On Shape and Material Recovery from Motion

We present a framework for the joint recovery of the shape and reflectance of an object with dichromatic BRDF, using motion cues. We show that four (small or differential) motions of the object, or three motions of the camera, suffice to yield a linear system that decouples shape and BRDF. The theoretical benefit is that precise limits on shape and reflectance recovery using motion cues may be derived. We show that shape may be recovered for unknown isotropic BRDF and light source. Simultaneous reflectance estimation is shown ambiguous for general isotropic BRDFs, but possible for restricted BRDFs representing commong materials like metals, plastics and paints. The practical benefit of the decoupling is that joint shape and BRDF recovery need not rely on alternating methods, or restrictive priors. Further, our theory yields conditions for the joint estimability of shape, albedo, BRDF and directional lighting using motion cues. Surprisingly, such problems are shown to be well-posed even for some non-Lambertian material types. Experiments on measured BRDFs from the MERL database validate our theory.