Scale-Free Image Keypoints Using Differentiable Persistent Homology

Giovanni Barbarani, Francesco Vaccarino, Gabriele Trivigno, Marco Guerra, Gabriele Berton, Carlo Masone
Proceedings of the 41st International Conference on Machine Learning, PMLR 235:2990-3002, 2024.

Abstract

In computer vision, keypoint detection is a fundamental task, with applications spanning from robotics to image retrieval; however, existing learning-based methods suffer from scale dependency, and lack flexibility. This paper introduces a novel approach that leverages Morse theory and persistent homology, powerful tools rooted in algebraic topology. We propose a novel loss function based on the recent introduction of a notion of subgradient in persistent homology, paving the way towards topological learning. Our detector, MorseDet, is the first topology-based learning model for feature detection, which achieves competitive performance in keypoint repeatability and introduces a principled and theoretically robust approach to the problem.

Cite this Paper

BibTeX
@InProceedings{pmlr-v235-barbarani24a, title = {Scale-Free Image Keypoints Using Differentiable Persistent Homology}, author = {Barbarani, Giovanni and Vaccarino, Francesco and Trivigno, Gabriele and Guerra, Marco and Berton, Gabriele and Masone, Carlo}, booktitle = {Proceedings of the 41st International Conference on Machine Learning}, pages = {2990--3002}, year = {2024}, editor = {Salakhutdinov, Ruslan and Kolter, Zico and Heller, Katherine and Weller, Adrian and Oliver, Nuria and Scarlett, Jonathan and Berkenkamp, Felix}, volume = {235}, series = {Proceedings of Machine Learning Research}, month = {21--27 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v235/main/assets/barbarani24a/barbarani24a.pdf}, url = {https://proceedings.mlr.press/v235/barbarani24a.html}, abstract = {In computer vision, keypoint detection is a fundamental task, with applications spanning from robotics to image retrieval; however, existing learning-based methods suffer from scale dependency, and lack flexibility. This paper introduces a novel approach that leverages Morse theory and persistent homology, powerful tools rooted in algebraic topology. We propose a novel loss function based on the recent introduction of a notion of subgradient in persistent homology, paving the way towards topological learning. Our detector, MorseDet, is the first topology-based learning model for feature detection, which achieves competitive performance in keypoint repeatability and introduces a principled and theoretically robust approach to the problem.} }
Endnote
%0 Conference Paper %T Scale-Free Image Keypoints Using Differentiable Persistent Homology %A Giovanni Barbarani %A Francesco Vaccarino %A Gabriele Trivigno %A Marco Guerra %A Gabriele Berton %A Carlo Masone %B Proceedings of the 41st International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2024 %E Ruslan Salakhutdinov %E Zico Kolter %E Katherine Heller %E Adrian Weller %E Nuria Oliver %E Jonathan Scarlett %E Felix Berkenkamp %F pmlr-v235-barbarani24a %I PMLR %P 2990--3002 %U https://proceedings.mlr.press/v235/barbarani24a.html %V 235 %X In computer vision, keypoint detection is a fundamental task, with applications spanning from robotics to image retrieval; however, existing learning-based methods suffer from scale dependency, and lack flexibility. This paper introduces a novel approach that leverages Morse theory and persistent homology, powerful tools rooted in algebraic topology. We propose a novel loss function based on the recent introduction of a notion of subgradient in persistent homology, paving the way towards topological learning. Our detector, MorseDet, is the first topology-based learning model for feature detection, which achieves competitive performance in keypoint repeatability and introduces a principled and theoretically robust approach to the problem.
APA
Barbarani, G., Vaccarino, F., Trivigno, G., Guerra, M., Berton, G. & Masone, C.. (2024). Scale-Free Image Keypoints Using Differentiable Persistent Homology. Proceedings of the 41st International Conference on Machine Learning, in Proceedings of Machine Learning Research 235:2990-3002 Available from https://proceedings.mlr.press/v235/barbarani24a.html.

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