Convexity Shape Constraints for Image Segmentation

TL;DR

This paper introduces a novel method to incorporate convexity constraints into image segmentation models, enabling the segmentation of components with convex shapes and improving accuracy over existing heuristics.

Contribution

It extends the Minimum Cost Multicut Problem with convexity constraints and solves the resulting APX-hard ILP optimally using branch-and-cut techniques.

Findings

Effective convexity-constrained segmentation on natural images

Outperforms state-of-the-art heuristic methods

Applicable to biological image segmentation

Abstract

Segmenting an image into multiple components is a central task in computer vision. In many practical scenarios, prior knowledge about plausible components is available. Incorporating such prior knowledge into models and algorithms for image segmentation is highly desirable, yet can be non-trivial. In this work, we introduce a new approach that allows, for the first time, to constrain some or all components of a segmentation to have convex shapes. Specifically, we extend the Minimum Cost Multicut Problem by a class of constraints that enforce convexity. To solve instances of this APX-hard integer linear program to optimality, we separate the proposed constraints in the branch-and-cut loop of a state-of-the-art ILP solver. Results on natural and biological images demonstrate the effectiveness of the approach as well as its advantage over the state-of-the-art heuristic.