A New Conceptually Attractive and Computationally Effective Approach to Shape from Shading

Abstract

A conceptually new, computationally simple approach to shape from shading is presented. It is assumed that objects of interest in 3-D space can be approximated by chunks of spheres, cylinders and planes, and that the formation of the true image can be modelled as the scattering from a Lambertian surface of light from a distant point source or distributed source. The observed image is modelled as this true image plus a white Gaussian perturbation. To permit parallel processing for computational speed, an image is partitioned into many small square windows (image patches) that can be processed simultaneously. It is assumed that a chunk of only one object type (plane, cylinder, sphere) is seen in a patch. Two kinds of results are presented. The first result is an algorithm for the recognition of the object type seen within a patch. This algorithm uses constrained 2-D quadric polynomial approximations to the picture function to implement true Bayesian recognitition. The second result is an algorithm for the estimation of the 3-space location (and orientation) of the recognized object seen within a patch. The image is thresholded with many pairs of thresholds and lines constrained to be parallel or ellipses constrained to have the same shapes and orientations are fit to the resulting swaths of data. Three-D location and orientation parameters are estimated from these statistics. The two algorithms are derived from a general formal statistical formulation of the shape from shading problem.