A Theory of Multiscale, Curvature-Based Shape Representation for Planar Curves
IEEE Transactions on Pattern Analysis and Machine Intelligence
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
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
Linear onesided stability of MAT for weakly injective 3D domain
Proceedings of the seventh ACM symposium on Solid modeling and applications
Hyperbolic Hausdorff distance for medial axis transform
Graphical Models
One-sided Stability of MAT and Its Applications
VMV '01 Proceedings of the Vision Modeling and Visualization Conference 2001
On the Local Form and Transitions of Symmetry Sets, Medial Axes, and Shocks
International Journal of Computer Vision - Special Issue on Computational Vision at Brown University
Linear onesided stability of MAT for weakly injective 3D domain
Proceedings of the seventh ACM symposium on Solid modeling and applications
Linear Time Algorithms for Exact Distance Transform
Journal of Mathematical Imaging and Vision
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Medial axis transform (MAT) is very sensitive to noise, 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. But it turns out that MAT is stable, if we view this phenomenon with the one-sided Hausdorff distance, rather than with the two-sided Hausdorff distance. In this paper, we show that, if the original domain is weakly injective, which means that the MAT of the domain has no end point which is the center of an inscribed circle osculating the boundary at only one point, the one-sided Hausdorff distance of the original domain's MAT with respect to that of the perturbed one is bounded linearly with the Hausdorff distance of the perturbation. We also show by example that the linearity of this bound cannot be achieved for the domains which are not weakly injective. In particular, these results apply to the domains with sharp corners, which were excluded in the past. One consequence of these results is that we can clarify theoretically the notion of extracting “the essential part of the MAT”, which is the heart of the existing pruning methods.