Parallel Unbalanced Optimal Transport Regularization for Large Scale Imaging Problems
arXiv:1909.00149
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.
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Cited by in corpus (5)
- The Unbalanced Gromov Wasserstein Distance: Conic Formulation and Relaxation
- On Unbalanced Optimal Transport: An Analysis of Sinkhorn Algorithm
- Partial Optimal Transport with Applications on Positive-Unlabeled Learning
- Entropy-Transport distances between unbalanced metric measure spaces
- Entropy Partial Transport with Tree Metrics: Theory and Practice