Fast multidimensional parallel Euclidean distance transform based on Mathematical Morphology

Roberto de Alencar LotufoFrancisco A. Zampirolli

This paper presents a novel Euclidean distance transform algorithm formulated under the Mathematical Morphology approach. The distance transform is an erosion by a structuring function dependent on the distance metric used. To achieve high speed perfomance, the squared Euclidean distance structuring function is decomposed into a family of four one- dimensional two-point structuring functions.The erosion algorithm is based on a propagation scheme which resulted in a overall Euclidean distance transform algorithm very simple to code and understand, yet with speed performance compared to the Chamfer 3-5-7 sequential raster and anti-raster algorithm.

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