Shape from Specular Flow with Near-Field Environment Motion Field

Reconstruction of curved, mirror-like surfaces in unknown lighting environments is a challenging problem. One well-known solution is the ‘shape from specular flow’ approach, which assumes far-field environment illumination. The assumption makes it impractical for the case of near-field environment. We show that with the presence of unknown nearby objects, the observed specular flow can be related to the surface shape and the environment motion through a group of nonlinear partial differential equations. This PDE system can be converted into a canonical form of hyperbolic equation. Stable, unique solution of such equation exists when the Cauchy boundary condition is given. Numerical methods are implemented to solve the PDE system for the case of translating near-field environment motions. Both the curved surface and the near-field environment are recovered. Experiments on both real and synthetic data support the proposed method.