Smoothness and geometry of boundaries associated to skeletal structures I: sufficient conditions for smoothness.

DOI10.17615/xgr2-f583zbMath1047.57014OpenAlexW4298842373MaRDI QIDQ1417742

James Damon

Publication date: 6 January 2004

Published in: Annales de l'Institut Fourier (Search for Journal in Brave)

Full work available at URL: http://www.numdam.org/item?id=AIF_2003__53_6_1941_0

zbMATH Keywords

shape operatortubular neighborhoodradial flowBlum medial axisgrassfire flowshock setskeletal strucutureWhitney stratified set

Mathematics Subject Classification ID

Higher-dimensional and -codimensional surfaces in Euclidean and related (n)-spaces (53A07) Computer graphics; computational geometry (digital and algorithmic aspects) (68U05) Stratified sets (58A35) Stratifications in topological manifolds (57N80)

Related Items (8)

Non-linear hypothesis testing of geometric object properties of shapes applied to hippocampi ⋮ Tree structure for contractible regions in \(\mathbb R^{3}\) ⋮ The global medial structure of regions in \(\mathbb R^3\) ⋮ Modeling multi-object configurations via medial/skeletal linking structures ⋮ Medial/Skeletal Linking Structures for Multi-Region Configurations ⋮ Rigidity properties of the Blum medial axis ⋮ Jacobi’s last geometric statement extends to a wider class of Liouville surfaces ⋮ Determining the geometry of boundaries of objects from medial data

Cites Work

• Stratified mappings - structure and triangulability
• Singularities of the maximum of a parametrically dependent function
• Topological stability of smooth mappings
• Shape description using weighted symmetric axis features
• Hamilton-Jacobi skeletons
• Symmetry sets
• Growth, motion and 1-parameter families of symmetry sets
• Differential Topology
• Triangulation of Stratified Objects
• Smoothness and geometry of boundaries associated to skeletal structures, II: Geometry in the Blum case
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