This paper describes a stereo‐matching algorithm which works effectively even for a scene with a large number of discontinuities such as in the case of multiple interlaced surfaces. Prazdny [6] pointed out that the discontinuity can be handled by dissolving the ambiguity based on the facilitation by the similarity, rather than employing the discontinuity of disparity as the penalty. However, his method has a problem in that the ability to dissolve the ambiguity is decreased in correspondence to the reduction of scene restriction. In this paper, to determine the dispartity field maximizing the facilitation of similarity, several matching rules and matching primitives are combined, and the result is integrated into an energy‐minimum model of a network similar to Hopfield's neural network [7]. This resulted in a strong disambiguation power. Especially, we propose a new multiresolution processing method robust against discontinuity, in which processing of the different levels is in parallel. Only the information data concerning the image features corresponding to the same physical entity are propagated from the coarse to fine levels. By the reasonings in this paper, a natural extension is derived for the Marr‐Poggio first stereo algorithm [2]. An experiment was made for a scene through a fence, and it was verified that the interactions built in the network work effectively.