平面欧氏曲线的长度学习
Length Learning for Planar Euclidean Curves
摘要：
在这项工作中，我们使用深度神经网络（DNN）来解决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、长度和其他几何性质的封闭形式表达式。由于我们知道这些概念，我们非常有动力通过使用深度神经网络来重建它们。在这个框架中，我们的目标是从例子中学习几何属性。最简单的几何对象是曲线。因此，这项工作的重点是学习由正弦波数据集创建的平面采样曲线的长度。为此，基本长度公理使用监督学习方法重建。根据这些公理，建立了一个简化的DNN模型，我们称之为ArcLengthNet。对加性噪声和离散化误差的鲁棒性进行了测试。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
