The Medial Axis (MA) or skeleton of a solid is the locus of centers of balls which are maximal within the solid, together with the limit points of this locus (a ball is maximal within a solid if it is contained in the solid but is not a proper subset of any other ball contained in the solid). The Medial Axis Transform (MAT) is composed of the medial axis together with the associated radius function which is the radius of the maximal ball with center any given point on the MA. The MA of a 2-D bracket-like region (2-D solid) is shown in Fig. 11.2. The maximal disc associated with a point at the intersection of three MA branches is also shown. Originally proposed by Blum [30,29], the MAT has been developed extensively since then. It has several properties which neither the Boundary Representation nor the Constructive Solid Geometry directly provide. First, because it elicits important symmetries of an object, it facilitates the design and interrogation of symmetrical objects [29]. Second, the MAT exhibits dimensional reduction [54,450]; for example, it transforms a 3-D solid into a connected set of points, curves, and surfaces, along with an associated radius function described in more detail below. Third, once a solid is represented with the MAT, the skeleton and radius function themselves may be manipulated, and the boundary will deform in a natural way, suggesting applications in computer animation [451]. Fourth, the skeleton may be used to facilitate the creation of coarse and fine finite element meshes of the region [139,140,141,142,298,406,12,418,338]. Fifth, the MAT determines constrictions and other global shape characteristics that are important in mesh generation, performance analysis, manufacturing simulation, and path planning [294,298]. Sixth, the MAT can be used in document encoding [43,42] and other image processing applications [38]. Finally, the MAT may be useful in tolerance specification [171].
The MA is closely related with equidistantial point sets, especially the well known Voronoi Diagram [335]. For a 2-D polygonal region or a 3-D polyhedral region, the Voronoi Diagram is a superset of MA, while for objects with nonlinear boundary, the Voronoi Diagram may not be a superset of MA. The major difference is in that the MA is intrinsic to a solid, while the Voronoi Diagram depends on the specific decomposition of the boundary of the solid.