Medial axis

Originally referred to as the topological skeleton, it was introduced in 1967 by Harry Blum[1] 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 generalizes to k-dimensional hypersurfaces by replacing 2D circles with k-dimension hyperspheres.

The 2D medial axis is useful for character and object recognition, while the 3D medial axis has applications in surface reconstruction for physical models, and for dimensional reduction of complex models.