The Curve Axis

In this paper we examine various aspects of the medial axis representation of shapes, resulting in a novel, highly accurate skeletonization algorithm suitable for shapes with parametrically described boundaries such as, for example, polygons or “spline”-gons. The medial axis representation is first shown to be efficient in calculating local boundary features. Then the problem of deciding whether an axis-like function is indeed an axis of a shape is addressed, and two necessary and locally sufficient restrictions on axis functions are derived. The proposed skeletonization approach is based on another result which shows that the medial axis is the solution of a system of first order differential equations. The new skeletonization algorithm provides a discrete parametric representation of the axis for smooth shapes, the input to the algorithm being a parametric description of the shape boundary. Skeletonization examples using the proposed algorithm are presented.

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