Learning Differential Invariants of Planar Curves

Roy Velich; Ron Kimmel

doi:10.1007/978-3-031-31975-4_44

Learning Differential Invariants of Planar Curves

Roy Velich, Ron Kimmel

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

Abstract

We propose a learning paradigm for the numerical approximation of differential invariants of planar curves. Deep neural-networks’ (DNNs) universal approximation properties are utilized to estimate geometric measures. The proposed framework is shown to be a preferable alternative to axiomatic constructions. Specifically, we show that DNNs can learn to overcome instabilities and sampling artifacts and produce consistent signatures for curves subject to a given group of transformations in the plane. We compare the proposed schemes to alternative state-of-the-art axiomatic constructions of differential invariants. We evaluate our models qualitatively and quantitatively and propose a benchmark dataset to evaluate approximation models of differential invariants of planar curves.

Original language	English
Title of host publication	Scale Space and Variational Methods in Computer Vision - 9th International Conference, SSVM 2023, Proceedings
Editors	Luca Calatroni, Marco Donatelli, Serena Morigi, Marco Prato, Matteo Santacesaria
Publisher	Springer Science and Business Media Deutschland GmbH
Pages	575-587
Number of pages	13
ISBN (Print)	9783031319747
DOIs	https://doi.org/10.1007/978-3-031-31975-4_44
State	Published - 2023
Externally published	Yes
Event	9th International Conference on Scale Space and Variational Methods in Computer Vision, SSVM 2023 - Santa Margherita di Pula, Italy Duration: 21 May 2023 → 25 May 2023

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	14009 LNCS
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	9th International Conference on Scale Space and Variational Methods in Computer Vision, SSVM 2023
Country/Territory	Italy
City	Santa Margherita di Pula
Period	21/05/23 → 25/05/23

Bibliographical note

Publisher Copyright:
© 2023, The Author(s), under exclusive license to Springer Nature Switzerland AG.

Keywords

computer vision
differential geometry
Differential invariants
shape analysis

ASJC Scopus subject areas

Theoretical Computer Science
General Computer Science

Access to Document

10.1007/978-3-031-31975-4_44

Cite this

Velich, R., & Kimmel, R. (2023). Learning Differential Invariants of Planar Curves. In L. Calatroni, M. Donatelli, S. Morigi, M. Prato, & M. Santacesaria (Eds.), Scale Space and Variational Methods in Computer Vision - 9th International Conference, SSVM 2023, Proceedings (pp. 575-587). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 14009 LNCS). Springer Science and Business Media Deutschland GmbH. https://doi.org/10.1007/978-3-031-31975-4_44

Velich, Roy ; Kimmel, Ron. / Learning Differential Invariants of Planar Curves. Scale Space and Variational Methods in Computer Vision - 9th International Conference, SSVM 2023, Proceedings. editor / Luca Calatroni ; Marco Donatelli ; Serena Morigi ; Marco Prato ; Matteo Santacesaria. Springer Science and Business Media Deutschland GmbH, 2023. pp. 575-587 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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abstract = "We propose a learning paradigm for the numerical approximation of differential invariants of planar curves. Deep neural-networks{\textquoteright} (DNNs) universal approximation properties are utilized to estimate geometric measures. The proposed framework is shown to be a preferable alternative to axiomatic constructions. Specifically, we show that DNNs can learn to overcome instabilities and sampling artifacts and produce consistent signatures for curves subject to a given group of transformations in the plane. We compare the proposed schemes to alternative state-of-the-art axiomatic constructions of differential invariants. We evaluate our models qualitatively and quantitatively and propose a benchmark dataset to evaluate approximation models of differential invariants of planar curves.",

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Velich, R & Kimmel, R 2023, Learning Differential Invariants of Planar Curves. in L Calatroni, M Donatelli, S Morigi, M Prato & M Santacesaria (eds), Scale Space and Variational Methods in Computer Vision - 9th International Conference, SSVM 2023, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 14009 LNCS, Springer Science and Business Media Deutschland GmbH, pp. 575-587, 9th International Conference on Scale Space and Variational Methods in Computer Vision, SSVM 2023, Santa Margherita di Pula, Italy, 21/05/23. https://doi.org/10.1007/978-3-031-31975-4_44

Learning Differential Invariants of Planar Curves. / Velich, Roy; Kimmel, Ron.
Scale Space and Variational Methods in Computer Vision - 9th International Conference, SSVM 2023, Proceedings. ed. / Luca Calatroni; Marco Donatelli; Serena Morigi; Marco Prato; Matteo Santacesaria. Springer Science and Business Media Deutschland GmbH, 2023. p. 575-587 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 14009 LNCS).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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Velich R, Kimmel R. Learning Differential Invariants of Planar Curves. In Calatroni L, Donatelli M, Morigi S, Prato M, Santacesaria M, editors, Scale Space and Variational Methods in Computer Vision - 9th International Conference, SSVM 2023, Proceedings. Springer Science and Business Media Deutschland GmbH. 2023. p. 575-587. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/978-3-031-31975-4_44