Digital distance functions on three-dimensional grids

In this paper, we examine five different three-dimensional grids suited for image processing. Digital distance functions are defined on the cubic, face-centered cubic, body-centered cubic, honeycomb, and diamond grids. We give the parameters that minimize an error function that favors distance functions with low rotational dependency. We also give an algorithm for computing the distance transform—the tool by which these distance functions can be applied in image processing applications.