Medial axis

The medial axis of an object is the set of all points having more than one closest point on the object's boundary. Originally referred to as the topological skeleton, it was introduced by Blum as a tool for biological shape recognition. In mathematics the closure of the medial axis is known as the cut locus.

In 2D, the medial axis of a subset S which is bounded by planar curve C is the locus of the centers of circles that are tangent to curve C in two or more points, where all such circles are contained in S. (It follows that the medial axis itself is contained in S.) The medial axis of a simple polygon is a tree whose leaves are the vertices of the polygon, and whose edges are either straight segments or arcs of parabolas.

The medial axis together with the associated radius function of the maximally inscribed discs is called the medial axis transform (MAT). The medial axis transform is a complete shape descriptor (see also shape analysis), meaning that it can be used to reconstruct the shape of the original domain.