t h e c o n d i t i o n s o f v a r y i n g i l l u m i n a t i o n , s i n c e i t c o n s i d e r s t h e g l o b a l i n f o r m a t i o n o f e a c h f a c e i m a g e a n d r e p r e s e n t s t h e m w i t h a s e t o f w e i g h t s . U n d e r t h i s c o n d i t i o n t h e w e i g h t v e c t o r s o f t h e t e s t i m a g e w i l l v a r y c o n s i d e r a b l y f r o m t h e w e i g h t v e c t o r s o f t h e t r a i n i n g i m a g e s w i t h n o r m a l i l l u m i n a t i o n , h e n c e i t i s d i f f i c u l t t o i d e n t i f y t h e m c o r r e c t l y . T h e h u g e i m p r o v e m e n t i n t h e c a s e o f m o d u l a r P C A w a s o b s e r v e d s i n c e t h e f a c e i m a g e s w e r e d i v i d e d i n t o s m a l l e r r e g i o n s a n d t h e w e i g h t v e c t o r s w e r e c o m p u t e d f o r e a c h o f t h e s e r e g i o n s , h e n c e w e i g h t v e c t o r s w i l l b e m o r e r e p r e s e n t a t i v e o f t h e l o c a l i n f o r m a t i o n o f t h e f a c e . T h e r e f o r e f o r v a r i a t i o n s i n i l l u m i n a t i o n , t h e w e i g h t s o f t h e f a c e r e g i o n s n o t a f f e c t e d b y v a r y i n g i l l u m i n a t i o n c l o s e l y m a t c h w i t h t h e w e i g h t s o f t h e s a m e i n d i v i d u a l ' s f a c e r e g i o n s u n d e r n o r m a l c o n d i t i o n s . T h i s l e a d s t o b e t t e r r e c o g n i t i o n r e s u l t s u s i n g m o d u l a r P C A a s o b s e r v e d i n t h e e x p e r i m e n t a l r e s u l t s .
6 . C o n c l u s i o n
A m o d u l a r P C A m e t h o d , w h i c h i s a n e x t e n s i o n o f t h e P C A m e t h o d f o r f a c e r e c o g n i t i o n h a s b e e n p r o p o s e d . T h e m o d u l a r P C A m e t h o d p e r f o r m s b e t t e r t h a n t h e P C A m e t h o d u n d e r t h e c o n d i t i o n s o f l a r g e v a r i a t i o n s i n e x p r e s s i o n a n d i l l u m i n a t i o n . F o r l a r g e v a r i a t i o n s i n p o s e t h e r e i s n o s i g n i f i c a n t i m p r o v e m e n t i n t h e p e r f o r m a n c e o f m o d u l a r P C A . F o r f a c e r e c o g n i t i o n , t h e m o d u l a r P C A m e t h o d c a n b e u s e d a s a n a l t e r n a t i v e t o t h e P C A m e t h o d . I n p a r t i c u l a r , t h e m o d u l a r P C A m e t h o d w i l l b e u s e f u l f o r i d e n t i f i c a t i o n s y s t e m s s u b j e c t e d t o l a r g e v a r i a t i o n s i n i l l u m i n a t i o n a n d f a c i a l e x p r e s s i o n .
R e f e r e n c e s
C h e l l a p p a , R . W i l s o n , C . L . S i r o h e y , S . 1 9 9 5 . H u m a n a n d m a c h i n e r e c o g n i t i o n o f f a c e s : A s u r v e y . P r o c . I E E E 8 3 ( 5 ) , 7 0 5 7 4 0 .
G r a h a m , D . B . A l l i n s o n , N . M . , 1 9 9 8 . C h a r a c t e r i z i n g v i r t u a l e i g e n s i g n a t u r e s f o r g e n e r a l p u r p o s e f a c e r e c o g n i t i o n . I n : F a c e R e c o g n i t i o n : F r o m T h e o r y t o A p p l i c a t i o n s , N A T O A S I S e r i e s F , C o m p u t e r a n d S y s t e m s S c i e n c e s , v o l . 1 6 3 , p p . 4 4 6 4 5 6 .
K i r b y , M . , S i r o v i c h , L . , 1 9 9 0 . A p p l i c a t i o n o f t h e K a r h u n e n L o e v e p r o c e d u r e f o r t h e c h a r a c t e r i z a t i o n o f h u m a n f a c e s . I E E E T r a n s . P a t t e r n A n a l . M a c h i n e I n t e l l . 1 2 ( 1 ) , 1 0 3 1 0 8 .
M a r t i n e z , A . M . , 2 0 0 0 . R e c o g n i t i o n o f p a r t i a l l y o c c l u d e d a n d / o r i m p r e c i s e l y l o c a l i z e d f a c e s u s i n g a p r o b a b i l i s t i c a p p r o a c h . I n : P r o c . o f C o m p u t e r V i s i o n a n d P a t t e r n R e c o g n i t i o n , v o l . 1 , p p . 7 1 2 7 1 7 .
M o g h a d d a m , B , P e n t l a n d , A . , 1 9 9 7 . P r o b a b i l i s t i c v i s u a l l e a r n i n g f o r o b j e c t r e p r e s e n t a t i o n . I E E E T r a n s . P a t t e r n A n a l . M a c h i n e I n t e l l . P A M I - 1 9 ( 7 ) , 6 9 6 7 1 0 .
M u r a s e , H . , K i m u r a , F . , Y o s h i m u r a , M . , M i y a k e , Y . , 1 9 8 1 . A n i m p r o v e m e n t o f t h e a u t o - c o r r e l a t i o n m a t r i x i n p a t t e r n m a t c h i n g m e t h o d a n d i t s a p p l i c a t i o n s t o h a n d p r i n t e d H I R A G A N A ' . T r a n s a c t i o n s o n I E C E J 6 4 - D ( 3 ) .
M u r a s e , H . , N a y a r , S . , 1 9 9 5 . V i s u a l l e a r n i n g a n d r e c o g n i t i o n o f 3 - D o b j e c t s f r o m a p p e a r a n c e . I n t . J . C o m p u t e r V i s i o n 1 4 , 5 2 4 .
N a y a r , S . K . , N e n e , N . A . , M u r a s e , H . , 1 9 9 6 . S u b s p a c e m e t h o d s f o r R o b o t v i s i o n . I E E E T r a n s . R o b o t . A u t o m a t . R A - 1 2 ( 5 ) , 7 5 0 7 5 8 .
P e n t l a n d , A . , M o g h a d d a m , B . , S t a r n e r , T . , 1 9 9 4 . V i e w - b a s e d a n d m o d u l a r e i g e n s p a c e s f o r f a c e r e c o g n i t i o n . I E E E C o n f . o n C o m p u t e r V i s i o n a n d P a t t e r n R e c o g n i t i o n .
S i r o v i c h , L . , K i r b y , M . , 1 9 8 7 . A l o w - d i m e n s i o n a l p r o c e d u r e f o r t h e c h a r a c t e r i z a t i o n o f h u m a n f a c e s . J . O p t . S o c . A m e r . A 4 ( 3 ) , 5 1 9 5 2 4 .
T u r k , M . , P e n t l a n d , A . , 1 9 9 1 E i g e n f a c e s f o r r e c o g n i t i o n . J . C o g n i t i v e N e u r o s c i . 3 ( 1 ) .
W e n g , J . J . , 1 9 9 6 . C r e s c e p t o n a n d S H O S L I F : t o w a r d s c o m p r e - h e n s i v e v i s u a l l e a r n i n g . I n : N a y a r , S . K . , P o g g i o , T . ( E d s . ) , E a r l y V i s u a l L e a r n i n g . O x f o r d U n i v e r s i t y P r e s s , p p . 1 8 3 2 1 4 .
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C h e l l a p p a , R . W i l s o n , C . L . S i r o h e y , S . 1 9 9 5 . H u m a n a n d m a c h i n e r e c o g n i t i o n o f f a c e s : A s u r v e y . P r o c . I E E E 8 3 ( 5 ) , 7 0 5 7 4 0 .
G r a h a m , D . B . A l l i n s o n , N . M . , 1 9 9 8 . C h a r a c t e r i z i n g v i r t u a l e i g e n s i g n a t u r e s f o r g e n e r a l p u r p o s e f a c e r e c o g n i t i o n . I n : F a c e R e c o g n i t i o n : F r o m T h e o r y t o A p p l i c a t i o n s , N A T O A S I S e r i e s F , C o m p u t e r a n d S y s t e m s S c i e n c e s , v o l . 1 6 3 , p p . 4 4 6 4 5 6 .
K i r b y , M . , S i r o v i c h , L . , 1 9 9 0 . A p p l i c a t i o n o f t h e K a r h u n e n L o e v e p r o c e d u r e f o r t h e c h a r a c t e r i z a t i o n o f h u m a n f a c e s . I E E E T r a n s . P a t t e r n A n a l . M a c h i n e I n t e l l . 1 2 ( 1 ) , 1 0 3 1 0 8 .
M a r t i n e z , A . M . , 2 0 0 0 . R e c o g n i t i o n o f p a r t i a l l y o c c l u d e d a n d / o r i m p r e c i s e l y l o c a l i z e d f a c e s u s i n g a p r o b a b i l i s t i c a p p r o a c h . I n : P r o c . o f C o m p u t e r V i s i o n a n d P a t t e r n R e c o g n i t i o n , v o l . 1 , p p . 7 1 2 7 1 7 .
M o g h a d d a m , B , P e n t l a n d , A . , 1 9 9 7 . P r o b a b i l i s t i c v i s u a l l e a r n i n g f o r o b j e c t r e p r e s e n t a t i o n . I E E E T r a n s . P a t t e r n A n a l . M a c h i n e I n t e l l . P A M I - 1 9 ( 7 ) , 6 9 6 7 1 0 .
M u r a s e , H . , K i m u r a , F . , Y o s h i m u r a , M . , M i y a k e , Y . , 1 9 8 1 . A n i m p r o v e m e n t o f t h e a u t o - c o r r e l a t i o n m a t r i x i n p a t t e r n m a t c h i n g m e t h o d a n d i t s a p p l i c a t i o n s t o h a n d p r i n t e d H I R A G A N A ' . T r a n s a c t i o n s o n I E C E J 6 4 - D ( 3 ) .
M u r a s e , H . , N a y a r , S . , 1 9 9 5 . V i s u a l l e a r n i n g a n d r e c o g n i t i o n o f 3 - D o b j e c t s f r o m a p p e a r a n c e . I n t . J . C o m p u t e r V i s i o n 1 4 , 5 2 4 .
N a y a r , S . K . , N e n e , N . A . , M u r a s e , H . , 1 9 9 6 . S u b s p a c e m e t h o d s f o r R o b o t v i s i o n . I E E E T r a n s . R o b o t . A u t o m a t . R A - 1 2 ( 5 ) , 7 5 0 7 5 8 .
P e n t l a n d , A . , M o g h a d d a m , B . , S t a r n e r , T . , 1 9 9 4 . V i e w - b a s e d a n d m o d u l a r e i g e n s p a c e s f o r f a c e r e c o g n i t i o n . I E E E C o n f . o n C o m p u t e r V i s i o n a n d P a t t e r n R e c o g n i t i o n .
S i r o v i c h , L . , K i r b y , M . , 1 9 8 7 . A l o w - d i m e n s i o n a l p r o c e d u r e f o r t h e c h a r a c t e r i z a t i o n o f h u m a n f a c e s . J . O p t . S o c . A m e r . A 4 ( 3 ) , 5 1 9 5 2 4 .
T u r k , M . , P e n t l a n d , A . , 1 9 9 1 E i g e n f a c e s f o r r e c o g n i t i o n . J . C o g n i t i v e N e u r o s c i . 3 ( 1 ) .
W e n g , J . J . , 1 9 9 6 . C r e s c e p t o n a n d S H O S L I F : t o w a r d s c o m p r e - h e n s i v e v i s u a l l e a r n i n g . I n : N a y a r , S . K . , P o g g i o , T . ( E d s . ) , E a r l y V i s u a l L e a r n i n g . O x f o r d U n i v e r s i t y P r e s s , p p . 1 8 3 2 1 4 .
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T r a i n D a t a b a s e P a t h = u i g e t d i r ( ' D : \ s o f t w a r e \ m a t l a b 1 \ b i n \ P C A _ b a s e d F a c e R e c o g n i t i o n S y s t e m \ T r a i n D a t a b a s e ' , ' S e l e c t t r a i n i n g d a t a b a s e p a t h ' ) ;
T e s t D a t a b a s e P a t h = u i g e t d i r ( ' D : \ s o f t w a r e \ m a t l a b 1 \ b i n \ P C A _ b a s e d F a c e R e c o g n i t i o n S y s t e m \ T e s t D a t a b a s e ' , ' S e l e c t t e s t d a t a b a s e p a t h ' ) ;
p r o m p t = { ' E n t e r t e s t i m a g e n a m e ( a n u m b e r b e t w e e n 1 t o 2 4 ) : ' } ;
d l g _ t i t l e = ' I n p u t o f P C A - B a s e d F a c e R e c o g n i t i o n S y s t e m ' ;
n u m _ l i n e s = 1 ;
d e f = { ' 1 ' } ;
T e s t I m a g e = i n p u t d l g ( p r o m p t , d l g _ t i t l e , n u m _ l i n e s , d e f ) ;
T e s t I m a g e = s t r c a t ( T e s t D a t a b a s e P a t h , ' \ ' , c h a r ( T e s t I m a g e ) , ' . j p g ' ) ;
i m = i m r e a d ( T e s t I m a g e ) ;
T = C r e a t e D a t a b a s e ( T r a i n D a t a b a s e P a t h ) ;
[ m , A , E i g e n f a c e s ] = E i g e n f a c e C o r e ( T ) ;
O u t p u t N a m e = R e c o g n i t i o n ( T e s t I m a g e , m , A , E i g e n f a c e s ) ;
S e l e c t e d I m a g e = s t r c a t ( T r a i n D a t a b a s e P a t h , ' \ ' , O u t p u t N a m e ) ;
S e l e c t e d I m a g e = i m r e a d ( S e l e c t e d I m a g e ) ;
s u b p l o t ( 1 , 2 , 1 )
i m s h o w ( i m )
t i t l e ( ' T e s t I m a g e ' ) ;
s u b p l o t ( 1 , 2 , 2 )
i m s h o w ( S e l e c t e d I m a g e ) ;
t i t l e ( ' m a t c h i n g I m a g e ' ) ;
s t r = s t r c a t ( ' M a t c h e d i m a g e i s : ' , O u t p u t N a m e ) ;
d i s p ( s t r )
C r e a t e D a t a b a s e . m
T r a i n F i l e s = d i r ( T r a i n D a t a b a s e P a t h ) ;
T r a i n _ N u m b e r = 0 ;
f o r i = 1 : s i z e ( T r a i n F i l e s , 1 )
i f n o t ( s t r c m p ( T r a i n F i l e s ( i ) . n a m e , ' . ' ) | s t r c m p ( T r a i n F i l e s ( i ) . n a m e , ' . . ' ) | s t r c m p ( T r a i n F i l e s ( i ) . n a m e , ' T h u m b s . d b ' ) )
T r a i n _ N u m b e r = T r a i n _ N u m b e r + 1 ;
e n d
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s t r = i n t 2 s t r ( i ) ;
s t r = s t r c a t ( ' \ ' , s t r , ' . j p g ' ) ;
s t r = s t r c a t ( T r a i n D a t a b a s e P a t h , s t r ) ;
i m g = i m r e a d ( s t r ) ;
i m g = r g b 2 g r a y ( i m g ) ;
[ i r o w i c o l ] = s i z e ( i m g ) ;
t e m p = r e s h a p e ( i m g ' , i r o w * i c o l , 1 ) ;
T = [ T t e m p ] ;
e n d
E i g e n f a c e C o r e . m
f u n c t i o n [ m , A , E i g e n f a c e s ] = E i g e n f a c e C o r e ( T )
m = m e a n ( T , 2 ) ;
T r a i n _ N u m b e r = s i z e ( T , 2 ) ;
A = [ ] ;
f o r i = 1 : T r a i n _ N u m b e r
t e m p = d o u b l e ( T ( : , i ) ) - m ;
A = [ A t e m p ] ;
E n d
L = A ' * A ;
L = 1 / 3 6 0 0 0 * L ;
[ V D ] = e i g ( L ) ;
L _ e i g _ v e c = [ ] ;
t e m p = [ ] ;
f o r i = 1 : s i z e ( V , 2 )
t e m p = [ t e m p D ( i , i ) ] ;
i f ( D ( i , i ) > 1 0 0 )
L _ e i g _ v e c = [ L _ e i g _ v e c V ( : , i ) ] ;
e n d
e n d
t e m p ;
E i g e n f a c e s = A * L _ e i g _ v e c ;
R e c o g n i t i o n . m
f u n c t i o n O u t p u t N a m e = R e c o g n i t i o n ( T e s t I m a g e , m , A , E i g e n f a c e s )
P r o j e c t e d I m a g e s = [ ] ;
T r a i n _ N u m b e r = s i z e ( E i g e n f a c e s , 2 ) ;
f o r i = 1 : T r a i n _ N u m b e r
t e m p = E i g e n f a c e s ' * A ( : , i ) ;
P r o j e c t e d I m a g e s = [ P r o j e c t e d I m a g e s t e m p ] ;
E n d
n p u t I m a g e = i m r e a d ( T e s t I m a g e ) ;
t e m p = I n p u t I m a g e ( : , : , 1 ) ;
[ i r o w i c o l ] = s i z e ( t e m p ) ;
I n I m a g e = r e s h a p e ( t e m p ' , i r o w * i c o l , 1 ) ;
D i f f e r e n c e = d o u b l e ( I n I m a g e ) - m ;
P r o j e c t e d T e s t I m a g e = E i g e n f a c e s ' * D i f f e r e n c e ;
E u c _ d i s t = [ ] ;
f o r i = 1 : T r a i n _ N u m b e r
q = P r o j e c t e d I m a g e s ( : , i ) ;
t e m p = ( n o r m ( P r o j e c t e d T e s t I m a g e - q ) ) ^ 2 ;
E u c _ d i s t = [ E u c _ d i s t t e m p ] ;
e n d
[ E u c _ d i s t _ m i n , R e c o g n i z e d _ i n d e x ] = m i n ( E u c _ d i s t ) ;
O u t p u t N a m e = s t r c a t ( i n t 2 s t r ( R e c o g n i z e d _ i n d e x ) , ' . j p g ' ) ;
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g [ i , j ] = = e "- ( i 2 + + j 2 ) 2 s 2
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