Fast Methods for Eikonal Equations: an Experimental Survey

TL;DR

This paper provides an experimental survey of nine methods that improve the computational efficiency of the Fast Marching Method for solving Eikonal equations in isotropic environments, highlighting their performance differences.

Contribution

It systematically compares nine single-threaded, isotropic Fast Marching Method variants within a unified framework through extensive experiments.

Findings

Fast Marching with Fibonacci Heap is faster than binary heap.

Simplified Fast Marching offers a good accuracy-speed trade-off.

Fast Sweeping Method performs well in certain environments.

Abstract

The Fast Marching Method is a very popular algorithm to compute times-of-arrival maps (distances map measured in time units). Since their proposal in 1995, it has been applied to many different applications such as robotics, medical computer vision, fluid simulation, etc. Many alternatives have been proposed with two main objectives: to reduce its computational time and to improve its accuracy. In this paper, we collect the main approaches which improve the computational time of the standard Fast Marching Method, focusing on single-threaded methods and isotropic environments. 9 different methods are studied under a common mathematical framework and experimentally in representative environments: Fast Marching Method with binary heap, Fast Marching Method with Fibonacci Heap, Simplified Fast Marching Method, Untidy Fast Marching Method, Fast Iterative Method, Group Marching Method, Fast Sweeping Method, Lock Sweeping Method and Double Dynamic Queue Method.