Identification Of Bodies in A Contour Image Of A Three-Dimensional Scene

The problem of i d e n t i f y i n g bodies on a contour image of a three-dimensional scene is s t a t e d as f o l l o w s (see, eg.g. I ) . A l i s t of t h e contour image r e gions i s g i v e n (each r e g i o n i s assumed to be associated w i t h an surface or p a r t of a surface of a three-dimensional body). The l i s t should be decomposed i n t o s u b l i s t s each c o n t a i n i n g a l l r e gions of one and only one body. There are a number of h e u r i s t i c a l g o r i t h m s f o r body i d e n t i f i c a t i o n ( 2 ) . To f o r m u l a t e the o b j e c t i v e o f t h i s research two s p e c i f i c f e a t u r e s of almost a l l these a l g o r i t h m s should b e noted. The f i r s t i s t h a t the source data i s i n f o r m a t i o n on t h e neighborhood of the r e g i o n s , on types of g r a p h i c a l t r a c i n g of t h e nodes and on p r o p e r t i e s of l a r g e segments o f l i n e s ( p a r a l l e l i s m coincidence of l i n e s when t h e segments are extended, e t c . ) . The need in data on l a r g e segments of l i n e s imposes r a t h e r s t r i n g e n t c o n s t r a i n t s o n the q u a l i t y o f t h e contour image t h a t i n r e a l l i f e f o l l o w from t h e h a l f tone i n i t i a l image of the scene. The second s p e c i f i c f e a t u r e i s u n c e r t a i n t y of image classes to which these a l g o r i t h m s are a p p l i c a b l e . A n a l gorithm i s o f t e n found t o b e a p p l i c a b l e to very complex images but may n o t work i n s i m p l e r cases. T o i d e n t i f y and describe an image c l a s s i s d i f f i c u l t because t h e correspondence between the image, e.g. types of the node t r a c i n g , and types of o b j e c t combination in space i s not u n i v a l e n t . The o b j e c t i v e o f t h i s paper i s t o enable a researcher to i s o l a t e a c l a s s o f images associated w i t h c e r t a i n simple types o f o b j e c t combination i n space and develop f o r t h i s c l a s s a body i d e n t i f i c a t i o n procedure which would use only t h e i n f o r m a t i o n on which regions are n e i g h b o r i n g and on the types of g r a p h i c a l t r a c i n g of nodes. J e t t i s o n i n g the data on p r o p e r t i e s of l a r g e segments of l i n e s n e c e s i t a t e s f o r m u l a t i o n o f f u r t h e r c o n s t r a i n t s o n the c l a s s of images to be analyzed. This c o n s t r a i n t s are caused by the p o s s i b i l i t y o f e s s e n t i a l shortage o f l o c a l data f o r s o l u t i o n o f the problem posed r a t h e r than by the above nonunlvalence of the space mapping on the p l a n e . I t w i l l be assumed h e r e i n a f t e r t h a t t he i n i t i a l c o ntour image corresponds to a c o n f i g u r a t i o n of convex bodies w i t h f l a t s u r f a c e s . Each body can be represent e d i n a p r o j e c t i o n o f any form w i t h the s o l e c o n s t r a i n t t h a t n o p a i r o f the image l i n e segment a s s o c i a t e d w i t h two edges of one body merge i n t o one l i n e . We w i l l assume t h a t t h e e n t i r e i n i t i a l i n f o r m a t i o n i s g i v e n a s a l i s t o f r e gions w i t h i n d i c a t i o n o f t h e i r neighborhood and a l i s t of nodes w i t h i n d i c a t i o n o f t h e type of g r a p h i c a l t r a c i n g of each node and i t s belonging to a c e r t a i n r e g i o n . The paper c o n s i s t s of t h r e e sections, Sect. I describes the c l a s s of images to be discussed and l i s t s t h e p r o p e r t i e s o f