field (CRF) and Bayesian network (BN), which has a clear statistical interpretation as the MAP estimate of a multi-class labeling problem. Given the graphical model structure, we derive the probability distribution of the model based on the factorization property implied in the model structure. The statistical model leads to an energy function that can be optimized approximately by either loopy belief propagation or graph cut based move making algorithm. We demonstrate the application of the pro- posed graphical model on the task of multi-class classification of building facade image regions.