The power crust, unions of balls, and the medial axis transform

By Nina Amenta, Sunghee Choi, R. Kolluri. Computational geometry, 2001

631 citations recorded by the source corpus.

Subfields: Computational Mechanics, Computer Graphics and Computer-Aided Design, Computer Vision and Pattern Recognition

View Paper: https://www.semanticscholar.org/paper/889df121b5be58ef9aee772f3854fd422daf6511

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In Computational Mechanics

In Computer Graphics and Computer-Aided Design

In Computer Vision and Pattern Recognition

Citations in the corpus

An image-based modeling framework for patient-specific computational hemodynamics (2008, background): “The envelope of all maximal inscribed spheres is the boundary surface of the object itself, therefore the (oriented) boundary surface and its medial axis are dual representations of the same shape [1].”
Skeleton based shape matching and retrieval (2003, neutral): “For 3D objects a medial surface is computed (see [21, 9]).”
Parallel Poisson Surface Reconstruction (2009, methodology): “Computational Geometry: Computational geometry based methods use geometric structures such as the Delaunay triangulation, alpha shapes or the Voronoi diagram [4–9] to partition space based on the input samples.”
Digital Topology and Geometry in Medical Imaging: A Survey (2015, methodology): “agrams to compute Voronoi skeletons [138], [278], [279], where”
A Framework for Geometric Analysis of Vascular Structures: Application to Cerebral Aneurysms (2009, methodology): “A classical approximation method for discrete surfaces relies on the concept of Voronoi diagram, defined as follows [24], [25].”
Direct visibility of point sets (2007, methodology): “…compute visibility of a point cloud is to reconstruct the surface [Hoppe et al. 1992; Bernardini et al. 1999; Curless and Levoy 1996; Carr et al. 2001; Amenta et al. 2001; Amenta et al. 2002; Amenta and Kil 2004; Fleishman et al. 2005] and determine visibility on the reconstructed triangular mesh.”
Consistent mesh partitioning and skeletonisation using the shape diameter function (2008, background): “However, computing the medial axis and the MAT of a surface mesh can be an expensive process, and the medial axis itself is difficult to handle [1, 9].”