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Length Learning for Planar Euclidean Curves
arXiv - CS - Computational Geometry Pub Date : 2021-02-03 , DOI: arxiv-2102.01895
Barak Or, Liam Hazan

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.

中文翻译:

平面欧几里得曲线的长度学习

在这项工作中,我们使用了深度神经网络(DNN)解决了微分几何中的一个基本问题。人们可以在文献中找到许多用于计算曲率,长度和其他几何特性的闭合形式的表达式。我们知道这些概念,因此我们非常热衷于使用深度神经网络来重构它们。在此框架中,我们的目标是从示例中学习几何特性。最简单的几何对象是曲线。因此,这项工作着重于学习由正弦波数据集创建的平面采样曲线的长度。因此,使用监督学习方法重构了基本长度公理。根据这些公理,建立了一个简化的DNN模型,我们称为ArcLengthNet。测试了对加性噪声和离散误差的鲁棒性。
更新日期:2021-02-04
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