This paper introduces a fast and reliable Belief Propagation based stereo matching algorithm to be equipped with mobile real-time stereo vision applications; such as autonomous navigation of robots, vehicles, UAVs and drones, mobility aid for visually impaired, and more.. The algorithm approximates the minimum energy solution on graphical Markov Chains based on intensities of consecutive stereo image scanlines. It can achieve real-time performance (30 frames per seconds) while maintaining accurate results. This algorithm can also produce reliable results under non-ideal environments. It is obtained by estimating unknown factors to deal with brightness, color offsets, and vertical misalignments between two images. These factors are the ones to minimize the energy passed through the Markov chain model at the centers of stereo images.