A Statistical Approach to Surface Shape Estimation *

A b s t r a c t . This paper is concerned with surface shape estimation by a method in which an empirically determined associative model relating appearance to surface shape is used. Significantly, the estimated model is more accurate than the algorithm that generates the examples. The method presented here is a generalization of shape from shading methods that does not rely upon idealized models of the image formation process. As a relative of shape from shading, this method more accurately recovers small surface detail than is possible with methods such as stereo and motion. The present approach is a continuous analogue of pattern recognition and is closely related to methods of joint space learning used in robotics. Experiments on real scenes are used to illustrate the concepts involved.