Exact Euclidean distance function by chain propagations

Up to now, all the known Euclidean distance function algorithms are either excessively slow or inaccurate, and even Danielsson´s method (1980) produces errors in some configurations. The author shows that these problems are due to the local way distances are propagated in images by this algorithm. To remedy these drawbacks, an algorithm which encodes the objects boundaries as chains and propagates these structures in the image using rewriting rules is introduced. The chains convey Euclidean distances and can be written above one another, thus yielding exact results. In addition, the proposed algorithm is particularly efficient. Some of its applications to skeletons and neighborhood graphs are described