Transitions of the 3D Medial Axis under a One-Parameter Family of Deformations

The instabilities of the medial axis of a shape under deformations have long been recognized as a major obstacle to its use in recognition and other applications. These instabilities, or transitions, occur when the structure of the medial axis graph changes abruptly under deformations of shape. The recent classification of these transitions in 2D for the medial axis and for the shock graph was a key factor both in the development of an object recognition system where the classified instabilities were utilized to represent deformation paths. The classification of generic transitions of the 3D medial axis could likewise potentially lead to a similar representation in 3D. In this paper, these transitions are classified, by examining the order of contact of spheres with the surface, leading to an enumeration of possible transitions, which are then examined on a case by case basis. Some cases are ruled out as never occurring in any family of deformations, while others are shown to be non-g...

• Type: Conference
• Year: 2002
• Where: ECCV
• Authors: Peter J. Giblin, Benjamin B. Kimia
• Keywords: Computer Vision, ECCV 2002, Generic Transitions, Medial Axis, Medial Axis Graph, Possible Transitions, Various Transitions