Approximation of Log-Aesthetic Curves using ODE-Net

Abstract

In conventional deep learning, it is difficult to obtain the desired accuracy unless the time interval is constant. A method called ODE-Net (Ordinary Differential Equation Network) that can adapt to data with an irregular time interval has been proposed. In this study, in order to examine the performance of ODE-Net, the logarithmic spiral used in the previous study is extended to log-aesthetic curves, and the approximation is performed with conditions such as how to sample the curve and from which region to perform approximation. The results show that a good approximation can be obtained by learning log-aesthetic curves toward approaching a circle, and by using arc length instead of tangential angle as a parameter.