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Loopy belief propagation (BP) is an effective solution for assigning labels to the nodes of a graphical model such as the Markov random field (MRF), but it requires high memory, bandwidth, and computational costs. Furthermore, the iterative, pixel-wise, and sequential operations of BP make it difficult to parallelize the computation. In this paper, we propose two techniques to address these issues. The first technique is a new message passing scheme named tile-based BP that reduces the memory and bandwidth to a fraction of the ordinary BP algorithms without performance degradation by splitting the MRF into many tiles and only storing the messages across the neighboring tiles. The tile-wise processing also enables data reuse and pipeline, resulting in efficient hardware implementation. The second technique is an O(L) fast message construction algorithm that exploits the properties of robust functions for parallelization. We apply these two techniques to a very large-scale integration circuit for stereo matching that generates high-resolution disparity maps in near real-time. We also implement the proposed schemes on graphics processing unit (GPU) which is four-time faster than standard BP on GPU.