Parsimonious Labeling

TL;DR

This paper introduces parsimonious labeling, a new energy minimization framework that encourages minimal label usage in computer vision tasks, with an efficient graph-cuts algorithm providing strong solution guarantees.

Contribution

The paper proposes a novel energy functional based on diversity of labels and an efficient graph-cuts algorithm with theoretical guarantees for parsimonious labeling.

Findings

Outperforms existing graph-cuts methods on synthetic and real datasets.

Effectively captures minimal label solutions in vision tasks.

Provides a scalable and theoretically sound approach.

Abstract

We propose a new family of discrete energy minimization problems, which we call parsimonious labeling. Specifically, our energy functional consists of unary potentials and high-order clique potentials. While the unary potentials are arbitrary, the clique potentials are proportional to the {\em diversity} of set of the unique labels assigned to the clique. Intuitively, our energy functional encourages the labeling to be parsimonious, that is, use as few labels as possible. This in turn allows us to capture useful cues for important computer vision applications such as stereo correspondence and image denoising. Furthermore, we propose an efficient graph-cuts based algorithm for the parsimonious labeling problem that provides strong theoretical guarantees on the quality of the solution. Our algorithm consists of three steps. First, we approximate a given diversity using a mixture of a novel hierarchical $P^n$ Potts model. Second, we use a divide-and-conquer approach for each mixture component, where each subproblem is solved using an effficient $\alpha$-expansion algorithm. This provides us with a small number of putative labelings, one for each mixture component. Third, we choose the best putative labeling in terms of the energy value. Using both sythetic and standard real datasets, we show that our algorithm significantly outperforms other graph-cuts based approaches.