ABSTRACT

The Medial Axis Transform (MAT) [21] is an attractive representation scheme for spatial occupancy of objects in 2-D and 3-D. In its lowest form, an object is represented as a set of points in an integral coordinate space that it occupies. We know that a point in this form of representation is called pixel in 2-D and voxel in 3-D. The MAT of these objects provides a relatively higher level of structural description, as it represents the object as a set of disks (circles in 2-D and spheres in 3-D). To reduce the number of such circles (or spheres), in this representation, only those are considered that are not totally contained in any one of them. These are called medial disks (or centers of maximal disks (CMD)) of the pattern or object. However, even with these medial disks, there is a scope of redundancy in the set. The disks may be overlapping. Moreover a medial disk may be contained by more than one member from the remaining

set. The representation of a binary object using medial disks is called its MAT. In this representation, individual disks are denoted by their centers and radii. In this chapter we discuss the MAT of binary objects in 2-D and 3-D, and its application to various geometric computation on images.