Parallel complexity of the medial axis computation

The main result of this paper shows that the block-based digital medial axis transform can be computed in parallel by a constant number of calls to scan (parallel prefix) operations. This gives time- and/or work-optimal parallel algorithms for the distance-based and the block-based medial axis transform in a wide variety of parallel architectures. In order to design such an algorithm, we first demonstrate that computing a block-based medial axis transform of a binary image reduces to computing the distance based medial axis transform of an oversampling of the image, by proving that their labelings are equivalent