Variational stereo matching with left right consistency constraint

Variational methods are one of the most useful techniques for stereo matching. Those methods usually take the following pipeline: first, the disparity is embedded in a functional; second, minimizing the functional is converted to solve an Euler-Lagrange(EL) function; third, fix point algorithm or other numerical algorithms are used to solve the EL function in a digital computer. If the functional is not convex, the solution easily bias towards a local minimal solution. Our work in this paper is to alleviate these biases. We model the disparity function in a maximum a posteriori(MAP) continuous Markov random field(MRF) framework and a symmetric functional is then deduced. In such a functional, more constraints can be applied to restrict the solution space. Left-right consistency constraints is introduced as a prior energy in our functional. Experiments on the test images from the Middlebury website show that the proposed functional gives less biases than the previously used one.