Medial axis

转自：http://en.wikipedia.org/wiki/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 thetopological skeleton, it was introduced by Blum ^[1] as a tool for biologicalshape recognition. In mathematics theclosure of the medial axis is known as thecut locus.

In 2D, the medial axis of a plane curve S is the locus of the centers of circles that are tangent to curveS in two or more points, where all such circles are contained inS. (It follows that the medial axis itself is contained inS.) The medial axis of asimple 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 themedial axis transform (MAT). The medial axis transform is a complete shape descriptor (see alsoshape analysis), meaning that it can be used to reconstruct theshape of the original domain.

The medial axis is a subset of the symmetry set, which is defined similarly, except that it also includes circles not contained inS. (Hence, the symmetry set of S generally extends to infinity, similar to theVoronoi diagram of a point set.)

The medial axis generalizes to k-dimensional hypersurfaces by replacing 2D circles with k-dimension hyperspheres. The 2D medial axis is useful forcharacter and object recognition, while the 3D medial axis has applications insurface reconstruction for physical models, and for dimensional reduction of complex models.