Computer Aided Geometric Design - Special issue: Topics in CAGD
Geometric and solid modeling: an introduction
Geometric and solid modeling: an introduction
Thinning Methodologies-A Comprehensive Survey
IEEE Transactions on Pattern Analysis and Machine Intelligence
Accurate computation of the medial axis of a polyhedron
Proceedings of the fifth ACM symposium on Solid modeling and applications
Two- and three-dimensional patterns of the face
Two- and three-dimensional patterns of the face
Computational Geometry: Theory and Applications
Geometric constraint solver using multivariate rational spline functions
Proceedings of the sixth ACM symposium on Solid modeling and applications
Proceedings of the sixth ACM symposium on Solid modeling and applications
International Journal of Computer Vision
An Algorithm for the Medial Axis Transform of 3D Polyhedral Solids
IEEE Transactions on Visualization and Computer Graphics
Shape Description By Medial Surface Construction
IEEE Transactions on Visualization and Computer Graphics
IEEE Computer Graphics and Applications
Surface Skeletons Detected on the D6 Distance Transform
Proceedings of the Joint IAPR International Workshops on Advances in Pattern Recognition
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
Homotopy-preserving medial axis simplification
Proceedings of the 2005 ACM symposium on Solid and physical modeling
The Medial Scaffold of 3D Unorganized Point Clouds
IEEE Transactions on Pattern Analysis and Machine Intelligence
Stability and homotopy of a subset of the medial axis
SM '04 Proceedings of the ninth ACM symposium on Solid modeling and applications
Retrieving articulated 3-D models using medial surfaces
Machine Vision and Applications
Medial Representations: Mathematics, Algorithms and Applications
Medial Representations: Mathematics, Algorithms and Applications
Computing the Voronoi cells of planes, spheres and cylinders in R3
Computer Aided Geometric Design
Tracing ridges on B-Spline surfaces
2009 SIAM/ACM Joint Conference on Geometric and Physical Modeling
Interior Medial Axis Transform computation of 3D objects bound by free-form surfaces
Computer-Aided Design
SMI 2012: Full Medial design of blades for hydroelectric turbines and ship propellers
Computers and Graphics
Research on 3D medial axis transform via the saddle point programming method
Computer-Aided Design
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A new approach is presented for computing the interior medial axes of generic regions in R^3 bounded by C^(^4^)-smooth parametric B-spline surfaces. The generic structure of the 3D medial axis is a set of smooth surfaces along with a singular set consisting of edge curves, branch curves, fin points and six junction points. In this work, the medial axis singular set is first computed directly from the B-spline representation using a collection of robust higher order techniques. Medial axis surfaces are computed as a time trace of the evolving self-intersection set of the boundary under the the eikonal (grassfire) flow, where the bounding surfaces are dynamically offset along the inward normal direction. The eikonal flow results in special transition points that create, modify or annihilate evolving curve fronts of the (self-) intersection set. The transition points are explicitly identified using the B-spline representation. Evolution of the (self-) intersection set is computed by adapting a method for tracking intersection curves of two different surfaces deforming over generalized offset vector fields. The proposed algorithm accurately computes connected surfaces of the medial axis as well its singular set. This presents a complete solution along with accurate topological structure.