Geotensity constraint for 3D surface reconstruction under multiple light sources

Abstract

We tackle the problem of 3D surface reconstruction by a single static camera, extracting the maximum amount of information from gray level changes caused by object motion under illumination by a fixed set of light sources. We basically search for the depth at each point on the surface of the object while exploiting the recently proposed Geotensity constraint [11] that accurately governs the relationship between four or more images of a moving object in spite of the illumination variance due to object motion. The thrust of this paper is then to ex- tend the availability of the Geotensity constraint to the case of multiple point light sources instead of a single light source. We first show that it is mathematically possible to identify multiple illumination subspaces for an arbitrary unknown number of light sources. We then propose a new technique to effectively carry out the separation of the subspaces by introducing the surface interaction matrix. Finally, we construct a framework for surface recovery, taking the multiple illumination subspaces into account. The theoretical propositions are investigated through experiments and shown to be practically useful.