Qualitative Comparison of Contraction-Based Curve Skeletonization Methods

In recent years, many new methods have been proposed for extracting curve skeletons of 3D shapes, using a mesh-contraction principle. However, it is still unclear how these methods perform with respect to each other, and with respect to earlier voxel-based skeletonization methods, from the viewpoint of certain quality criteria known from the literature. In this study, we compare six recent contraction-based curve-skeletonization methods that use a mesh representation against six accepted quality criteria, on a set of complex 3D shapes. Our results reveal previously unknown limitations of the compared methods, and link these limitations to algorithmic aspects of the studied methods.

[1]  Hans-Christian Hege,et al.  Fast visualization of plane-like structures in voxel data , 2002, IEEE Visualization, 2002. VIS 2002..

[2]  Attila Kuba,et al.  Directional 3D Thinning Using 8 Subiterations , 1999, DGCI.

[3]  Alexandru Telea,et al.  An Augmented Fast Marching Method for Computing Skeletons and Centerlines , 2002, VisSym.

[4]  Gábor Székely,et al.  Multiscale Medial Loci and Their Properties , 2003, International Journal of Computer Vision.

[5]  P. Frey.  Anisotropic surface remeshing , 2001 .

[6]  Tamal K. Dey,et al.  Defining and computing curve-skeletons with medial geodesic function , 2006, SGP '06.

[7]  Benjamin B. Kimia,et al.  The Medial Scaffold of 3D Unorganized Point Clouds , 2007, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[8]  D. Cohen-Or,et al.  Curve skeleton extraction from incomplete point cloud , 2009, SIGGRAPH 2009.

[9]  Wim H. Hesselink,et al.  Euclidean Skeletons of Digital Image and Volume Data in Linear Time by the Integer Medial Axis Transform , 2008, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[10]  Pascal Frey,et al.  YAMS A fully Automatic Adaptive Isotropic Surface Remeshing Procedure , 2001 .

[11]  Aly A. Farag,et al.  Variational Curve Skeletons Using Gradient Vector Flow , 2009, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[12]  Gabriella Sanniti di Baja,et al.  Distance-Driven Skeletonization in Voxel Images , 2011, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[13]  Dinesh Manocha,et al.  Homotopy-preserving medial axis simplification , 2005, SPM '05.

[14]  Kaleem Siddiqi,et al.  Medial Representations: Mathematics, Algorithms and Applications , 2008 .

[15]  Kaleem Siddiqi,et al.  Flux driven automatic centerline extraction , 2005, Medical Image Anal..

[16]  Andrea Tagliasacchi,et al.  Mean Curvature Skeletons , 2012, Comput. Graph. Forum.

[17]  Alexandru Telea,et al.  Computing Multiscale Curve and Surface Skeletons of Genus 0 Shapes Using a Global Importance Measure , 2008, IEEE Transactions on Visualization and Computer Graphics.

[18]  Ariel Shamir,et al.  On‐the‐fly Curve‐skeleton Computation for 3D Shapes , 2007, Comput. Graph. Forum.

[19]  Benjamin B. Kimia,et al.  A formal classification of 3D medial axis points and their local geometry , 2000, Proceedings IEEE Conference on Computer Vision and Pattern Recognition. CVPR 2000 (Cat. No.PR00662).

[20]  Tong-Yee Lee,et al.  Skeleton extraction by mesh contraction , 2008, SIGGRAPH 2008.

[21]  Sang Won Bae,et al.  3D medial axis point approximation using nearest neighbors and the normal field , 2011, The Visual Computer.

[22]  Serge Beucher.  Digital skeletons in Euclidean and geodesic spaces , 1994, Signal Process..

[23]  Junjie Cao,et al.  Point Cloud Skeletons via Laplacian Based Contraction , 2010, 2010 Shape Modeling International Conference.

[24]  Olaf Kübler,et al.  Hierarchic Voronoi skeletons , 1995, Pattern Recognit..

[25]  W. Marsden.  I and J , 2012 .

[26]  F. Meyer.  Skeletons and perceptual graphs , 1989 .

[27]  J. Damon.  The global medial structure of regions in R 3 , 2006, 0903.0394.

[28]  Jean Serra,et al.  Image Analysis and Mathematical Morphology , 1983 .

[29]  Alexandru Telea,et al.  Computing Curve Skeletons from Medial Surfaces of 3D Shapes , 2012, TPCG.

[30]  Greg Turk,et al.  Simplification and Repair of Polygonal Models Using Volumetric Techniques , 2003, IEEE Trans. Vis. Comput. Graph..

[31]  Wenyu Liu,et al.  Skeleton Pruning by Contour Partitioning with Discrete Curve Evolution , 2007, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[32]  Deborah Silver,et al.  Curve-Skeleton Properties, Applications, and Algorithms , 2007, IEEE Transactions on Visualization and Computer Graphics.

[33]  G. G. Stokes.  "J." , 1890, The New Yale Book of Quotations.

[34]  Benjamin B. Kimia,et al.  Surface Reconstruction from Point Clouds by Transforming the Medial Scaffold , 2007, Sixth International Conference on 3-D Digital Imaging and Modeling (3DIM 2007).

[35]  Alexandru Telea,et al.  Surface and Curve Skeletonization of Large 3D Models on the GPU , 2013, IEEE Transactions on Pattern Analysis and Machine Intelligence.