Mumford-Shah Meets Stereo: Integration of Weak Depth Hypotheses

Recent results on stereo indicate that an accurate segmentation is crucial for obtaining faithful depth maps. Variational methods have successfully been applied to both image segmentation and computational stereo. In this paper we propose a combination in a unified framework. In particular, we use a Mumford-Shah-like functional to compute a piecewise smooth depth map of a stereo pair. Our approach has two novel features: First, the regularization term of the functional combines edge information obtained from the color segmentation with flow-driven depth discontinuities emerging during the optimization procedure. Second, we propose a robust data term which adoptively selects the best matches obtained from different weak stereo algorithms. We integrate these features in a theoretically consistent framework. The final depth map is the minimizer of the energy functional, which can be solved by the associated functional derivatives. The underlying numerical scheme allows an efficient implementation on modern graphics hardware. We illustrate the performance of our algorithm using the Middlebury database as well as on real imagery.