Parallel relaxation computations such as those of connectionist networks offer a useful model for constraint integration and intrinsic image combination in developing a general-purpose stereo matching algorithm. This paper describes such a stereo algorithm that incorporates hierarchical, surface structure and edge appearance constraints that are redefined and are integrated at the level of individual candidate matches. The algorithm produced a high percentage of correct decisions on a wide-variety of stereo pairs. Its few errors arose when the correlation measures defined by the constraints were either weakened, or ambiguous, as in the case of periodic patterns in the images. Two additional mechanisms are discussed for overcoming the remaining errors. First, an independent estimate of disparity, obtained through a depth-from-focus algorithm, can resolve the ambiguity in periodic regions. Second, a third image, taken from a position above the left image, is incorporated into matching. This is accomplished by defining matches between the new image and the left image, and relating the new and old matches through new constraints. Both of the new approaches are easily easily incorporated into the connectionist network computations of the original algorithm.