Beyond Lambert: Reconstructing Surfaces with Arbitrary BRDFs

W e address a n open and hitherto neglected problem i n 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 f rom motion, laser range finding, etc. make explicit or implicit assumptions about the B R D F . Here, we introduce two methods that were developed by re-examining the underlying image formation process; the methods make n o assumptions about the object’s shape, the presence or absence of shadowing, o r . the nature of the B R D F 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. I n 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 f rom our implementations lend empirical support to both techniques.