Robust Estimation of Shape from Shading

Abstract

We have developed a solution to the problem of obtaining robust estimates of surface orientation from local analysis of shading. By robust we mean an algorithm that can cope with general, but realistic, assumptions about local surface geometry, in order to be tolerant of image noise and of imprecise estimates of light source direction. It is based on the minimization of a residual form that measures the total deviation from an implicit model of surface curvature. This model is similar to the one used by [3,6,7] in local estimation of shape from shading, but it is less restrictive. In fact, one may view our procedure as a second stage of processing that interprets these local estimates of shape subject to constraints about how the (differential) geometry of the surface can change between neighbouring estimates. Our experiments show that the algorithm not only improves the noise immunity of the local method, but also "undoes" some of the distortion that is incurred as a result of assumptions in the local shading model [3]. Practical machine vision applications based on this approach are a possibility given the development of low-cost parallel processing hardware.