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Spatiotemporal stereo matching has attracted much interest over the last few years. The problem is to maintain the temporally consistent disparity of video sequences and to avoid the flickering-artifacts occurring in consecutive disparity maps. In this paper, we propose a constant time spatiotemporal local stereo matching based on the information permeability method that was recently proposed and achieves good stereo results for static image pairs. The proposed three-pass aggregation method takes into account multiple preceding and following frames of the video instead of a single image pair as in the conventional method. Consequently, the temporal disparity consistency is enforced without requiring an explicit motion estimation as several spatiotemporal approaches have done. Experiments showed that our method improves the disparity consistency compared to the conventional information permeability method, and that it outperforms existing spatiotemporal stereo matching techniques.