A note on "distance transformations in digital images"

Abstract The influence of using distinct optimization criteria for determining the coefficients of a distance transform is studied. The criteria studied are (1) minimizing the maximum of the absolute value of the difference between the distance transform and Euclidaan distance, and (2) minimizing the root-mean-square difference between the distance transform and Euclidean distance. By allowing an overall scaling factor to have other than integer values, other integer approximations of the distance transform's coefficients result as optimal. Emphasis is given to isotropy, or invariance with respect to rotation, and to the use of unbiased distance estimates.