On Maximal Balls in Three Volume Grids

Abstract

A volume image can be digitized in different grids, not only the cubic one. The fcc and bcc grids have many advantages, as they are more dense than the cubic one. The set of maximal balls in a shape in a volume image is a compact but complete description of the shape. The original set, identified by rules dependent on the metric used, can be further reduced, by observing that some balls are covered by groups of other balls. The set of maximal balls can, for example, be used for compression, manipulation and as anchor points for topologically correct medial representations.