Shape from specular reflection in calibrated environments and the integration of spatial normal fields

Reflections of a scene in a mirror surface contain information on its shape. This information is accessible by measurement through an optical metrology technique called deflectometry. The result is a field of normal vectors to the unknown surface having the remarkable property that it equally changes in all spatial directions, unlike normal maps occurring, e.g., in Shape from Shading. Its integration into a zero-order reconstruction of the surface thus deserves special attention. We develop a novel algorithm for this purpose which is relatively straightforward to implement yet outperforms existing ones in terms of efficiency and robustness. Experimental results on synthetic and real data complement the theoretical discussion.