The Curve Axis

often reduces similar shapes to the same set of pixels, it should be no surprise that skeletonization algorithms suffer In this paper we examine various aspects of the medial axis representation of shapes, resulting in a novel, highly accurate from many implementation problems. Those problems folskeletonization algorithm suitable for shapes with parametrilow mainly from various implicit assumptions about the cally described boundaries such as, for example, polygons or pre-image of the digital shape. Some skeletonization algo‘‘spline’’-gons. The medial axis representation is first shown to rithms stress this point by incorporating parameters setting be efficient in calculating local boundary features. Then the the scale at which the shape should be interpreted, e.g., problem of deciding whether an axis-like function is indeed an [1, 7]. axis of a shape is addressed, and two necessary and locally Most skeletonization algorithms are area oriented. sufficient restrictions on axis functions are derived. The proThose algorithms refer to and use pixels inside the shape. posed skeletonization approach is based on another result which Their complexity is therefore proportional to the shape shows that the medial axis is the solution of a system of first area. On the other hand, boundary oriented skeletonizaorder differential equations. The new skeletonization algorithm provides a discrete parametric representation of the axis for tion algorithms refer to and use only boundary descriptors. smooth shapes, the input to the algorithm being a parametric Their complexity is potentially lower. Boundary oriented description of the shape boundary. Skeletonization examples skeletonization algorithms traditionally assume that the using the proposed algorithm are presented.  1996 Academic pre-image (i.e., the image before digitization) was a polyPress, Inc. gon. Skeletonization relying on boundary descriptions has been addressed by Montanari [13] and by Lee [11], who suggested exact solutions for polygonal shapes. Some good