Matching Photometric Observation Vectors with Shadows and Variable Albedo

We describe a procedure to solve the basic problem of variable lighting photometric stereo - namely, recovering the normal directions and intrinsic albedos at all visible points of an opaque object, by analyzing three or more photos of the same taken with different illuminations. We follow the gauge-based approach, where the lighting conditions and light scattering properties of the surface are given indirectly by photographing a gauge object with known shape and albedo, under the same lighting conditions. Unlike previous solutions, our method yields reliable results even when some of the images contain cast shadows, penumbras, highlights, or inter-object lighting, at a cost. The cost of inner loop grows quadratically, (rather than exponentially) with the number m of input images. Usable approximations can be obtained in m log m time.