Optimal transport-based metric for SMLM

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 introduce the foundations of Flat Metric and validate this measure by applying it to controlled synthetic examples and to data from the SMLM 2016 Challenge.

[1]  Sjoerd Stallinga,et al.  Measuring image resolution in optical nanoscopy , 2013, Nature Methods.

[2]  Joakim Jaldén,et al.  Cell Detection by Functional Inverse Diffusion and Nonnegative Group Sparsity—Part I: Modeling and Inverse Problems , 2017, IEEE Transactions on Signal Processing.

[3]  L. Hanin.  Kantorovich-Rubinstein norm and its application in the theory of Lipschitz spaces , 1992 .

[4]  Filippo Santambrogio,et al.  Optimal Transport for Applied Mathematicians , 2015 .

[5]  Joakim Jaldén,et al.  Cell Detection by Functional Inverse Diffusion and Non-Negative Group Sparsity—Part II: Proximal Optimization and Performance Evaluation , 2017, IEEE Transactions on Signal Processing.

[6]  F. Santambrogio.  Optimal Transport for Applied Mathematicians: Calculus of Variations, PDEs, and Modeling , 2015 .

[7]  Gabriel Peyré,et al.  Computational Optimal Transport , 2018, Found. Trends Mach. Learn..

[8]  Bernhard Schmitzer,et al.  A Framework for Wasserstein-1-Type Metrics , 2017, ArXiv.

[9]  Christophe Leterrier,et al.  NanoJ-SQUIRREL: quantitative mapping and minimisation of super-resolution optical imaging artefacts , 2018, Nature Methods.

[10]  Gabriel Peyré,et al.  A Low-Rank Approach to Off-the-Grid Sparse Superresolution , 2019, SIAM J. Imaging Sci..

[11]  Michael Unser,et al.  Publisher Correction: Super-resolution fight club: assessment of 2D and 3D single-molecule localization microscopy software , 2019, Nature Methods.

[12]  A. Descloux,et al.  Parameter-free image resolution estimation based on decorrelation analysis , 2019, Nature Methods.

[13]  C. Villani.  Optimal Transport: Old and New , 2008 .

[14]  Michael Unser,et al.  Super-resolution fight club: Assessment of 2D & 3D single-molecule localization microscopy software , 2019, Nature Methods.

[15]  Vibor Laketa,et al.  Microscopy in Infectious Disease Research-Imaging Across Scales. , 2018, Journal of molecular biology.

[16]  M. Beck,et al.  Fourier ring correlation as a resolution criterion for super-resolution microscopy. , 2013, Journal of structural biology.

[17]  Matthew D. Lew,et al.  Quantifying accuracy and heterogeneity in single-molecule super-resolution microscopy , 2020, Nature communications.

[18]  Yi Sun.  Root Mean Square Minimum Distance as a Quality Metric for Stochastic Optical Localization Nanoscopy Images , 2018, Scientific Reports.

[19]  T. O’Neil.  Geometric Measure Theory , 2002 .

[20]  M. Heilemann,et al.  Single-Molecule Localization Microscopy in Eukaryotes. , 2017, Chemical reviews.

[21]  Carola-Bibiane Schönlieb,et al.  Imaging with Kantorovich-Rubinstein Discrepancy , 2014, SIAM J. Imaging Sci..