# Fast Marching method

tags
Applied maths, Algorithm

The fast marching method can be seen as a way to improve the metric issue with Dijkstra’s algorithm (which actually computes the $$\ell_1$$ distance on a grid). The graph update is replaced with the Eikonal equation resolution in the FM method. This reduces the bias of using a grid and converges towards the underlying geodesic distance when the grid step size tends towards 0.

The FM algorithm replaces the graph update ($$D_j \leftarrow \min_{k \sim j} D_k + W_j$$) with a local resolution of the Eikonal equation