A Graph Multi-separator Problem for Image Segmentation

TL;DR

This paper introduces the multi-separator problem as a new combinatorial optimization framework for image segmentation, providing efficient solutions for special cases and effective algorithms for complex scenarios.

Contribution

It formulates a novel multi-separator problem for image segmentation, contrasting it with existing models, and develops algorithms with demonstrated effectiveness on simulated data.

Findings

Efficient solutions for two special cases of the multi-separator problem.

Two local search algorithms effectively segment simulated volume images.

The multi-separator framework offers a new perspective on image segmentation tasks.

Abstract

We propose a novel abstraction of the image segmentation task in the form of a combinatorial optimization problem that we call the multi-separator problem. Feasible solutions indicate for every pixel whether it belongs to a segment or a segment separator, and indicate for pairs of pixels whether or not the pixels belong to the same segment. This is in contrast to the closely related lifted multicut problem where every pixel is associated to a segment and no pixel explicitly represents a separating structure. While the multi-separator problem is NP-hard, we identify two special cases for which it can be solved efficiently. Moreover, we define two local search algorithms for the general case and demonstrate their effectiveness in segmenting simulated volume images of foam cells and filaments.