The.Algorithm.Design.Manual.Springer-Verlag.1998

Medial-Axis Transformation
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Medial-Axis Transformation
Input description: A polygon or polyhedron P.
Problem description: What is the set of points within P that have more than one closest point on the
boundary of P?
Discussion: The medial-axis transformation is useful in thinning a polygon, or, as is sometimes said,
finding its skeleton. The goal is to extract a simple, robust representation of the shape of the polygon. As
can be seen from the figures above, the thinned versions of the letters capture the essence of the shape of
an `A' and a `B', and would be relatively unaffected by changing the thickness of strokes or by adding
font-dependent flourishes such as serifs.
The medial-axis transformation of a polygon is always a tree, making it fairly easy to use dynamic
programming to measure the ``edit distance'' between the skeleton of a known model and the skeleton of
an unknown object. Whenever the two skeletons are close enough, we can classify the unknown object as
an instance of our model. This technique has proven useful in computer vision and in optical character
recognition. The skeleton of a polygon with holes (like the `A' and `B') is not a tree, but an embedded
planar graph, but it remains easy to work with.
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