Learning Differential Invariants of Planar Curves

Roy Velich, Ron Kimmel

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-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 languageAmerican English
Title of host publicationScale Space and Variational Methods in Computer Vision - 9th International Conference, SSVM 2023, Proceedings
EditorsLuca Calatroni, Marco Donatelli, Serena Morigi, Marco Prato, Matteo Santacesaria
PublisherSpringer Science and Business Media Deutschland GmbH
Pages575-587
Number of pages13
ISBN (Print)9783031319747
DOIs
StatePublished - 2023
Event9th International Conference on Scale Space and Variational Methods in Computer Vision, SSVM 2023 - Santa Margherita di Pula, Italy
Duration: 21 May 202325 May 2023

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume14009 LNCS

Conference

Conference9th International Conference on Scale Space and Variational Methods in Computer Vision, SSVM 2023
Country/TerritoryItaly
CitySanta Margherita di Pula
Period21/05/2325/05/23

Keywords

  • Differential invariants
  • computer vision
  • differential geometry
  • shape analysis

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • General Computer Science

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