Takashi T o r i u , Hiromichi Iwase, and Toshiyuki Gotoh, Members P a t t e r n I n f o r m a t i o n P r o c e s s i n g Laboratory, F u j i t s u L a b o r a t o r i e s , L t d . , Kawasaki, Japan 211 SUMMARY A s a b i n a r i z a t i o n t h r e s h o l d s e l e c t i o n method t o u t i l i z e f u l l y edge i n f o r m a t i o n , a method h a s been proposed t o s e l e c t t h e t h r e s h o l d so t h a t t h e edge and boundary are a s c l o s e t o each o t h e r as p o s s i b l e . I n such a method, t h e b i n a r i z a t i o n a c t u a l l y is performed f o r v a r i o u s t h r e s h o l d v a l u e s , an.d t h e d e g r e e of c o i n c i d e n c e i s c a l c u l a t e d . Conseq u e n t l y , a v e r y l a r g e p r o c e s s i n g time i s r e q u i r e d . The d e g r e e of c o i n c i d e n c e i s def i n e d as t h e r a t i o between t h e number of boundary p o i n t s i n t h e edge r e g i o n t o t h e t o t a l number of boundary p o i n t s i n t h e image. The a u t h o r s have d e v i s e d a method which can determine w i t h a h i g h speed t h e number of boundary p o i n t s f o r each t h r e s h o l d witho u t a c t u a l l y performing t h e b i n a r i z a t i o n . In t h i s method, t h e r e s u l t of a p p l y i n g s h r i n k f i l t e r i n g a f t e r b i n a r i z a t i o n i s t h e same as t h a t of a p p l y i n g t h e b i n a r i z a t i o n w i t h t h e same t h r e s h o l d a f t e r a p p l y i n g t h e minimum f i l t e r i n g . By u t i l i z i n g t h i s p r o p e r t y , i t i s shown t h a t t h e d i f f e r e n c e of t h e c u m u l a t i v e h i s t ograms between t h e o r i g i n a l image and t h e res u l t of p r o c e s s i n g by t h e minimum f i l t e r is t h e same as t h e number of boundary p o i n t s f o r t h e t h r e s h o l d . Furthermore, t h e followi n g p r o p e r t y i s shown by e x t e n d i n g t h e method. The d e g r e e of c o i n c i d e n c e between t h e edge and t h e boundary i s d e f i n e d a s a two-variable f u n c t i o n of t h e t h r e s h o l d of edge d e t e c t i o n and t h e t h r e s h o l d of b i n a ri z a t i o n . Then i t i s shown that t h e d e g r e e of c o i n c i d e n c e between t h e two can be c a l c ul a t e d f o r any t h r e s h o l d w i t h o u t a c t u a l l y d e t e c t i n g t h e edges and boundaries. By u t i l i z i n g t h i s p r o p e r t y , n o t o n l y t h e t h r e s h o l d f o r b i n a r i z a t i o n of t h e
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.