Finding the Minimal Set of Maximum Disks for Binary Objects

Abstract

A two-dimensional binary object can be totally covered by a set of disks. From this follows that any object might be represented by these disks rather than by the pixels. This paper deals with the problem of finding the most efficient version of this representation which is called the minimal set of maximum disks (MSD). The proposed algorithm picks candidate disks from the local maxima in the Euclidean distance transform. Then a relation table for the pixel coverage of these disks is estabished, but only for the border pixels which makes the table size reasonable. Three basic table reduction steps are executed to extract and include necessary disks to MSD while eliminating and excluding the unnecessary disks.