A Wavefront Marching Method for Solving the Eikonal Equation on Cartesian Grids

This paper presents a new wavefront propagation method for dealing with the classic Eikonal equation. While classic Dijkstra-like graph-based techniques achieve the solution in O(M log M), they do not approximate the unique physically relevant solution very well. Fast Marching Methods (FMM) were created to efficiently solve the continuous problem. The proposed approximation tries to maintain the complexity, in order to make the algorithm useful in a wide range of contexts. The key idea behind our method is the creation of 'mini wave-fronts', which are combined to propagate the solution. Experimental results show the improvement in the accuracy with respect to the state of the art, while the average computational speed is maintained in O(M log M), similar to the FMM techniques.