Fast and Exact: ADMM-Based Discriminative Shape Segmentation with Loopy Part Models

In this work we use loopy part models to segment ensembles of organs in medical images. Each organ´s shape is represented as a cyclic graph, while shape consistency is enforced through inter-shape connections. Our contributions are two-fold: firstly, we use an efficient decomposition-coordination algorithm to solve the resulting optimization problems: we decompose the model´s graph into a set of open, chain-structured, graphs each of which is efficiently optimized using Dynamic Programming with Generalized Distance Transforms. We use the Alternating Direction Method of Multipliers (ADMM) to fix the potential inconsistencies of the individual solutions and show that ADMM yields substantially faster convergence than plain Dual Decomposition-based methods. Secondly, we employ structured prediction to encompass loss functions that better reflect the performance criteria used in medical image segmentation. By using the mean contour distance (MCD) as a structured loss during training, we obtain clear test-time performance gains. We demonstrate the merits of exact and efficient inference with rich, structured models in a large X-Ray image segmentation benchmark, where we obtain systematic improvements over the current state-of-the-art.