Convexity Shape Constraints for Image Segmentation
This work addresses the need for prior knowledge integration in segmentation for computer vision applications, offering a novel constraint-based method that is incremental in improving optimization accuracy.
The paper tackles the problem of incorporating convex shape constraints into image segmentation by extending the Minimum Cost Multicut Problem with convexity constraints and solving it optimally using a branch-and-cut ILP solver, achieving effectiveness and advantages over state-of-the-art heuristics on natural and biological images.
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.