THE Z-HYPOTHESIS OR HOW CAN WE STEP OVER “NO-MAN’S LAND”

((J. Geier)) Eotvos Lorand University, Budapest, Hungary

Purpose. I present a correlation type computational model and a computer simulation for solving the stereo matching problem, in particular the perception of no-man's lands (ie. the points in the left retina that have no pairs in the right retina, or vice versa). Methods. The goal of all well-known models is first to find a match between the left and right retina (ie. matching two 2D images), and only when this step is completed, then to make the depth computation (ie. going to 3D). Because of the "2D-consideration" these algorithms give bad matching for the points in no-man's land, and each algorithm must therefore seek further constraints for resolving these ambiguities (Marr & Poggio 1979, Frisby & Pollard 1991). My algorithm begins with an (x,y,z) 3D point (direction of x axis is to the right, y is upward, and z is backward; -z is the depth). While x and y are fixed, we choose a z value (z-hypothesis), we project the (x,y,z) point to the left and right retina, and then compute the similarity (or correlational type) measure between the two windows constructed around the projected points. The best z-hypothesis will be the z value that gives the best similarity. This is equivalent to solving a one-dimensional minimum problem for z, at each fixed (x,y) point. The similarity measure is the same as that which was presented in Geier (1993, ARVO'93/2370). Results. The computer algorithm has been tested on real-life images and computer generated RDS's. The matching is correct at each 3D point. Conclusions. The model gives sufficient explanation for human stereo vision that are connected with perception of no-man's lands. The algorithm steps over the no-man's lands, without need for further constraints.

Supported by OTKA 2207 and MAKA J.F. no. 360.