The vector distance transform in two and three dimensions

The application of the distance transform (DT) to three-dimensional image data, collected, for example, by a confocal scanning laser microscope, requires special modifications to account for the possible anisotropic nature of these images. If anisotropic sampling is not properly accounted for, large errors can occur when simple image processing and image analysis operations related to the DT, such as erosions, dilations, skeletonizations, and distance measurements, are performed. This paper presents a simple, relatively fast way to account for this problem that is suitable for the large sizes typically associated with 3-D images.