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The focus of this paper is on real-time obstacle detection using linear stereo vision. This paper presents a multilevel neural method for matching edges extracted from stereo linear images. The method described performs edge stereo matching at different levels with a neural-network-based procedure. At each level, the process starts by selecting, in the left and right linear images, the most significant edges, i.e., those with the largest gradient magnitudes. The selected edges are then matched and the obtained pairs are used as reference pairs for matching less significant edges in the next level. In each level, the matching problem is formulated as an optimization task in which an objective function, representing the constraints on the solution, is minimized thanks to a Hopfield neural network.