We present a convex optimization approach to dense stereo matching in computer vision. Instead of directly solving for disparities of pixels, by establishing the connection between a permutation matrix and a disparity vector, we are able to formulate stereo matching as a continuous convex quadratic program without performing complicated relaxations or approximations on the objective function. When disparity is modeled as a discrete random variable, the theoretical foundation of our approach can be analyzed from the perspective of probability theory. Our convex optimization framework supports adaptive correlation windows and can be implemented using CVX, the Matlab software for disciplined convex programming, in a straightforward manner. Furthermore, effective techniques for disparity refi...[ Read more ]

We present a convex optimization approach to dense stereo matching in computer vision. Instead of directly solving for disparities of pixels, by establishing the connection between a permutation matrix and a disparity vector, we are able to formulate stereo matching as a continuous convex quadratic program without performing complicated relaxations or approximations on the objective function. When disparity is modeled as a discrete random variable, the theoretical foundation of our approach can be analyzed from the perspective of probability theory. Our convex optimization framework supports adaptive correlation windows and can be implemented using CVX, the Matlab software for disciplined convex programming, in a straightforward manner. Furthermore, effective techniques for disparity refinement, which include an occlusion detection algorithm performed on a single disparity map that takes advantage of the valuable information provided by the permutation matrix, and a plane fitting method mainly based on minimizing the l₁ norm of the disparity errors caused by a disparity plane, are also proposed. Experimental results show that by minimizing our convex objective function and applying the proposed disparity refinement techniques, we are able to generate good quality disparity maps.