Surface representation from photometric stereo with wavelets

Given multiple images of a diffuse surface taken from the same point of view, a photometric approach yields the surface normals which provide a good representation for a 1- 1 surface. This representation can be filtered and compressed using wavelets. In this work, two different applications based upon the wavelet approximations of the surface normals are presented. For the first application, surface reconstruction, compressed wavelet transforms of the images are used to reconstruct a surface. The surface shape is first interpolated from a 3D triangulated description, and then transformed into two and three images based solely upon the surface normals and the lighting direction. When the surface is compressed, the rational wavelets used in integrating the surface can produce singularities. A technique for handling compression of rational wavelets is presented. The second application is object differentiation, a subset of object recognition. The surface normals are used to derive the Gaussian curvature of an object. The Gaussian curvature is used as a primitive for classification. The actual object signature comes from the high magnitude coefficients in the Haar wavelet decomposition. By storing a library of objects indexed by extreme wavelet coefficients as opposed to the object name, a fast query can be performed to find a list of possible matches.