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A mesh-based approach to optimally and densely matching two epipolar row-rectified stereo images with small (even subpixel) maximal disparity is presented. It is a global matching approach that only requires specifying the size of the mesh to work with-no search windows, regions or other such typical heuristics are needed. We show how the parameters of the ordering constrained mesh are determined in an unconstrained manner via auxiliary parameterization. We illustrate algorithm performance on a real stereo pair.