Medial axis
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The medial axis is a method for representing the shape of objects by finding the topological skeleton, a set of curves which roughly run along the middle of an object.
In 2D, the medial axis of a plane curve S is the locus of the centers of circles that are tangent to curve S 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 is a subset of the symmetry set, which is defined similarly, except that it also includes circles not contained in S. (Hence, the symmetry set of S generally extends to infinity, similar to the Voronoi diagram of a point set.)
The medial axis generalizes to k-dimensional hypersurfaces by replacing 2D circles with k-dimension hyperspheres. 2D medial axis is useful for character and object recognition, while 3D medial axis has applications in surface reconstruction for physical models, and for dimensional reduction of complex models.
If S is given by a unit speed parametrisation 
, and 
is the unit tangent vector at each point. Then there will be a bitangent circle with center c and radius r if
For most curves, the symmetry set will form a one dimensional curve and can contain cusp. The symmetry set has end points corresponding to the vertices of S.
The medial axis together with the associated radius function of the maximally indiscribed discs is called the medial axis transform. 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.
[edit] See also
- Voronoi diagram - which can be regarded as a discrete form of the medial axis.
[edit] External links
[edit] References
- From the Infinitely Large to the Infinitely Small: Applications of Medial Symmetry Representations of Shape Frederic F. Leymarie1 and Benjamin B. Kimia2 [1]
