Disparity Estimation Based on Bayesian Maximum A Posteriori (MAP) Algorithm∗

In this paper, a general formula of disparity estimation based on Bayesian Maximum A Posteriori (MAP) algorithm is derived and implemented with simplified probabilistic models. The formula is the generalized probabilistic diffusion equation based on Bayesian model, and can be implemented into some different forms corresponding to the probabilistic models in the disparity neighborhood system or configuration. The probabilistic models are independence and similarity among the neighboring disparities in the configuration. The independence probabilistic model guarantees the discontinuity at the object boundary region, and the similarity model does the continuity or the high correlation of the disparity distribution. According to the experimental results, the proposed algorithm had good estimation performance. This result showes that the derived formula generalizes the probabilistic diffusion based on Bayesian MAP algorithm for disparity estimation. Also, the proposed probabilistic models are reasonable and approximate the pure joint probability distribution very well with decreasing the computations to O(n(D)) from O(n(D)) of the generalized formula. key words: disparity estimation, Bayesian maximum a posteriori (MAP) algorithm, Markov random field, plane configuration model, probabilistic diffusion