This paper presents a unified propagation method for dealing with both the classic Eikonal equation, where the motion direction does not affect the propagation, and the more general static Hamilton-Jacobi equations, where it does. While classic Fast Marching Method (FMM) techniques achieve the solution to the Eikonal equation with a O(M log M) (or O(M) assuming some modifications), solving the more general static Hamilton-Jacobi equation requires a higher complexity. The proposed framework maintains the O(M log M) complexity for both problems, while achieving higher accuracy than available state-of-the-art. The key idea behind the proposed method is the creation of ‘mini wave-fronts’, where the solution is interpolated to minimize the discretization error. Experimental results show how our algorithm can outperform the state-of-the-art both in precision and computational cost.

中文翻译：

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波前行进方法：求解 Eikonal 和静态 Hamilton-Jacobi 方程的统一算法

本文提出了一种统一的传播方法，用于处理运动方向不影响传播的经典 Eikonal 方程和更一般的静态 Hamilton-Jacobi 方程。虽然经典的快速行进方法 (FMM) 技术使用 O(M log M)（或假设一些修改为 O(M)）来解决 Eikonal 方程，但求解更一般的静态 Hamilton-Jacobi 方程需要更高的复杂性。所提出的框架对这两个问题都保持了 O(M log M) 复杂度，同时实现了比现有最先进技术更高的准确度。所提出的方法背后的关键思想是创建“迷你波前”，其中对解决方案进行插值以最小化离散化误差。