Belief propagation (BP) is an effective algorithm for solving energy minimization problems in computer vision. However, it requires enormous memory, bandwidth, and computation because messages are iteratively passed between nodes in the Markov random field (MRF). In this paper, we propose two methods to address this problem. The first method is a message passing scheme called tile-based belief propagation. The key idea of this method is that a message can be well approximated from other faraway ones. We split the MRF into many tiles and perform BP within each one. To preserve the global optimality, we store the outgoing boundary messages of a tile and use them when performing BP in the neighboring tiles. The tile-based BP only requires 1-5 % memory and 0.2-1% bandwidth of the ordinary BP. The second method is an O(L) message construction algorithm for the robust functions commonly used for describing the smoothness terms in the energy function. We find that many variables in constructing a message are repetitive; thus these variables can be calculated once and reused many times. The proposed algorithms are suitable for parallel implementations. We design a low-power VLSI circuit for disparity estimation that can construct 440M messages per second and generate high quality disparity maps in near real-time. We also implement the proposed algorithms on a GPU, which can calculate messages 4 times faster than the sequential O (L) method. 1
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