title: Shape complexes: the intersection of label orderings and star convexity constraints in continuous max-flow medical image segmentation.
abstract: Optimization-based segmentation approaches deriving from discrete graph-cuts and continuous max-flow have become increasingly nuanced, allowing for topological and geometric constraints on the resulting segmentation while retaining global optimality. However, these two considerations, topological and geometric, have yet to be combined in a unified manner. The concept of "shape complexes," which combine geodesic star convexity with extendable continuous max-flow solvers, is presented. These shape complexes allow more complicated shapes to be created through the use of multiple labels and super-labels, with geodesic star convexity governed by a topological ordering. These problems can be optimized using extendable continuous max-flow solvers. Previous approaches required computationally expensive coordinate system warping, which are ill-defined and ambiguous in the general case. These shape complexes are demonstrated in a set of synthetic images as well as vessel segmentation in ultrasound, valve segmentation in ultrasound, and atrial wall segmentation from contrast-enhanced CT. Shape complexes represent an extendable tool alongside other continuous max-flow methods that may be suitable for a wide range of medical image segmentation problems.
authors.affiliation: Western University, Robarts Research Institute, 1151 Richmond Street N., London, Ontario N6A 5B7, Canada; Western University, Biomedical Engineering Graduate Program, 1151 Richmond Street N., London, Ontario N6A 5B7, Canada.
authors.forename: John S H
authors.initials: JS
authors.lastname: Baxter
authors.affiliation: Western University , Robarts Research Institute, 1151 Richmond Street N., London, Ontario N6A 5B7, Canada.
authors.forename: Jiro
authors.initials: J
authors.lastname: Inoue
authors.affiliation: Western University, Robarts Research Institute, 1151 Richmond Street N., London, Ontario N6A 5B7, Canada; Western University, Biomedical Engineering Graduate Program, 1151 Richmond Street N., London, Ontario N6A 5B7, Canada.
authors.forename: Maria
authors.initials: M
authors.lastname: Drangova
authors.affiliation: Western University, Robarts Research Institute, 1151 Richmond Street N., London, Ontario N6A 5B7, Canada; Western University, Biomedical Engineering Graduate Program, 1151 Richmond Street N., London, Ontario N6A 5B7, Canada.
authors.forename: Terry M
authors.initials: TM
authors.lastname: Peters
keywords: ASETS library; continuous max-flow segmentation; convex optimization; optimization-based segmentation; star convexity constraint