@inproceedings{3b51ab67a58e4a1285df8e6e61f99a56,
title = "Deep Eikonal Solvers",
abstract = "A deep learning approach to numerically approximate the solution to the Eikonal equation is introduced. The proposed method is built on the fast marching scheme which comprises of two components: a local numerical solver and an update scheme. We replace the formulaic local numerical solver with a trained neural network to provide highly accurate estimates of local distances for a variety of different geometries and sampling conditions. Our learning approach generalizes not only to flat Euclidean domains but also to curved surfaces enabled by the incorporation of certain invariant features in the neural network architecture. We show a considerable gain in performance, validated by smaller errors and higher orders of accuracy for the numerical solutions of the Eikonal equation computed on different surfaces. The proposed approach leverages the approximation power of neural networks to enhance the performance of numerical algorithms, thereby, connecting the somewhat disparate themes of numerical geometry and learning.",
keywords = "Deep learning for PDE, Geodesic distance, The Eikonal equation",
author = "Moshe Lichtenstein and Gautam Pai and Ron Kimmel",
note = "Publisher Copyright: {\textcopyright} 2019, Springer Nature Switzerland AG.; 7th International Conference on Scale Space and Variational Methods in Computer Vision, SSVM 2019 ; Conference date: 30-06-2019 Through 04-07-2019",
year = "2019",
doi = "10.1007/978-3-030-22368-7\_4",
language = "الإنجليزيّة",
isbn = "9783030223670",
series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",
pages = "38--50",
editor = "Jan Lellmann and Jan Modersitzki and Martin Burger",
booktitle = "Scale Space and Variational Methods in Computer Vision - 7th International Conference, SSVM 2019, Proceedings",
}