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 extend 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.