Computing the medial surface of a solid from a domain Delaunay triangulation
SMA '95 Proceedings of the third ACM symposium on Solid modeling and applications
Computing and simplifying 2D and 3D continuous skeletons
Computer Vision and Image Understanding
Accurate computation of the medial axis of a polyhedron
Proceedings of the fifth ACM symposium on Solid modeling and applications
Approximate medial axis as a voronoi subcomplex
Proceedings of the seventh ACM symposium on Solid modeling and applications
An Algorithm for the Medial Axis Transform of 3D Polyhedral Solids
IEEE Transactions on Visualization and Computer Graphics
Approximate medial axis for CAD models
SM '03 Proceedings of the eighth ACM symposium on Solid modeling and applications
Deformable M-Reps for 3D Medical Image Segmentation
International Journal of Computer Vision - Special Issue on Research at the University of North Carolina Medical Image Display Analysis Group (MIDAG)
A Formal Classification of 3D Medial Axis Points and Their Local Geometry
IEEE Transactions on Pattern Analysis and Machine Intelligence
Determining the Geometry of Boundaries of Objects from Medial Data
International Journal of Computer Vision
A Tracing Algorithm for Constructing Medial Axis Transform of 3D Objects Bound by Free-Form Surfaces
SMI '05 Proceedings of the International Conference on Shape Modeling and Applications 2005
The Medial Scaffold of 3D Unorganized Point Clouds
IEEE Transactions on Pattern Analysis and Machine Intelligence
A divide and conquer algorithm for medial surface calculation of planar polyhedra
Computer-Aided Design
Medial Representations: Mathematics, Algorithms and Applications
Medial Representations: Mathematics, Algorithms and Applications
Rational two-parameter families of spheres and rational offset surfaces
Journal of Symbolic Computation
MOS surfaces: medial surface transforms with rational domain boundaries
Proceedings of the 12th IMA international conference on Mathematics of surfaces XII
Interior Medial Axis Transform computation of 3D objects bound by free-form surfaces
Computer-Aided Design
Computing medial axes of generic 3D regions bounded by B-spline surfaces
Computer-Aided Design
Three-Dimensional Shape Description Using the Symmetric Axis Transform I: Theory
IEEE Transactions on Pattern Analysis and Machine Intelligence
| Hi-index | 0.00 |
The present paper investigates the 3D medial axis transform of objects bounded by freeform surfaces via the saddle point programming method, a mathematical programming approach used to identify the saddle points of a function. After exploring the local geometry and saddle point property of 3D medial axis transform, the mathematical programming method is employed to construct the saddle point programming models. Based on the optimality conditions that the optimal solutions should satisfy, a generic algorithm for computing various medial axis points is developed. In order to identify the junction points and localize the problem, the boundary and the skeletal curves are divided into skeletal segments, and it is proved to be efficient and accurate by numerical examples.