Published online by Cambridge University Press: 20 May 2010
Medial Representations of Objects
A medial representation of an object describes a locus midway between (at the center of a sphere bitangent to) two sections of the boundary, and gives the distance to the boundary, called the medial radius. The object is obtained as the union of overlapping bitangent spheres. This results in a locus of (p, r), where p gives the sphere center and r gives the radius of the sphere. In some representations, the vectors from the medial point to the two or more corresponding boundary points are included; in others they are derived.
The Blum medial axis is a transformation of an object boundary that has the same topology as the object; thus, the boundary can generate the medial locus (p, r), and the latter can also generate the object boundary. In the first direction the transformation is a function, but in the second direction it is one-to-many, because a medial point describes more than one boundary point. One of the strengths of using the medial representation as a primitive is that any unbranching, connected subset of the medial locus generates intrinsic space coordinates for the part of the object interior corresponding to it. These coordinates include positional location in the medial sheet, a choice of spoke (left or right) and length along that spoke.