Chamfer metrics, the medial axis and mathematical morphology

This paper describes a number of efficient algorithms for morphological operations which use discs defined by chamfer distances as structuring elements. It presents an extension to previous work on extending metrics (such as the p-q-metrics). Theoretical results and algorithms are presented for p-q-r-metrics, which are not extending. These metrics can approximate the Euclidean metric close enough for most practical situations. The algorithms are based on an analysis of the structure of shortest paths in the p-q-r-metric and of the set of values this metric can assume. Efficient algorithms are presented for the medial axis and the opening transform. The opening transform algorithm is two orders of magnitude faster than a more straightforward algorithm.