Spatial tessellations: concepts and applications of Voronoi diagrams
Spatial tessellations: concepts and applications of Voronoi diagrams
International Journal of Computer Vision
The fast construction of extension velocities in level set methods
Journal of Computational Physics
Stochastic Jump-Diffusion Process for Computing Medial Axes in Markov Random Fields
IEEE Transactions on Pattern Analysis and Machine Intelligence
Shock Graphs and Shape Matching
International Journal of Computer Vision
Symmetry Sets and Medial Axes in Two and Three Dimensions
Proceedings of the 9th IMA Conference on the Mathematics of Surfaces
Scale-Space '01 Proceedings of the Third International Conference on Scale-Space and Morphology in Computer Vision
ICCV '99 Proceedings of the International Conference on Computer Vision-Volume 2 - Volume 2
Representation and Self-Similarity of Shapes
ICCV '98 Proceedings of the Sixth International Conference on Computer Vision
Local Symmetries of Shapes in Arbitrary Dimension
ICCV '98 Proceedings of the Sixth International Conference on Computer Vision
Image Analysis and Mathematical Morphology
Image Analysis and Mathematical Morphology
Distance functions and skeletal representations of rigid and non-rigid planar shapes
Computer-Aided Design
A family of skeletons for motion planning and geometric reasoning applications
Artificial Intelligence for Engineering Design, Analysis and Manufacturing - Representing and Reasoning About Three-Dimensional Space
Scale-Space'05 Proceedings of the 5th international conference on Scale Space and PDE Methods in Computer Vision
Medial zones: Formulation and applications
Computer-Aided Design
Poisson Skeleton Revisited: a New Mathematical Perspective
Journal of Mathematical Imaging and Vision
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Noise presents a major difficulty in implementing various methods of shape analysis currently in use. A way to deal with this problem is to presmooth shapes. However, this is problematic on several counts. It makes extensions to 3D shapes difficult. The shape may lack sufficiently many pixels in its narrow regions for computing high-order smoothing operators. How constructs such as shape skeletons are affected by smoothing is not at all clear. The objective of this paper is to demonstrate a new approach to shape analysis which does not require presmoothing of the shape. The basic tool is the ''gray skeleton'' which is the shape skeleton whose points are associated with significance numbers. A pruning method is developed for extracting a ''noise-free'' skeleton from the gray skeleton. The problem of segmenting shapes is addressed by formulating a segmetation functional in terms of gray skeletons. Fast algorithms for computing and pruning gray skeletons, and for finding an approximate minimum of the segmentation functional make the approach practical to implement.