Detection of broken ellipses by the hough transforms and multiresolutional images

Abstract

s of a r b i t r a r y shapes are mixed and c o n n e c t i v i t i e s of contours are missing completely due t o n o i s e and t h a t p a r t s of contours are l o s t due t o overlapping. The proposed algorithm i s based on t h e Merlin-Farber method, a kind of Hough transform, and t h e m u l t i r e s o l u t i o n a l images and t h e l e a s t -s q u a r e method are incorporated. Good d e t e c t i o n r e s u l t s were obtained i n t h e experiments implemented t o demonstrate t h e e f f e c t i v e n e s s of t h e proposed method. 1. I n t r o d u c t i o n One of t h e most fundamental tasks i n image r e c o g n i t i o n and image measurement i s t o d e t e c t a f i g u r e p a t t e r n of a s p e c i f i c shape from an image and t o measure i t s parameters such as l o c a t i o n , s i z e , and r o t a t i o n angle. Especially, i t i s a very important r e s e a r c h t o p i c t o e s t a b l i s h a f i g u r e detect i o n method which is i n v a r i a n t with r e s p e c t t o t h e Affine transform. W e can cope with i t by using a normalization procedure i n the case such as p r i n t e d c h a r a c t e r recognit i o n where f i g u r e segmentation i s r e l a t i v e l y easy. However, i n t h e r e c o g n i t i o n of genera l f i g u r e s , segmentation i s a p a r t of patt e r n d e t e c t i o n and t h i s makes t h e problem harder. r o b o t v i s i o n . Moreover, t h e d e t e c t i o n method of a r b i t r a r y e l l i p s e s i s a t y p i c a l one t h a t i s i n v a r i a n t with r e s p e c t t o t h e A f f i n e transform. Thus, i t i s expected t h a t by studying i t , w e may o b t a i n an approach toward t h e d e t e c t i o n method of g e n e r a l f i g u r e s . The problem i s To d e t e c t e l l i p s e p a t t e r n s , t r a d i t i o na l l y t h e Hough transform h a s been used [ 1-31. The Hough transform performs f i g u r e d e t e c t i o n by searching f o r a peak i n t h e histogram c o n s t r u c t e d i n t h e f i g u r e parameter space and h a s a f e a t u r e t h a t i t is strong a g a i n s t n o i s e [ 4 , 51. However, t h e e x i s t i n g e l l i p s e d e t e c t i o n methods r e q u i r e connected contours because they depend s t r o n g l y on t h e geometric p r o p e r t i e s of t h e e l l i p s e . Thus, they have t h e disadvantage t h a t they cannot d e t e c t those e l l i p s e s whose contours are missing considerably due t o n o i s e and overlapping. When contours are missing only because of overlapping, t h e method we proposed, which i s based on t h e l e a s t -s q u a r e method, can d e t e c t them [6]. However, t h e methods needed t o assume connectedness of remaining contours i n t h i s case, too. In t h i s paper, w e propose a new e l l i p s e d e t e c t i o n method which can cope w i t h such images where: (1) there are a number of e l l i p s e s of a r b i t r a r y shapes; (2) t h e connectedness of contours is l o s t completely because of n o i s e ; and (3) p a r t s of contou...

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