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Most dense stereo correspondence algorithms start by establishing discrete pixel matches and later refine these matches to sub-pixel precision. Traditional sub-pixel refinement methods attempt to determine the precise location of points, in the secondary image, that correspond to discrete positions in the reference image. We show that this strategy can lead to a systematic bias associated with the violation of the general symmetry of matching cost functions. This bias produces random or coherent noise in the final reconstruction, but can be avoided by refining both image coordinates simultaneously, in a symmetric way. We demonstrate that the symmetric sub-pixel refinement strategy results in more accurate correspondences by avoiding bias while preserving detail.