A Simple Method for Recovering a Relative Depth Map in the Case of a Translating Sensor

When an o p t i c a l sensor t r a n s l a t e s a l o n g a known d i r e c t i o n I n a s t a t i o n a r y w o r l d the r e l a t i v e dep th map of o b j e c t p o i n t s on the s u r f a c e can be e a s i l y o b t a i n e d when some s i m p l i f y i n g assumpt ions a re made. Under these assumpt ions the angu la r speeds o f p r o j e c t i n g r a y s can be o b t a i n e d f rom ( a p p r o x i m a t i o n s t o ) t empora l and s p a t i a l d e r i v a t i v e s o f Image b r i g h t n e s s . The r e l a t i v e dep th o f any two image p o i n t s i s then d i r e c t l y computable as a s imp le r a t i o o f l i n e a r f u n c t i o n s o f t h e i r angu la r v e l o c i t i e s because the d i r e c t i o n s o f angu la r v e l o c i t i e s a re known i n t h i s s p e c i a l s i t u a t i o n .