Fast methods are very popular algorithms to compute time-of-arrival maps (distance maps measured in time units) solving the Eikonal equation. Since fast marching was proposed in 1995, it has been applied to many different applications, such as robotics, medical computer vision, fluid simulation, and so on. From then on, many alternatives to the original method have been proposed with two main objectives: reducing its computational time and improving its accuracy. In this paper, we collect the main single-threaded approaches, which improve the computational time of the standard fast marching method and study them within a common mathematical framework. Then, they are evaluated using isotropic environments, which are representative of their possible applications. The studied methods are the fast marching method with the binary heap, the fast marching method with Fibonacci heap, the simplified fast marching method, the untidy fast marching method, the fast iterative method, the group marching method, the fast sweeping method, the locking sweeping method, and the double dynamic queue method.
eikonal equation; fast methods; fast marching method; fast sweeping method; two dimensional displays; mathematical model; iterative methods; computer vision; indexes; image segmentation