The goal of this study is to provide a theoretical framework for accurately optimizing the segmentation energy considering all of the possible shapes generated from the level-set-based statistical shape model (SSM). The proposed algorithm solves the well-known open problem, in which a shape prior may not be optimal in terms of an objective functional that needs to be minimized during segmentation. The algorithm allows the selection of an optimal shape prior from among all possible shapes generated from an SSM by conducting a branch-and-bound search over an eigenshape space. The proposed algorithm does not require predefined shape templates or the construction of a hierarchical clustering tree before graph-cut segmentation. It jointly optimizes an objective functional in terms of both the shape prior and segmentation labeling, and finds an optimal solution by considering all possible shapes generated from an SSM. We apply the proposed algorithm to both pancreas and spleen segmentation using multiphase computed tomography volumes, and we compare the results obtained with those produced by a conventional algorithm employing a branch-and-bound search over a search tree of predefined shapes, which were sampled discretely from an SSM. The proposed algorithm significantly improves the segmentation performance in terms of the Jaccard index and Dice similarity index. In addition, we compare the results with the state-of-the-art multiple abdominal organs segmentation algorithm, and confirmed that the performances of both algorithms are comparable to each other. We discuss the high computational efficiency of the proposed algorithm, which was determined experimentally using a normalized number of traversed nodes in a search tree, and the extensibility of the proposed algorithm to other SSMs or energy functionals.
Keywords: Branch-and-bound search; Computed tomography; Graph cuts; Segmentation; Statistical shape model.
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