Redundancy in All Pairs Fast Marching Method

In this paper, we analyze the redundancy in calculating all pairs of geodesic distances on a rectangular grid. Fast marching method is an efficient way to estimate the geodesic distances from a point. But when calculated for all the points on the grid, this introduces certain redundancy. Our analysis shows that over 90% of the distances are actually recalculated. We propose a novel solution which exploits this redundancy to reduce the number of distances evaluated using the fast marching method and enforces the symmetry of the distance matrix. Experimental results show the improved accuracy obtained with our implementation.