Multi-Modal Mean-Fields via Cardinality-Based Clamping

Mean Field inference is central to statistical physics. It has attracted much interest in the Computer Vision community to efficiently solve problems expressible in terms of large Conditional Random Fields. However, since it models the posterior probability distribution as a product of marginal probabilities, it may fail to properly account for important dependencies between variables. We therefore replace the fully factorized distribution of Mean Field by a weighted mixture of such distributions, that similarly minimizes the KL-Divergence to the true posterior. By introducing two new ideas, namely, conditioning on groups of variables instead of single ones and using a parameter of the conditional random field potentials, that we identify to the temperature in the sense of statistical physics to select such groups, we can perform this minimization efficiently. Our extension of the clamping method proposed in previous works allows us to both produce a more descriptive approximation of the true posterior and, inspired by the diverse MAP paradigms, fit a mixture of Mean Field approximations. We demonstrate that this positively impacts real-world algorithms that initially relied on mean fields.Comment: Submitted for review to CVPR 201

Cellular automata segmentation of brain tumors on post contrast MR images

In this paper, we re-examine the cellular automata(CA) al- gorithm to show that the result of its state evolution converges to that of the shortest path algorithm. We proposed a complete tumor segmenta- tion method on post contrast T1 MR images, which standardizes the VOI and seed selection, uses CA transition rules adapted to the problem and evolves a level set surface on CA states to impose spatial smoothness. Val- idation studies on 13 clinical and 5 synthetic brain tumors demonstrated the proposed algorithm outperforms graph cut and grow cut algorithms in all cases with a lower sensitivity to initialization and tumor type