# A Graph Multi-separator Problem for Image Segmentation

arXiv: https://arxiv.org/abs/2307.04592 · HTML: https://mlsanity.com/paper/2307.04592/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 66 references that are in the map.
- First posted on arXiv 10 Jul 2023.

## Builds on (most cited first, 12 of 12)

- [Image Segmentation Using Deep Learning: A Survey](https://mlsanity.com/paper/2001.05566/) (2020)
- [Relationformer: A Unified Framework for Image-to-Graph Generation](https://mlsanity.com/paper/2203.10202/) (2022)
- [Lifted Disjoint Paths with Application in Multiple Object Tracking](https://mlsanity.com/paper/2006.14550/) (2020)
- [InstanceCut: from Edges to Instances with MultiCut](https://mlsanity.com/paper/1611.08272/) (2016)
- [Efficient Decomposition of Image and Mesh Graphs by Lifted Multicuts](https://mlsanity.com/paper/1505.06973/) (2015)
- [Higher-Order Minimum Cost Lifted Multicuts for Motion Segmentation](https://mlsanity.com/paper/1704.01811/) (2017)
- [Learning and Segmenting Dense Voxel Embeddings for 3D Neuron Reconstruction](https://mlsanity.com/paper/1909.09872/) (2019)
- [Higher-order Segmentation via Multicuts](https://mlsanity.com/paper/1305.6387/) (2013)
- [Multicuts and Perturb & MAP for Probabilistic Graph Clustering](https://mlsanity.com/paper/1601.02088/) (2016)
- [Coalition Structure Generation over Graphs](https://mlsanity.com/paper/1401.6428/) (2014)
- [Uncertainty in Minimum Cost Multicuts for Image and Motion Segmentation](https://mlsanity.com/paper/2105.07469/) (2021)
- [A Polyhedral Study of Lifted Multicuts](https://mlsanity.com/paper/2202.08068/) (2022)

## Built on by (most cited first, 1 of 1)

- [The canonical facets of multi-separator polytopes](https://mlsanity.com/paper/2608.16861/) (2026)

## Abstract (arXiv)

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.