Abstract: A progressive 3D triangular mesh compression algorithm built on the MOG-based Bayesian entropy coding and the gradual prediction scheme is proposed in this work. For connectivity coding, we employ MOG models to estimate the posterior probabilities of topology symbols given vertex geometries. Then, we encode the topology symbols using an arithmetic coder with different contexts, which depend on the posterior probabilities. For geometry coding, we propose the gradual prediction labeling and the dual-ring prediction to divide vertices into groups and predict later groups more efficiently using the information in already encoded groups. Simulation results demonstrate that the proposed algorithm provides significantly better performance than the conventional wavemesh coder, with the average bit rate reduction of about 16.9%.