A Formal Classification of 3D Medial Axis Points and Their Local Geometry

This paper proposes a novel hypergraph skeletal representation for 3D shape based on a formal derivation of the generic structure of its medial axis. By classifying each skeletal point by its order of contact, we show that generically the medial axis consists of five types of points which are then organized into sheets, curves, and points: (i) sheets (manifolds with boundary) which are the locus of bitangent spheres with regular tangency1 A2 1; two types of curves (ii) the intersection curve of three sheets and the locus of centers of tri-tangent spheres, A3 1, and (iii) the boundary of sheets which are the locus of centers of spheres whose radius equals the larger principal curvature, i.e., higher order contact A3 points; and two types of points (iv) centers of quad-tangent spheres, A4 1, and, (v) centers of spheres with one regular tangency and one higher order tangency, A1A3. The geometry of the 3D medial axis thus consists of sheets (A2 1) bounded by one type of curve (A3) on thei...

• Type: Conference
• Year: 2000
• Where: CVPR
• Authors: Peter J. Giblin, Benjamin B. Kimia
• Keywords: Computer Vision, Contact A3 Points, CVPR 2000, Hypergraph Skeletal Representation, Medial Axis Hypergraph, Quad-tangent Spheres, Tri-tangent Spheres