A Simplified And Fast Version Of The Huockel Operator For Finding Optimal Edges in Pictures

A s i m p l i f i e d v e r s i o n o f t h e H u e c k e l oper a t o r was w o r k e d o u t t o p r e s e r v e a l l t h e a d v a n t a g e s o f t h e o r i g i n a l one w i t h a r u n n i n g t i m e c o n s i d e r a b l y s h o r t e r . I t s c o n c e p t i s based o n t h e r e i n t e r p r e t a t i o n o f t h e H u e c k e l o p e r a t o r a s a t e m p l a t e m a t c h i n g method. T h i s r e i n t e r p r e t a t i o n r e n d e r s some t h e o r e t i c a l and c o m p u t a t i o n a l s i m p l i f i c a t i o n s p o s s i b l e . A s a r e s u l t , a n o p t i m a l edge-shaped t e m p l a t e i s c o n s t r u c t e d b y l i n e a r c o m b i n a t i o n o f two s u i t a b l y chosen o r i g i n a l ones. The p a r a m e t e r s o f t h i s o p t i m a l t e m p l a t e c h a r a c t e r i z e t h e edge segment f o u n d i n a p i c t u r e a r e a . I n t r o d u c t i o n H u e c k e l ' s o p e r a t o r f o r edge d e t e c t i o n i n p i c t u r e s i s one o f t h e b e s t t o o l s w h i c h have been i n v e n t e d f o r t h i s k i n d o f t a s k s . I n v e r y n o i s y p i c t u r e s i t s h i g h e f f e c t i v e ness can b e c o m p a r a b l e o n l y w i t h t h e g l o b a l o p t i m i z a t i o n p r o c e d u r e s e . g . b y Mont a n a r i and M a r t e l l i ( 8 ) , ( 9 ) , b u t w i t h o u t t h e i r drawbacks i n p r o c e s s i n g t i m e and memory r e q u i r e m e n t . The H u e c k e l o p e r a t o r p r o c e s s e s a p i c t u r e b l o c k c o n t a i n i n g 5 2 p o i n t s on PDP-10 i n 10 msec, e. g. i f i t scanned f o r example a 2,56 by 256 p o i n t p i c t u r e s o t h a t t h e b l o c k s o v e r l a p b y one t h i r d s o f each o t h e r , t h e p r o c e s s i n g t i m e w o u l d be a b o u t 40 seconds. Of c o u r s e , by means o f s o p h i s t i c a t e d e d g e f o l l o w i n g met h o d s t h i s t i m e can b e r e d u c e d s i g n i f i c a n t l y , t h u s t h e a p p l i c a b i l i t y o f t h i s o p e r a t o r i s n o t beyond t h e p o s s i b i l i t i e s t o p r o c e s s a r e a l p i c t u r e . These 10 msec a r e , however, r a t h e r l a r g e t o l o o k f o r some m o d i f i c a t i o n s based o n i t s b a s i c i d e a t o speed u p t h e o p e r a t i o n , even b y p o s s i b l e s i m p l i f i c a t i o n s w h i c h p r e s e r v e t h e e x c e l l e n t p r o p e r t i e s o f t h e o r i g i n a l one. I n t h i s p a p e r w e p r e s e n t a method a i m i n g a t t h i s b y r e i n t e r p r e t i n g t h e p r i n c i p l e o f t h e H u e c k e l o p e r a t o r and g i v i n g a m o d i f i c a t i o n o f i t based o n o u r i n t e r p r e t a t i o n . H u e c k e l ' s method i n i t s o r i g i n a l f o r m The o r i g i n a l i n t e r p r e t a t i o n o f t h e H u e c k e l o p e r a t o r can be summarized as f o l l o w s : a/ We seek f o r a f u n c t i o n S on a D a r e a in t h e i n p u t p i c t u r e , w h i c h f u n c t i o n has a c o n s t a n t b v a l u e on one s i d e and