@inproceedings{9cf4863b2fb248a08ee22556b8f50803,
title = "Learning Differential Invariants of Planar Curves",
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.",
keywords = "Differential invariants, computer vision, differential geometry, shape analysis",
author = "Roy Velich and Ron Kimmel",
note = "Publisher Copyright: {\textcopyright} 2023, The Author(s), under exclusive license to Springer Nature Switzerland AG.; 9th International Conference on Scale Space and Variational Methods in Computer Vision, SSVM 2023 ; Conference date: 21-05-2023 Through 25-05-2023",
year = "2023",
doi = "10.1007/978-3-031-31975-4\_44",
language = "American English",
isbn = "9783031319747",
series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",
publisher = "Springer Science and Business Media Deutschland GmbH",
pages = "575--587",
editor = "Luca Calatroni and Marco Donatelli and Serena Morigi and Marco Prato and Matteo Santacesaria",
booktitle = "Scale Space and Variational Methods in Computer Vision - 9th International Conference, SSVM 2023, Proceedings",
address = "Germany",
}