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In the robotic domain, stereo vision is a popular technique for extracting 3-D depth information of a scene seen by two or more video cameras. The key problem is the matching task, which consists of identifying correspondences between features extracted from two stereo images. This paper presents a hierarchical neural approach for matching edges extracted from stereo linear images. The principle of the proposed method is to perform edge stereo matching at different levels with a neural network based procedure. At each level, the process starts by selecting edges with respect to their gradient magnitude. The selected edges are then matched in order to obtain reference pairs from which the remaining edges will be matched in the next level. In each level, the matching task is formulated as an optimization problem where an objective function, representing the constraints on the solution, is minimized thanks to a Hopfield neural network. To demonstrate its effectiveness, the hierarchical neural stereo matching method is evaluated for real-time obstacle detection in front of a moving vehicle.