Beyond Lambert: reconstructing surfaces with arbitrary BRDFs

We address an open and hitherto neglected problem in computer vision, how to reconstruct the geometry of objects with arbitrary and possibly anisotropic bidirectional reflectance distribution functions (BRDFs). Present reconstruction techniques, whether stereo vision, structure from motion, laser range finding, etc. make explicit or implicit assumptions about the BRDF. Here, we introduce two methods that were developed by re-examining the underlying image formation process; the methods make no assumptions about the object's shape, the presence or absence of shadowing, or the nature of the BRDF which may vary over the surface. The first method takes advantage of Helmholtz reciprocity, while the second method exploits the fact that the radiance along a ray of light is constant. In particular, the first method uses stereo pairs of images in which point light sources are co-located at the centers of projection of the stereo cameras. The second method is based on double covering a scene's incident light field; the depths of surface points are estimated using a large collection of images in which the viewpoint remains fixed and a point light source illuminates the object. Results from our implementations lend empirical support to both techniques.