Finding corresponding edges is considered being the most difficult part of edge-based stereo matching algorithms. Usually, correspondence for a feature point in the first image is obtained by searching in a predefined region of the second image, based on epipolar line and maximum disparity. Reduction of search region can increase performances of the matching process, in the context of execution time and accuracy. Traditionally, hierarchical multiresolution techniques, as the fastest methods are used to decrease the search space and therefore increase the processing speed. Considering maximum of directional derivative of disparity in real scenes, we formulated some relations between maximum search space in the second images with respect to relative displacement of connected edges (as the feature points), in successive scan lines of the first images. Then we proposed a new matching strategy to reduce the search space for edge-based stereo matching algorithms. Afterward, we developed some fast stereo matching algorithms based on the proposed matching strategy and the hierarchical multiresolution techniques. The proposed algorithms have two stages: feature extraction and feature matching. We applied these new algorithms on some stereo images and compared their results with those of some hierarchical multiresolution ones. The execution times of our proposed methods are decreased between 30% to 55%, in the feature matching stage. Moreover, the execution time of the overall algorithms (including the feature extraction and the feature matching) is decreased between 15% to 40% in real scenes. Meanwhile in some cases, the accuracy is increased too. Theoretical investigation and experimental results show that our algorithms have a very good performance with real complex scenes, therefore these new algorithms are very suitable for fast edge-based stereo applications in real scenes like robotic applications.