Building skeleton models via 3-D medial surface/axis thinning algorithms
CVGIP: Graphical Models and Image Processing
A new Voronoi-based surface reconstruction algorithm
Proceedings of the 25th annual conference on Computer graphics and interactive techniques
Implicit fairing of irregular meshes using diffusion and curvature flow
Proceedings of the 26th annual conference on Computer graphics and interactive techniques
Topology matching for fully automatic similarity estimation of 3D shapes
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Distance-field based skeletons for virtual navigation
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Extended Reeb Graphs for Surface Understanding and Description
DGCI '00 Proceedings of the 9th International Conference on Discrete Geometry for Computer Imagery
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International Journal of Computer Vision - Special Issue on Research at the University of North Carolina Medical Image Display Analysis Group (MIDAG)
A remeshing approach to multiresolution modeling
Proceedings of the 2004 Eurographics/ACM SIGGRAPH symposium on Geometry processing
Simultaneous shape decomposition and skeletonization
Proceedings of the 2006 ACM symposium on Solid and physical modeling
Curve-Skeleton Properties, Applications, and Algorithms
IEEE Transactions on Visualization and Computer Graphics
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ACM SIGGRAPH 2007 papers
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SGP '06 Proceedings of the fourth Eurographics symposium on Geometry processing
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SGP '07 Proceedings of the fifth Eurographics symposium on Geometry processing
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Skeleton extraction by mesh contraction
ACM SIGGRAPH 2008 papers
Medial Representations: Mathematics, Algorithms and Applications
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Curve skeleton extraction from incomplete point cloud
ACM SIGGRAPH 2009 papers
Variational Curve Skeletons Using Gradient Vector Flow
IEEE Transactions on Pattern Analysis and Machine Intelligence
Discrete scale axis representations for 3D geometry
ACM SIGGRAPH 2010 papers
Point Cloud Skeletons via Laplacian Based Contraction
SMI '10 Proceedings of the 2010 Shape Modeling International Conference
The power crust, unions of balls, and the medial axis transform
Computational Geometry: Theory and Applications
Centroidal Voronoi Tessellation of Line Segments and Graphs
Computer Graphics Forum
Computer Graphics Forum
Reconstructing the Curve-Skeletons of 3D Shapes Using the Visual Hull
IEEE Transactions on Visualization and Computer Graphics
L1-medial skeleton of point cloud
ACM Transactions on Graphics (TOG) - SIGGRAPH 2013 Conference Proceedings
Extracting curve-skeletons from digital shapes using occluding contours
The Visual Computer: International Journal of Computer Graphics
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Inspired by recent developments in contraction-based curve skeleton extraction, we formulate the skeletonization problem via mean curvature flow (MCF). While the classical application of MCF is surface fairing, we take advantage of its area-minimizing characteristic to drive the curvature flow towards the extreme so as to collapse the input mesh geometry and obtain a skeletal structure. By analyzing the differential characteristics of the flow, we reveal that MCF locally increases shape anisotropy. This justifies the use of curvature motion for skeleton computation, and leads to the generation of what we call “mean curvature skeletons”. To obtain a stable and efficient discretization, we regularize the surface mesh by performing local remeshing via edge splits and collapses. Simplifying mesh connectivity throughout the motion leads to more efficient computation and avoids numerical instability arising from degeneracies in the triangulation. In addition, the detection of collapsed geometry is facilitated by working with simplified mesh connectivity and monitoring potential non-manifold edge collapses. With topology simplified throughout the flow, minimal post-processing is required to convert the collapsed geometry to a curve. Formulating skeletonization via MCF allows us to incorporate external energy terms easily, resulting in a constrained flow. We define one such energy term using the Voronoi medial skeleton and obtain a medially centred curve skeleton. We call the intermediate results of our skeletonization motion meso-skeletons; these consist of a mixture of curves and surface sheets as appropriate to the local 3D geometry they capture. © 2012 Wiley Periodicals, Inc.