Binary Volume Optimization Based on Maximum a Posteriori-Markov Random Field

Many 3D reconstruction algorithms produce binary volume data. However, directly extracting iso-surfaces from them results in serious aliasing. To this end, we introduce a binary volume optimization method based on a maximum a posteriori-Markov random field（MAP-MRF）. We assume that the target values are random variables and have the Markov property. By maximizing their posteriori probability, we deduce a general optimization formula, as well as formulae in several special cases. Based on these formulae, users can choose different prior and observation models to predict the most possible data values, which is considered as optimal. Experimental results show that our method can be applied in visualization, smoothing, de-noising, and repairing.