Thinning Algorithms for Document Processing Systems

The aim of t h i s paper is t o p r e s e n t t h e r e s u l t s o f a s t u d y which was performed t o a s s e s s t h e f e a s i b i l i t y of t h i n n i n g methods f o r document p r o c e s s i n g . A s a r e s u l t of t h e s e i n v e s t i g a t i o n s , b o t h t h e o r e t i c a l and numer ica l , a new t h i n n i n g method i s d e s c r i b e d and some of i t s p r o p e r t i e s a r e g iven . I n t r o d u c t i o n . When a document p roces s i n g system i s deve loped , s p e c i a l a t t e n t i o n has t o be p a i d t o low l e v e l p r o c e s s i n g a l g o r i t h m s . Even t h e most fundamental and well-known methodsneed p e r i o d i c r e e v a l u a t i o n i n o r d e r t o a d a p t them t o v a r y i n g p r a c t i c a l needs and t o c o n t i n u o u s l y deve lop ing computer a r c h i t e c t u r e s . The aim of t h i s p a p e r i s t o communicat e r e s u l t s of an i n v e s t i g a t i o n o f t h i n n i n g methods i n t h e c o n t e x t o f document p r o c e s s i n g and t o p r e s e n t a method which e x h i b i t s some f a v o u r a b l e propert i es w h i l e n o t s h a r i n g t h e d i sadvant a g e s o f o t h e r known approaches . The method was proposed by Ogawa and Taniguch i 171 and s p e c i f i c a l l y by Xia 1121. I ts t h e o r e t i c a l b a i s was l a i d by one o f t h e a u t h o r s 12 1 . I n document p r o c e s s i n g sys tems , t h e r e a r e two d i f f e r e n t a p p l i c a t i o n s of t h i n n i n g methods. F i r s t , i f t h e c o n t e n t of a (black-and-white) document is t h i n ned , t h e amount o f d a t a c o n t a i n e d i n it i s reduced w h i l e t h e i n f o r m a t i o n cont e n t i s ( n e a r l y ) t h e same a s b e f o r e . T y p i c a l l y , a t h i n n e d document c o n t a i n s o n l y 1 / 2 t o 1/10 a s much b l a c k p o i n t s a s t h e o r i g i n a l . Th is d a t a r e d u c t i o n is e s p e c i a l l y a t t r a c t i v e when more complex methods f o r image a n a l y s i s a r e cons ider e d . We mention h e r e t h e Hough-transform which can be used e .g . f o r f i n d i n g prominent d i r e c t i o n s i n o r d e r t o a l i g n a document. The e f f i c i e n c y of t h i s t r a n s f o r m s e v e r e l y depends on t h e numb e r of b l a c k p o i n t s i n t h e image. The second a p p l i c a t i o n f o r t h i n n i n g met h o d s i s t h e segmenta t ion o f o b j e c t s i n t h e image. Thinning t h e background y i e l d s c u r v e s s e p a r a t i n g t h e o b j e c t s l e t o n o f t h e image) . Together w i t h d i s t a n c e i n f o r m a t i o n one g e t s a l a r g e amount o f s t r u c t u r a l knowledge about t h e document. P r o p e r t i e s o f Thinning Methods. I f a t h i n n i n s method is i n t e n d e d f o r p r a c t i c a l use; it should be implemented i n par a l l e l s i n c e computing t i m e s become proh i b i t i v e w i t h s e q u e n t i a l implementat ions even f o r documents of o n l y moderate s i z e ( s e e e .g . 191) . Any p a r a l l e l t h i n n i n g method c o n s i s t s of two p a r t s , a t o p o l o g i c a l c r i t e r i o n f o r f i n d i n g c a n d i d a t e s f o r removal from t h e set of b l a c k p o i n t s and a mechanism f o r a v o i d i n g c o l l i s i o n s when removing p o i n t s i n p a r a l l e l . Assume t h a t t h e set o f b l a c k p o i n t s of a b i n a r y d i g i t a l p i c t u r e is equipped w i t h t h e 8-connect ion topo logy and t h e set o f w h i t e p o i n t s w i t h t h e 4-topology. The most g e n e r a l c r i t e r i o n f o r removing a b l a c k p o i n t ( i .e . changing i t s c o l o r t o w h i t e ) was g iven by Rosenfeld 181 : A b l a c k p o i n t i s a c a n d i d a t e f o r removal i f i t s c o l o r n e i t h e r i n f l u e n c e s t h e numb e r of b l a c k (8-) connec t ion components n o r t h e number of w h i t e ( 4 ) connec t ion components o f t h e image. I t was shown by Rosenfeld t h a t t h e q u e s t i o n whether a p o i n t i s a c a n d i d a t e f o r removal o r n o t can be d e c i d e d by i n s p e c t i o n of i t s 3 x 3-neighborhood i n t h e d i g i t a l p lane . Any p o i n t which meets t h i s c r i t e r i o n i s c a l l e d a s imple p o i n t 181. Some a u t h o r s (see e.g . 1141) p r e f e r t h e s o c a l l e d s t r i c t boundary p o i n t s i n s t e a d f o r t h i n n ing . These a r e s imple p o i n t s hav ing t h e p r o p e r t y t h a t i n a d d i t i o n a l s o t h e numb e r o f b l a c k 4-connect ion components is p r e s e r v e d by e l i m i n a t i n g them. Generall y it is a c c e p t e d t h a t end p o i n t s , i . e . b l a c k p o i n t s having o n l y one b l a c k (8-1 ne ighbor , a r e n o t removed under t h i n n ing . I n o r d e r t o avo id c o l l i s i o n s i n p a r a l l e l e l i m i n a t i o n , a number o f t e c h n i q u e s was proposed. These t e c h n i q u e s can be a p p l i e d independent ly o f t h e t o p o l o g i c a l c r i t e r i o n used. A l l t h e s e methods have i n common t h a t among t h e candidates p a s s i n g t h e t o p o l o g i c a l test o n l y a lAPR Workshop on CV Spedal Hardware and Industrial Applications OCT.12-14. 1988. Tokyo f r a c t i o n ( t y p i c a l l y one q u a r t e r o r one h a l f ) is a c t u a l l y e l i m i n a t e d . The f o l lowing approaches were p u b l i s h e d i n t h e l i t e r a t u r e : Four phase ENWS method. I n t h e f i r s t (second ... ) p h a s e of t h i s approach on ly c a n d i d a t e s a r e removed hav ing a whi te d i r e c t ne ighbor i n e a s t ( n o r t h ... ) d i r e c t i o n . Four phase method of K r e i f e l t s 161. A l l p o i n t s i n t h e d i g i t a l p l a n e a r e g i ven numbers 1 t o 4 a c c o r d i n g t o t h e scheme . . . . . . . . 1 3 . . . . 4 2 . . I n phase i o n l y p o i n t s having number i a r e a l lowed f o r d e l e t i o n . Two phase checkerboard method. Here, a l l p o i n t s i n t h e d i g i t a l p l a n e a r e g i ven c o l o r s e:g. r e d and green i n a checkerboardl ike manner. I n t h e f i r s t phase o n l y r e d p o i n t s and i n t h e se cond phase o n l y g reen p o i n t s a r e inves t i g a t e d . Two phase method o f R u t o v i t z . Th is method c a n b e fo rmula ted a s f o l l o w s 13 1 : I n t h e f i r s t phase o n l y p o i n t s hav ing a d i r e c t whi te neighbor i n e a s t o r n o r t h d i r e c t i o n a r e a l lowed f o r e l i mina t ion , i n t h e second phase p o i n t s w i t h w h i t e d i r e c t ne ighbors i n wes t o r s o u t h d i r e c t i o n a r e c o n s i d e r e d . A l l t h e s e methods a r e n o t i n v a r i a n t w i t h r e s p e c t t o t r a n s l a t i o n s of t h e d i g i t a l p l a n e ( K r e i f e l t s ' and t h e checkerbord methods) o r w i t h r e s p e c t t o 90 ' ro ta t ions o f t h e d i g i t a l p l a n e (ENWS and R u t o v i t z ' methods) . S t e i n p r e i s 1 10 1 i n v e s t i g a t e d e l e v e n met h o d s known from t h e l i t e r a t u r e . The r e s u l t o f S t e i n p r e i s ' paper i s t h a t t h e main d i f f e r e n c e s o f t h e methods c o n s i d e r e d i n h i s s t u d y w e r e a c t u a l l y d i f f e r e n c e s i n t h e implementat ion o f more o r less t h e same a l g o r i t h m . T h i s a g r e e s w i t h Tamura's f i n d i n g s 11 1 I . D e f i n i t i o n o f Requirements. From t h e i n v e s t i g a t i o n of e x i s t i n g methods f o r t h i n n i n g we a r r i v e a t a c a t a l o g u e of r e q u i r e m e n t s f o r an " i d e a l " t h i n n i n g method. Here, t h e t e r m " t h i n n i n g method" i s used f o r any combinat ion of an e l i m i n a t i o n c r i t e r i o n t o g e t h e r w i t h a mechanism f o r a v o i d i n g c o l l i s i o n s i n p a r a l l e l implementat ion. These r e q u i r e ments a r e : The method should be c o r r e c t , i .e. t h e s k e l e t o n o b t a i n e d by its a p p l i c a t i o n should have t h e same number of b l a c k and w h i t e connec t ion components a s t h e o r i g i n a l p i c t u r e . Indeed, some methods p u b l i s h e d i n t h e l i t e r a t u r e a r e n o t c o r r e c t (see e .g . 131) . The method should be w e l l d e f i n e d , i .e. any two d i f f e r e n t implementat ions of it should y i e l d i d e n t i c a l r e s u l t s . The method should be i n v a r i a n t w i t h r e s p e c t t o t r a n s l a t i o n s , r o t a t i o n s and r e f l e c t i o n s mapping t h e d i g i t a l p l a n e i n t o i t s e l f . Whereas t h e t o p o l o g i c a l c r i t e r i a e x h i b i t t h e s e i n v a r i a n c e s , t h e methods f o r c o l l i s i o n avoidance u s u a l l y a r e n o t comple te ly i n v a r i a n t ( s e e re marks above) . Davies and Plummer 11 I add t h e r e q u i rement t h a t it should be p o s s i b l e t o rec o n s t r u c t t h e o r i g i n a l image from t h e s k e l e t o n o b t a i n e d by t h i n n i n g i f t h e p o i n t s of t h e l a t t e r a r e l a b e l e d s o t h a t t h e y c a r r y d i s t a n c e in format ion . I f a method is n o t we l l -def ined o r i f it does n o t e x h i b i t t h e fundamental i n v a r i ances of t h e d i g i t a l p l a n e , t h e r e s u l t s of i t s a p p l i c a t i o n can o n l y be unders t o o d and i n t e r p r e t e d w i t h r e s p e c t t o a s p e c i f i c implementat ion and a s p e c i f i c p o s i t i o n o f t h e b i n a r y image under cons i d e r a t i o n w i t h i n t h e d i g i t a l p lane . So any p r a c t i c a l comparison whi th o t h e r m e t hods is made d i f f i c u l t ( i f n o t imposs i b l e ) by t h e s i d e e f f e c t s o f unknown magnitude caused by i n s u f f i c i e n t d e f i n i t i o n of t h e method under cons idera t i o n . The requ i rement o f r e c o n s t r u c t a b i l i t y h a s t o be handled d i f f e r e n t l y . On t h e one hand, any method w i t h t h e p r o p e r t y o f be ing i n v e r t i b l e a t l e a s t c a u s e s no l o s s o f i n f o r m a t i o n , and c e r t a i n l y no in format ion e s s e n t i a l f o r unders tand ing t h e image c o n t e n t i s d e s t r o y e d by it. On t h e o t h e r hand, any method f o r image p r o c e s s i n g n e c e s s a r i l y should reduce t h e raw image d a t a by e l i m i n a t i n g i r r e l e v a n t in format ion s i n c e u s u a l l y t h e amount of d a t a i s very huge. An I d e a l Method. On t h e b a s i s o f t h e in v e s t i g a t i o n s mentioned and o f a l a r g e number of numer ica l exper iments a method was chosen having f a v o u r a b l e prop e r t i e s and f u l f i l l i n g t h e requ i rements mentioned above. Th is method was propos e d by Ogawa and Taniguchi 17 1 and spec i f i c a l l y by Xia 1121. I t was reformul a t e d and some p r o p e r t i e s o f it were roved by t h e a u t h o r s ( 12 1 , 13 1 , 14 1 , 7 5 1 ) . The b a s i c concep t of t h e method i s t h e n o t i o n of a p e r f e c t p o i n t . A b l a c k p o i n t P i s termed D-perfect i f it has a d i r e c t ne ighbor which is an i n t e r i o r p o i n t of t h e set of a l l b l a c k p o i n t s ( i . e . a l l i t s f o u r d i r e c t ne ighbors a r e b l a c k ) and i f t h e d i r e c t ne ighbor oppos i t e t o t h e i n t e r i o r p o i n t is whi te : . X . . x b l a c k p o i n t x # P o o whi te p o i n t . x . . # i n t e r i o r p o i n t . A b l a c k p o i n t P is termed I p e r f e c t i f it h a s an i n d i r e c t ne ighbor which is an i n t e r i o r p o i n t and i f t h e i n d i r e c t neighbor of P which is o p p o s i t e t o t h e i n t e r i o r p o i n t i s whi te t o g e t h e r w i t h t h e d i r e c t ne ighbors o f it be ing a l s o d i r e c t ne ighbors o f P: