Inspection of Printed Circuit Boards by Connectivity Preserving Shrinking
IEEE Transactions on Pattern Analysis and Machine Intelligence
A Theory of Multiscale, Curvature-Based Shape Representation for Planar Curves
IEEE Transactions on Pattern Analysis and Machine Intelligence
Differential and topological properties of medial axis transforms
Graphical Models and Image Processing
New algorithm for medial axis transform of plane domain
Graphical Models and Image Processing
Veinerization: A New Shape Description for Flexible Skeletonization
IEEE Transactions on Pattern Analysis and Machine Intelligence
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
A Method for Obtaining Skeletons Using a Quasi-Euclidean Distance
Journal of the ACM (JACM)
Ligature instabilities in the perceptual organization of shape
Computer Vision and Image Understanding
Proceedings of the sixth ACM symposium on Solid modeling and applications
Hyperbolic Hausdorff distance for medial axis transform
Graphical Models
Linear One-Sided Stability of MAT for Weakly Injective Domain
Journal of Mathematical Imaging and Vision
An Algorithm for the Medial Axis Transform of 3D Polyhedral Solids
IEEE Transactions on Visualization and Computer Graphics
One-sided Stability of MAT and Its Applications
VMV '01 Proceedings of the Vision Modeling and Visualization Conference 2001
Stability Analysis of Medial Axis Transform under Relative Hausdorff Distance
ICPR '00 Proceedings of the International Conference on Pattern Recognition - Volume 3
Linear One-Sided Stability of MAT for Weakly Injective Domain
Journal of Mathematical Imaging and Vision
Any open bounded subset of Rn has the same homotopy type than its medial axis
SM '03 Proceedings of the eighth ACM symposium on Solid modeling and applications
Automating the CAD/CAE dimensional reduction process
SM '03 Proceedings of the eighth ACM symposium on Solid modeling and applications
Efficient computation of a simplified medial axis
SM '03 Proceedings of the eighth ACM symposium on Solid modeling and applications
Stability and Finiteness Properties of Medial Axis and Skeleton
Journal of Dynamical and Control Systems
Curve-Skeleton Properties, Applications, and Algorithms
IEEE Transactions on Visualization and Computer Graphics
The Geometric Stability of Voronoi Diagrams with Respect to Small Changes of the Sites
Proceedings of the twenty-seventh annual symposium on Computational geometry
New algorithm to extract centerline of 2D objects based on clustering
ICIAR'07 Proceedings of the 4th international conference on Image Analysis and Recognition
Hi-index | 0.00 |
Despite its usefulness in many applications, the medial axis transform (MAT) is very sensitive to the change of the boundary in the sense that, even if a shape is perturbed only slightly, the Hausdorff distance between the MATs of the original shape and the perturbed one may be large. However, it is known that MATs of 2D domains are stable if we view this phenomenon with the one-sided Hausdorff distance. This result depends on the fact that MATs are stable if the differences between them are measured with the recently introduced hyperbolic Hausdorff distance. In this paper, we extend the result for the one-sided stability of the MAT to a class of 3D domains called weakly injective, which contains many important 3D shapes typically appearing in solid modeling. Especially, the weakly injective 3D domains can have sharp features like corners or edges. In fact, by using the stability of the MAT under the hyperbolic Hausdorff distance, we obtain an explicit bound for the one-sided Hausdorff distance of the MAT of a weakly injective 3D domain with respect to that of a perturbed domain, which is linear with respect to the domain perturbation. We discuss some consequences of this result concerning the computation and the approximation of the medial axis transform of 3D objects.