Tracking Level Sets by Level Sets: A Method for Solving the Shape from Shading Problem

Abstract

A new algorithm for recovering depth to a Lambertian L 1 smooth object given its gray-level image under uniform illumination from the viewing direction is presented. To recover depth, an almost arbitrarily initialized surface is numerically propagated on a rectangular grid, so that a level set of this surface tracks the height contours of the depth function. The image shading controls the propagation of the surface. When the light direction is tilted with respect to the viewing direction the problem is solved by tracking the projection of equal-height contours defined with respect to the light source direction. This projection approach provides a solution that overcomes ambiguity problems encountered in previous work, while the level set approach of implementing the contour propagation overcomes numerical problems and some of the topology problems of the evolving contours.