Abstract

The shading pattern over a surface provides information about the shape of the surface. The problem of deriving shape from shading, however, is underconstrained. Current modeling solutions to the problem employ heuristic local constraints on shape, such as smoothness or the umbilical point approximation, in solving the problem. The approach taken here is to assume that the constraints are embodied in the statistical structure of natural surfaces. We apply a linear associative algorithm to learn a shape from shading operator from pairs of example surfaces and images. The training set is generated using a fractal model of natural surfaces. Images are represented as contrast values at each pixel, and surfaces are represented as surface normal vectors at each pixel. The learned operator consists of two spatially localized convolution filters for computing the x and y components of the surface normal at each pixel in an image. Application of these filters to novel images results in qualitatively good reconstructions. The model is insensitive to changes in incident light flux and may easily accommodate changes in light source direction by reorientation of the filters. Due to the spatial localization of the filters, very low-frequency changes in surface shape are lost in the reconstruction. This correlates well with human perception of shape from shading away from edges.

© 1987 Optical Society of America