The Implicit Constraints of the Primal Sketch

Abstract

Computational theories of structure-from-motion and stereo vision only specify the computation of three-dimensional surface information at points in the image at which the irradiance changes. Yet, the visual perception is clearly of complete surfaces, and this perception is consistent for different observers. Since mathematically the class of surfaces which could pass through the known boundary points provided by the stereo system is infinite and contains widely varying surfaces, the visual system must incorporate some additional constraints besides the known points in order to compute the complete surface. Using the image irradiance equation, we derive the surface consistency constraint, informally referred to as no news is good news. The constraint implies that the surface must agree with the information from stereo or motion correspondence, and not vary radically between these points. An explicit form of this surface consistency constraint is derived, by relating the probability of a zero-crossing in a region of the image to the variation in the local surface orientation of the surface, provided that the surface albedo and the illumination are roughly constant. The surface consistency constraint can be used to derive an algorithm for reconstructing the surface that "best" fits the surface information provided by stereo or motion correspondence.