Parallel Unbalanced Optimal Transport Regularization for Large Scale Imaging Problems

TL;DR

This paper introduces a scalable unbalanced optimal transport regularizer for large-scale imaging, reducing computational costs and handling natural images, with demonstrated effectiveness in video tracking tasks.

Contribution

It proposes a novel unbalanced optimal transport regularizer with linear complexity and a parallelizable optimization method, addressing previous computational and modeling limitations.

Findings

Superior empirical performance on synthetic and real video data.

Effective handling of natural images without mass-balancing constraints.

Reduced computational complexity enabling large-scale applications.

Abstract

The modeling of phenomenological structure is a crucial aspect in inverse imaging problems. One emerging modeling tool in computational imaging is the optimal transport framework. Its ability to model geometric displacements across an image's support gives it attractive qualities similar to those of optical flow methods which are effective at capturing visual motion, but are restricted to operate in significantly smaller state-spaces. Despite this advantage, two major drawbacks make it unsuitable for general deployment: (i) it suffers from exorbitant computational costs due to a quadratic optimization-variable complexity, and (ii) it has a mass-balancing assumption that limits applications with natural images. We tackle these issues simultaneously by proposing a novel formulation for an unbalanced optimal transport regularizer that has linear optimization-variable complexity. In addition, we present a general parallelizable proximal method for this regularizer, and demonstrate superior empirical performance on novel dynamical tracking applications in synthetic and real video.