Geometrical Pattern Feature Extraction by Projection on Haar Orthonormal Basis

The c l a s s i f i c a t i o n o f a s e t o f p a t t e r n s i s a p rob lem t h a t appears i n v e r y many f i e l d s . I n g e n e r a l , the number o f p o s s i b l e c l asses i s unknown. To d e f i n e a d i s t a n c e ( o r s i m i l a r i t y ) m a t r i x on the s e t o f p a t t e r n s , we must summarize the a v a i l a b l e da te i n the fo rm o f a f i n i t e s e t o f f e a t u r e s w i t h an i n f o r m a t i o n l o s s as sma l l as p o s s i b l e . To e v a l u a t e d i s t a n c e c o e f f i c i e n t s , the b e s t i s t o p r o j e c t t he p a t t e r n on a t o t a l o r thono rma l b a s i s ; on the c o n d i t i o n of choos ing a base match ing the p a t t e r n p r o p e r t i e s wh ich concern t he c l a s s i f i c a t i o n prob lem to be s o l v e d . In the case o f geomet r i c p a t t e r n s where the d i s c o n t i n u i t i e s p l a y a n e s s e n t i a l r o l e , H a a r ! s d i s c o n t i n u o u s f u n c t i o n s appears to be v e r y p r o m i s i n g as shown in t h e g i v e n examples. Morever , Haa r ' s f u n c t i o n s are w e l l adapt e d t o d i g i t a l c o m p u t a t i o n .