LengthNet: Length Learning for Planar Euclidean Curves

In this work, we used a deep learning (DL) model 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 properties, we are highly motivated to reconstruct them by using DL models. In this framework, our goal is to learn geometric properties from many examples. The simplest geometric object is a curve, and one of the fundamental properties is the length. Therefore, this work focuses on learning the length of planar sampled curves created by a simulation. The fundamental length axioms were reconstructed using a supervised learning approach. Following these axioms, a DL-based model, we named LengthNet, was established. For simplicity, we focus on the planar Euclidean curves.