Deep Eikonal Solvers
A deep learning approach to numerically approximate the solution to the Eikonal equation is introduced. The proposed method is built on the fast marching scheme which comprises of two components: a local numerical solver and an update scheme. We replace the formulaic local numerical solver with a trained neural network to provide highly accurate estimates of local distances for a variety of different geometries and sampling conditions. Our learning approach generalizes not only to flat Euclidean domains but also to curved surfaces enabled by the incorporation of certain invariant features in the neural network architecture. We show a considerable gain in performance, validated by smaller errors and higher orders of accuracy for the numerical solutions of the Eikonal equation computed on different surfaces The proposed approach leverages the approximation power of neural networks to enhance the performance of numerical algorithms, thereby, connecting the somewhat disparate themes of numerical geometry and learning.
Code (0)
등록된 구현이 없습니다.
Similar Papers 제목 키워드 기반
Equivariant Eikonal Neural Networks: Grid-Free, Scalable Travel-Time Prediction on Homogeneous Spaces
We introduce Equivariant Neural Eikonal Solvers, a novel framework that integrates Equivariant Neural Fields (ENFs) with Neural Eikonal Solvers. Our approach employs a single neural field where a unified shared backbone …
Computing distances and means on manifolds with a metric-constrained Eikonal approach
Computing distances on Riemannian manifolds is a challenging problem with numerous applications, from physics, through statistics, to machine learning. In this paper, we introduce the metric-constrained Eikonal solver to…
A fast eikonal equation solver using the Schrodinger wave equation
We use a Schr\"odinger wave equation formalism to solve the eikonal equation. In our framework, a solution to the eikonal equation is obtained in the limit as Planck's constant $\hbar$ (treated as a free parameter) tends…
From Active Contours to Minimal Geodesic Paths: New Solutions to Active Contours Problems by Eikonal Equations
In this chapter, we give an overview of part of our previous work based on the minimal path framework and the Eikonal partial differential equation (PDE). We show that by designing adequate Riemannian and Randers geodesi…
Boundary DetectionImage SegmentationSemantic SegmentationHamilton-Jacobi equations on graphs with applications to semi-supervised learning and data depth
Shortest path graph distances are widely used in data science and machine learning, since they can approximate the underlying geodesic distance on the data manifold. However, the shortest path distance is highly sensitiv…