Minimal Surfaces for Stereo

Abstract

Determining shape from stereo has often been posed as a global minimization problem. Once formulated, the minimization problems are then solved with a variety of algorithmic approaches. These approaches include techniques such as dynamic programming min-cut and alpha-expansion. In this paper we show how an algorithmic technique that constructs a discrete spatial minimal cost surface can be brought to bear on stereo global minimization problems. This problem can then be reduced to a single min-cut problem. We use this approach to solve a new global minimization problem that naturally arises when solving for three-camera (trinocular) stereo. Our formulation treats the three cameras symmetrically, while imposing a natural occlusion cost and uniqueness constraint.KeywordsMinimal SurfaceUniqueness ConstraintDual GraphPrimal GraphSpatial ComplexThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.