Open Access
2022 Optimal detection of the feature matching map in presence of noise and outliers
Tigran Galstyan, Arshak Minasyan, Arnak S. Dalalyan
Author Affiliations +
Electron. J. Statist. 16(2): 5720-5750 (2022). DOI: 10.1214/22-EJS2076


We consider the problem of finding the matching map between two sets of d-dimensional vectors from noisy observations, where the second set contains outliers.The matching map is then an injection, which can be consistently detected only if the vectors of the second set are well separated. The main result shows that, in the high-dimensional setting, a detection region of unknown injection may be characterized by the sets of vectors for which the inlier-inlier distance is of order at least d14 and the inlier-outlier distance is of order at least d12. These rates are achieved using the matching minimizing the sum of logarithms of distances between matched pairs of points. We also prove lower bounds establishing optimality of these rates. Finally, we report the results of numerical experiments on both synthetic and real world data that illustrate our theoretical results and provide further insight into the properties of the algorithms studied in this work.

Funding Statement

This work was supported by the grant Investissements d’Avenir (ANR-11-IDEX-0003/Labex Ecodec/ANR-11-LABX-0047) and by the FAST Advance grant.


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Tigran Galstyan. Arshak Minasyan. Arnak S. Dalalyan. "Optimal detection of the feature matching map in presence of noise and outliers." Electron. J. Statist. 16 (2) 5720 - 5750, 2022.


Received: 1 October 2021; Published: 2022
First available in Project Euclid: 27 October 2022

arXiv: 2106.07044
MathSciNet: MR4500636
zbMATH: 07633946
Digital Object Identifier: 10.1214/22-EJS2076

Primary: 62H12
Secondary: 62F35

Keywords: Feature matching , Minimax optimality , robustness

Vol.16 • No. 2 • 2022
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