^August September – 2008 ^October

Shape inference is a crucial part of image understanding and indeed many studies have addressed this problem in different ways over the years. However, when the object is specular, existing studies usually allow only spare reconstruction and have strong restrictions such as known or calibrated environment. We suggest a new approach for specular shape reconstruction when the environment is neither calibrated nor known. Furthermore unlike previous work, our approach considers general surfaces and allows dense reconstruction. We consider far-field illumination, where the object-environment distance is relatively large, and we examine the dense specular flow that is induced on the image plane through relative object-environment motion. We show that, under these very practical conditions, the observed specular flow can be related to surface shape through a pair of coupled nonlinear partial-differential equation, which we call the '3D shape from specular flow' equation. We show that by solving this equation one can recover the surface. Importantly, this relationship depends only on the environment's relative motion and not on its content. We present two novel reconstruction algorithms. The first one presents an analytic method for recovery of the shape under special environment rotation. In the second algorithm a specular surface is recovered in the presence of arbitrary environment motion. We show that by a linear combination of the observed specular flows we reduce the problem to the same special case that the first algorithm can solve. Finally, we discuss some numerical issues related to the suggested reconstruction algorithms and validate our results in several experiments.