Ordinal and metric structure of smooth surfaces from parallax

The work presented in this paper is a first attempt at evaluating an ordinal representation for the local shape of smooth surface patches. To this end we investigate the reliability of estimating the tilt and slant components of the local surface orientation from binocular parallax. This is of interest because parallax is a commonly used cue, but has not been evaluated as to its susceptibility to image measurement errors. Our theoretical sensitivity analysis shows that the tilt is less sensitive than the slant to errors in the estimation of the viewing geometry, but that image measurement errors affect both slant and tilt seriously. In view of these results, it can not be claimed that the tilt is more reliably estimated from parallax than the slant. Despite the discovered sensitivity to image measurement errors, the tilt remains a very useful piece of information, in that it still specifies partial ordinal relations even when substantially degraded. We present a simple and efficient method to keep track of such partial information during all ongoing computation.