Wavefront Marching Methods: A Unified Algorithm to Solve Eikonal and Static Hamilton-Jacobi Equations

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.