Fast Methods for Eikonal Equations: an Experimental Survey
This work provides a comparative analysis for researchers and practitioners in fields like robotics and medical imaging, but it is incremental as it reviews existing methods without introducing new ones.
The paper surveys nine computational methods aimed at reducing the runtime of the Fast Marching Method for solving Eikonal equations, comparing their performance in isotropic environments.
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.