Comparison of curve and surface skeletonization methods for voxel shapes

Surface and curve skeletons are important shape descriptors with applications in shape matching, simplification, retrieval, and animation. In recent years, many surface and curve skeletonization methods for 3D shapes have been proposed. However, practical comparisons of such methods against each other and against given quality criteria are quite limited in the literature. In this paper, we compare 4 surface and 6 recent curve skeletonization methods that operate on voxel shapes. We first compare the selected methods from a global perspective, using the quality criteria established by a reference paper in the field. Next, we propose a detailed comparison that refines the gained insights by highlighting small-scale differences between skeletons obtained by different methods.

[1]  H. Blum Biological shape and visual science (part I) , 1973 .

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

[3]  Sunghee Choi,et al.  The power crust , 2001, SMA '01.

[4]  Piet W. Verbeek,et al.  Surface area estimation of digitized planes , 1993 .

[5]  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.

[6]  H. Blum Biological shape and visual science. I. , 1973, Journal of theoretical biology.

[7]  Michel Couprie,et al.  Discrete bisector function and Euclidean skeleton in 2D and 3D , 2007, Image Vis. Comput..

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

[9]  Chris Pudney,et al.  Distance-Ordered Homotopic Thinning: A Skeletonization Algorithm for 3D Digital Images , 1998, Comput. Vis. Image Underst..

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

[11]  M. Pauly,et al.  Discrete scale axis representations for 3D geometry , 2010, SIGGRAPH 2010.

[12]  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).

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

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

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

[16]  Aykut Erdem,et al.  Disconnected Skeleton: Shape at Its Absolute Scale , 2008, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[17]  Hans-Peter Seidel,et al.  An efficient construction of reduced deformable objects , 2013, ACM Trans. Graph..

[18]  Daniel Cohen-Or,et al.  L1-medial skeleton of point cloud , 2013, ACM Trans. Graph..

[19]  Kaleem Siddiqi,et al.  Hamilton-Jacobi Skeletons , 2002, International Journal of Computer Vision.

[20]  Tiow Seng Tan,et al.  Parallel Banding Algorithm to compute exact distance transform with the GPU , 2010, I3D '10.

[21]  Alfred M. Bruckstein,et al.  Skeletonization via Distance Maps and Level Sets , 1995, Comput. Vis. Image Underst..

[22]  Erin W. Chambers,et al.  A simple and robust thinning algorithm on cell complexes , 2010, Comput. Graph. Forum.

[23]  Gilles Bertrand,et al.  A parallel thinning algorithm for medial surfaces , 1995, Pattern Recognit. Lett..

[24]  Dinesh Manocha,et al.  Efficient computation of a simplified medial axis , 2003, SM '03.

[25]  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).

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

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

[28]  Hugues Talbot,et al.  A Discrete lambda-Medial Axis , 2009, DGCI.

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

[30]  Stina Svensson Reversible Surface Skeletons of 3D Objects by Iterative Thinning of Distance Transforms , 2000, Digital and Image Geometry.

[31]  Hans-Peter Seidel,et al.  Skeleton‐based Variational Mesh Deformations , 2007, Comput. Graph. Forum.

[32]  Martin Styner,et al.  Standardized evaluation methodology and reference database for evaluating coronary artery centerline extraction algorithms , 2009, Medical Image Anal..

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

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

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

[36]  Deborah Silver,et al.  Parameter-Controlled Volume Thinning , 1999, Graph. Model. Image Process..

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

[38]  Tamal K. Dey,et al.  Approximate medial axis as a voronoi subcomplex , 2002, SMA '02.

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

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

[41]  Tiow Seng Tan,et al.  Decomposing polygon meshes for interactive applications , 2001, I3D '01.

[42]  Ming Wan,et al.  Distance-field based skeletons for virtual navigation , 2001, Proceedings Visualization, 2001. VIS '01..

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

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

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

[46]  Michael Breuß,et al.  Refined Homotopic Thinning Algorithms and Quality Measures for Skeletonisation Methods , 2013, Innovations for Shape Analysis, Models and Algorithms.

[47]  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.

[48]  Edwin R. Hancock,et al.  Correcting Curvature-Density Effects in the Hamilton–Jacobi Skeleton , 2006, IEEE Transactions on Image Processing.

[49]  Alexandru Telea,et al.  Qualitative Comparison of Contraction-Based Curve Skeletonization Methods , 2013, ISMM.

[50]  Frederic Fol Leymarie,et al.  Simulating the Grassfire Transform Using an Active Contour Model , 1992, IEEE Trans. Pattern Anal. Mach. Intell..

[51]  Narendra Ahuja,et al.  Shape Representation Using a Generalized Potential Field Model , 1997, IEEE Trans. Pattern Anal. Mach. Intell..

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

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

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

[55]  Yaorong Ge,et al.  On the Generation of Skeletons from Discrete Euclidean Distance Maps , 1996, IEEE Trans. Pattern Anal. Mach. Intell..

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

[57]  Riccardo Scateni,et al.  Reconstructing the Curve-Skeletons of 3D Shapes Using the Visual Hull , 2012, IEEE Transactions on Visualization and Computer Graphics.

[58]  Balasubramanian Raman,et al.  Computing hierarchical curve-skeletons of 3D objects , 2005, The Visual Computer.

[59]  Matthew L. Baker,et al.  Computing a Family of Skeletons of Volumetric Models for Shape Description , 2006, GMP.