Graph Cuts with Interacting Edge Costs - Examples, Approximations, and Algorithms

TL;DR

This paper extends the classical graph cut problem by incorporating submodular edge costs, exploring its complexity, proposing algorithms, and empirically comparing their performance across applications in signal processing, machine learning, and computer vision.

Contribution

It introduces the concept of cooperative graph cuts with submodular edge costs, analyzes their complexity, develops algorithms, and connects them to polymatroidal network flows.

Findings

Algorithms are empirically evaluated and compared.

The problem generalizes classical graph cuts with submodular costs.

Connections to polymatroidal network flows are established.

Abstract

We study an extension of the classical graph cut problem, wherein we replace the modular (sum of edge weights) cost function by a submodular set function defined over graph edges. Special cases of this problem have appeared in different applications in signal processing, machine learning, and computer vision. In this paper, we connect these applications via the generic formulation of "cooperative graph cuts", for which we study complexity, algorithms, and connections to polymatroidal network flows. Finally, we compare the proposed algorithms empirically.