2021/02/03 by Barak Or, Or, Barak, Liam Hazan +1
Computer Science · #Computational Geometry (cs.CG) #FOS: Computer and information sciences #Graphics (cs.GR) #Image Processing and 3D Reconstruction #Image and Object Detection Techniques #Machine Learning (cs.LG) #Machine Learning and Algorithms #cs.CG #cs.GR #cs.LG
paper · pdf · doi:10.48550/arxiv.2102.01895
5 pages
arxiv created 2021/02/03 · openalex publication_date 2021/02/03 · arxiv updated 2021/02/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this work, we used deep neural networks (DNNs) to solve a fundamental problem in differential geometry. One can find many closed-form expressions for calculating curvature, length, and other geometric properties in the literature. As we know these concepts, we are highly motivated to reconstruct them by using deep neural networks. In this framework, our goal is to learn geometric properties from examples. The simplest geometric object is a curve. Therefore, this work focuses on learning the length of planar sampled curves created by a sine waves dataset. For this reason, the fundamental length axioms were reconstructed using a supervised learning approach. Following these axioms a simplified DNN model, we call ArcLengthNet, was established. The robustness to additive noise and discretization errors were tested.