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Optimal transport (OT) is a framework that can guide the design of efficient resource allocation strategies in a network of multiple sources and targets. This paper applies discrete OT to a swarm of UAVs in a novel way to achieve…
Motion planning is still an open problem for many disciplines, e.g., robotics, autonomous driving, due to their need for high computational resources that hinder real-time, efficient decision-making. A class of methods striving to provide…
Optimal transport aims to estimate a transportation plan that minimizes a displacement cost. This is realized by optimizing the scalar product between the sought plan and the given cost, over the space of doubly stochastic matrices. When…
Flow models parameterized as time-dependent velocity fields can generate data from noise by integrating an ODE. These models are often trained using flow matching, i.e. by sampling random pairs of noise and target points…
Optimal transport has recently started to be successfully employed to define misfit or loss functions in inverse problems. However, it is a problem intrinsically defined for positive (probability) measures and therefore strategies are…
Entropic regularization provides a generalization of the original optimal transport problem. It introduces a penalty term defined by the Kullback-Leibler divergence, making the problem more tractable via the celebrated Sinkhorn algorithm.…
The Sinkhorn algorithm is a widely used method for solving the optimal transport problem, and the Greenkhorn algorithm is one of its variants. While there are modified versions of these two algorithms whose computational complexities are…
Mass transport problems arise in many areas of machine learning whereby one wants to compute a map transporting one distribution to another. Generative modeling techniques like Generative Adversarial Networks (GANs) and Denoising Diffusion…
Optimal transport is an important tool in machine learning, allowing to capture geometric properties of the data through a linear program on transport polytopes. We present a single-loop optimization algorithm for minimizing general convex…
Computing optimal transport (OT) for general high-dimensional data has been a long-standing challenge. Despite much progress, most of the efforts including neural network methods have been focused on the static formulation of the OT…
This paper addresses the limitations of standard uncertainty models, e.g., robust (norm-bounded) and stochastic (one fixed distribution, e.g., Gaussian), and proposes to model uncertainty via Optimal Transport (OT) ambiguity sets. These…
We propose a new colour transfer method with Optimal Transport (OT) to transfer the colour of a sourceimage to match the colour of a target image of the same scene that may exhibit large motion changes betweenimages. By definition OT does…
This paper presents a novel two-step approach for the fundamental problem of learning an optimal map from one distribution to another. First, we learn an optimal transport (OT) plan, which can be thought as a one-to-many map between the two…
Optimal Transport is a useful metric to compare probability distributions and to compute a pairing given a ground cost. Its entropic regularization variant (eOT) is crucial to have fast algorithms and reflect fuzzy/noisy matchings. This…
Clustering is a fundamental task in the computer vision and machine learning community. Although various methods have been proposed, the performance of existing approaches drops dramatically when handling incomplete high-dimensional data…
We consider the fundamental problem of sampling the optimal transport coupling between given source and target distributions. In certain cases, the optimal transport plan takes the form of a one-to-one mapping from the source support to the…
Diffusion Models (DMs) have achieved remarkable progress in generative modeling. However, the mismatch between the forward terminal distribution and reverse initial distribution introduces prior error, leading to deviations of sampling…
Optimal transport (OT) has recently been shown as a promising criterion for unsupervised restoration when no explicit prior model is available. Despite its theoretical appeal, OT still significantly falls short of supervised methods on…
Evaluating lesion evolution in longitudinal CT scans of can cer patients is essential for assessing treatment response, yet establishing reliable lesion correspondence across time remains challenging. Standard bipartite matchers, which rely…
The optimal transport (OT) map offers the most economical way to transfer one probability measure distribution to another. Classical OT theory does not involve a discussion of preserving topological connections and orientations in…