Optimal-Transport-Based Metric For SMLM

Abstract

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.

Off-The-Grid Variational Sparse Spike Recovery: Methods and Algorithms

“…Still, it would be way more convenient to incorporate the case of differing masses in the metric. The proper metric to compare two measures of different masses is called the Kantorovtich-Rubinstein norm also referred as the Flat Metric [37][38][39]. Definition 8 (Unbalanced optimal transport).…”

“…Then, it may be seen as an interpolation between the total variation norm and the 1-Wasserstein norm. Moreover, when the number of δ-peaks is correctly estimated, the Flat Metric stands for the mean error in terms of localisation and is similar to the RMSE [39]. Eventually, the Flat metric can be extended to discrete reconstruction i.e., images on a fine grid; this metric is then a method applicable to discrete reconstruction, namely images with a finer grid.…”