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We propose the use of Flat Metric to assess the performance of reconstruction methods for single-molecule localization microscopy (SMLM) in scenarios where the ground-truth is available. Flat Metric is intimately related to the concept of optimal transport between measures of different mass, providing solid mathematical foundations for SMLM evaluation and integrating both localization and detection performance. In this paper, we provide the foundations of Flat Metric and validate this measure by applying it to controlled synthetic examples and to data from the SMLM 2016 Challenge.
Regularization in Optimal Transport (OT) problems has been shown to critically affect the associated computational and sample complexities. It also has been observed that regularization effectively helps in handling noisy marginals as well as margina
Generalizing knowledge to unseen domains, where data and labels are unavailable, is crucial for machine learning models. We tackle the domain generalization problem to learn from multiple source domains and generalize to a target domain with unknown
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 the entropy
Recently, much progress has been made in unsupervised restoration learning. However, existing methods more or less rely on some assumptions on the signal and/or degradation model, which limits their practical performance. How to construct an optimal
This paper introduces a new nonlinear dictionary learning method for histograms in the probability simplex. The method leverages optimal transport theory, in the sense that our aim is to reconstruct histograms using so-called displacement interpolati