A Graph-Based Implementation of the Anti-aliased Euclidean Distance Transform

With this paper, we present an algorithm for the anti-aliased Euclidean distance transform, based on wave front propagation, that can easily be extended to images of arbitrary dimensionality and sampling lattices. We investigate the behavior and weaknesses of the algorithm, applied to synthetic two-dimensional area-sampled images, and suggest an enhancement to the original method, with complexity proportional to the number of edge elements, that may reduce the amount and relative magnitude of the errors in the transformed image by as much as a factor of 10.