Classification of the distance transformation algorithms under the mathematical morphology approach

The distance transform (DT) is a morphological erosion of the binary image by a given structuring function, that dictates the distance metric in the transformation. There are many known algorithms and structuring function decompositions to efficiently implement a morphological erosion. Most of the erosion algorithms are classified as parallel, sequential raster (and anti-raster), and propagation. Based on this classification and decomposition, we review and classify most of the DT algorithms reported in the literature. As a result of this study, we have contributed not only to better classify and understand the diversity of the DT algorithms in the literature, but also to create a collection of efficient erosion algorithms suitable to different computer architectures.