Segmentation with area constraints

Image segmentation approaches typically incorporate weak regularity conditions such as boundary length or curvature terms, or use shape information. High-level information such as a desired area or volume, or a particular topology are only implicitly specified. In this paper we develop a segmentation method with explicit bounds on the segmented area. Area constraints allow for the soft selection of meaningful solutions, and can counteract the shrinking bias of length-based regularization. We analyze the intrinsic problems of convex relaxations proposed in the literature for segmentation with size constraints. Hence, we formulate the area-constrained segmentation task as a mixed integer program, propose a branch and bound method for exact minimization, and use convex relaxations to obtain the required lower energy bounds on candidate solutions. We also provide a numerical scheme to solve the convex subproblems. We demonstrate the method for segmentations of vesicles from electron tomography images.

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► We develop a segmentation method that can include bounds on the desired segmentation area.
► We analyze the inherent problems with a standard relaxation approach to solve the area-constrained segmentation problem.
► We demonstrate the method for the segmentation of vesicles.
► We show improvements over various other segmentation methods.