A Continuous Max-Flow Approach to General Hierarchical Multi-Labeling Problems

John S. H. Baxter, Martin Rajchl, Jing Yuan, Terry M. Peters

Multi-region segmentation algorithms often have the onus of incorporating complex anatomical knowledge representing spatial or geometric relationships between objects, and general-purpose methods of addressing this knowledge in an optimization-based manner have thus been lacking. This paper presents Generalized Hierarchical Max-Flow (GHMF) segmentation, which captures simple anatomical part-whole relationships in the form of an unconstrained hierarchy. Regularization can then be applied to both parts and wholes independently, allowing for spatial grouping and clustering of labels in a globally optimal convex optimization framework. For the purposes of ready integration into a variety of segmentation tasks, the hierarchies can be presented in run-time, allowing for the segmentation problem to be readily specified and alternatives explored without undue programming effort or recompilation.

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