Stereo Matching Algorithm Using Belief Propagation

Belief Propagation (BP) is a graph model-based inference algorithm widely applied to stereo matching problems in computer vision. This algorithm iteratively updates message passing between adjacent nodes, eventually converging to the optimal solution of an energy function to produce high-precision disparity maps. In implementation, BP typically involves initializing message arrays and performing iterative updates using parallelizable operations.

The core objective of stereo matching is to find correct disparity values for corresponding pixels in left-right image pairs. Belief Propagation models this problem as a Markov Random Field (MRF), where each pixel corresponds to a node whose disparity selection is influenced by neighboring nodes. The energy function consists of data terms and smoothness terms—data terms represent matching costs between corresponding pixels through functions like Census transform or normalized cross-correlation, while smoothness terms enforce disparity continuity using Potts model or quadratic penalties.

Belief Propagation optimizes global energy through message passing. Each iteration involves nodes sending "messages" to neighbors, conveying confidence about disparity distributions. Message updates often follow the min-sum algorithm formula: m_ij(d_j) = min_di[V(d_i,d_j) + D(d_i) + Σ_k≠j m_ki(d_i)]. After convergence, nodes select disparities minimizing local energy via argmin operations.

Compared to local matching methods, BP-based algorithms effectively overcome mismatches in textureless regions and maintain smoothness at occlusion boundaries. However, computational complexity requires acceleration through multiscale strategies (e.g., pyramid processing) or parallel computing (GPU implementation). Recent improvements integrate deep learning for cost volume initialization or employ efficient message approximation like max-product or tree-reweighted methods.