Segmentation with area constraints

• Published in: Medical image analysis Vol. 17; no. 1; pp. 101 - 112
• Main Authors: Niethammer, Marc, Zach, Christopher
• Format: Journal Article
• Language: English
• Published: Netherlands Elsevier B.V 01.01.2013; Published by Elsevier B.V
• Subjects: Algorithms; Alternating direction method of multipliers; Area-constraint; Branch and bound; Humans; Image Processing, Computer-Assisted - methods; Segmentation; Area-constraint; Alternating direction method of multipliers; Segmentation; Branch and bound
• ISSN: 1361-8415; 1361-8423
• DOI: 10.1016/j.media.2012.09.002

[Display omitted] ► 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. 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.