Superpixel-Based Image Segmentation Using Squared 2-Wasserstein Distances

TL;DR

This paper introduces a novel image segmentation method that uses squared 2-Wasserstein distances within a two-level clustering framework, improving accuracy in challenging images while maintaining efficiency.

Contribution

The method uniquely employs a distributional optimal transport distance for superpixel merging, unifying the segmentation process mathematically and enhancing performance.

Findings

Improved segmentation accuracy on challenging images.

Maintains high computational efficiency.

Unifies clustering levels through optimal transport distances.

Abstract

We present an efficient method for image segmentation in the presence of strong inhomogeneities. The approach can be interpreted as a two-level clustering procedure: pixels are first grouped into superpixels via a linear least-squares assignment problem, which can be viewed as a special case of a discrete optimal transport (OT) problem, and these superpixels are subsequently greedily merged into object-level segments using the squared 2-Wasserstein distance between their empirical distributions. In contrast to conventional superpixel merging strategies based on mean-color distances, our framework employs a distributional OT distance, yielding a mathematically unified formulation across both clustering levels. Numerical experiments demonstrate that this perspective leads to improved segmentation accuracy on challenging images while retaining high computational efficiency.