Toward Reconstructing Surfaces With Arbitrary Isotropic Reflectance : A Stratified Photometric Stereo Approach

We consider the problem of reconstructing the shape of a surface with an arbitrary, spatially varying isotropic bidirectional reflectance distribution function (BRDF), and introduce a novel, stratified photometric stereo method. By using a particular configuration of lights, it is possible to use symmetry in the image measurements resulting from BRDF isotropy to estimate at each point a plane containing the surface normal. For differentiable surfaces, this allows us to recover the isocontours of the depth map, but not the actual depth associated with each contour. The isocontour structure provides topological information about the surface (critical points, Reeb graph, etc.). By using additional cues in the image data or imposing additional constraints on the surface (e.g., shadows, specular highlights, Helmholtz reciprocity, uniform BRDF), the unknown height of each isocontour can be estimated and the metric structure is resolved. We validate this technique on real and synthetic data by successfully recovering the isocontours of the depth map from images.