Example based skeletonization using harmonic one-forms

This paper presents a method to extract skeletons using examples. Our method is based on the observation that many deformations in real world applications are isometric or near isometric. By taking advantage of the intrinsic property of harmonic 1-form, i.e., it is determined by the metric and independent of the resolution and embedding, our method can easily find a consistent mapping between the reference and example poses which can be in different resolutions and triangulations. We first construct the skeleton-like Reeb graph of a harmonic function defined on the given poses. Then by examining the changes of mean curvatures, we identify the initial locations of joints. Finally we refine the joint locations by solving a constrained optimization problem. To demonstrate the efficacy of our method, we apply the extracted skeletons to pose space deformation and skeleton transfer.

[1]  Dinesh K. Pai,et al.  EigenSkin: real time large deformation character skinning in hardware , 2002, SCA '02.

[2]  Peter-Pike J. Sloan,et al.  Shape by example , 2001, I3D '01.

[3]  J. Tierny,et al.  3D Mesh Skeleton Extraction Using Topological and Geometrical Analyses , 2006 .

[4]  Michael Garland,et al.  Harmonic functions for quadrilateral remeshing of arbitrary manifolds , 2005, Comput. Aided Geom. Des..

[5]  Jovan Popović,et al.  Deformation transfer for triangle meshes , 2004, SIGGRAPH 2004.

[6]  Yalin Wang,et al.  Optimal global conformal surface parameterization , 2004, IEEE Visualization 2004.

[7]  Ayellet Tal,et al.  Hierarchical mesh decomposition using fuzzy clustering and cuts , 2003, ACM Trans. Graph..

[8]  Silvia Biasotti,et al.  Extended Reeb Graphs for Surface Understanding and Description , 2000, DGCI.

[9]  J. Hart,et al.  Fair morse functions for extracting the topological structure of a surface mesh , 2004, SIGGRAPH 2004.

[10]  Silvia Biasotti,et al.  Shape Abstraction Using Computational Topology Techniques , 2002, Workshop on Geometric Modeling.

[11]  Hans-Peter Seidel,et al.  Marker-free kinematic skeleton estimation from sequences of volume data , 2004, VRST '04.

[12]  W SederbergThomas,et al.  Free-form deformation of solid geometric models , 1986 .

[13]  Tsuneya Kurihara,et al.  Modeling deformable human hands from medical images , 2004, SCA '04.

[14]  Jirí Zára,et al.  Spherical blend skinning: a real-time deformation of articulated models , 2005, I3D '05.

[15]  Christine Depraz,et al.  Harmonic skeleton for realistic character animation , 2007, SCA '07.

[16]  Daniel Cohen-Or,et al.  To appear in the ACM SIGGRAPH conference proceedings Handle-Aware Isolines for Scalable Shape Editing , 2022 .

[17]  Xiaohua Xian,et al.  A Powell Optimization Approach for Example-Based Skinning in a Production Animation Environment , 2006 .

[18]  John P. Lewis,et al.  Pose Space Deformation: A Unified Approach to Shape Interpolation and Skeleton-Driven Deformation , 2000, SIGGRAPH.

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

[20]  Daniel Thalmann,et al.  Joint-dependent local deformations for hand animation and object grasping , 1989 .

[21]  T. Pavlidis.  A thinning algorithm for discrete binary images , 1980 .

[22]  Ilya Baran,et al.  Automatic rigging and animation of 3D characters , 2007, SIGGRAPH 2007.

[23]  Hong Qin,et al.  Manifold splines , 2006, Graph. Model..

[24]  Yoshifumi Kitamura,et al.  Interactive skeleton extraction for 3D animation using geodesic distances , 2006, SIGGRAPH '06.

[25]  Giuseppe Patanè,et al.  Affine-Invariant Skeleton of 3D Shapes , 2002, Shape Modeling International.

[26]  Silvia Biasotti,et al.  An overview on properties and efficacy of topological skeletons in shape modeling , 2003, 2003 Shape Modeling International..

[27]  Doug L. James,et al.  Skinning mesh animations , 2005, ACM Trans. Graph..

[28]  Thomas W. Sederberg,et al.  Free-form deformation of solid geometric models , 1986, SIGGRAPH.

[29]  Mathieu Desbrun,et al.  Removing excess topology from isosurfaces , 2004, TOGS.

[30]  Scott Schaefer,et al.  Example-based skeleton extraction , 2007, Symposium on Geometry Processing.

[31]  Partha Pratim Das,et al.  Thinning of 3-D images using the Safe Point Thinning Algorithm (SPTA) , 1989, Pattern Recognit. Lett..

[32]  Valerio Pascucci,et al.  Loops in Reeb Graphs of 2-Manifolds , 2004, Discret. Comput. Geom..

[33]  Pierre Alliez,et al.  Designing quadrangulations with discrete harmonic forms , 2006, SGP '06.

[34]  Nancy M. Amato,et al.  Simultaneous shape decomposition and skeletonization , 2006, SPM '06.

[35]  Wan-Chun Ma,et al.  Skeleton extraction of 3D objects with radial basis functions , 2003, 2003 Shape Modeling International..

[36]  Daniel Cohen-Or,et al.  Salient geometric features for partial shape matching and similarity , 2006, TOGS.

[37]  James E. Gain,et al.  Animation space: A truly linear framework for character animation , 2006, TOGS.

[38]  Hong Qin,et al.  A C1 Globally Interpolatory Spline of Arbitrary Topology , 2005, VLSM.

[39]  Nadia Magnenat-Thalmann,et al.  Knowledge-based extraction of control skeletons for animation , 2007, IEEE International Conference on Shape Modeling and Applications 2007 (SMI '07).

[40]  Tong-Yee Lee,et al.  Mesh pose-editing using examples , 2007 .

[41]  Hong Qin,et al.  Meshless thin-shell simulation based on global conformal parameterization , 2006, IEEE Transactions on Visualization and Computer Graphics.

[42]  Michael Gleicher,et al.  Building efficient, accurate character skins from examples , 2003, ACM Trans. Graph..

[43]  Olga Sorkine-Hornung,et al.  Context‐Aware Skeletal Shape Deformation , 2007, Comput. Graph. Forum.

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

[45]  Paul Merrell,et al.  Example-based model synthesis , 2007, SI3D.

[46]  Valerio Pascucci,et al.  Robust on-line computation of Reeb graphs: simplicity and speed , 2007, SIGGRAPH 2007.

[47]  Hong Qin,et al.  Manifold T-Spline , 2006, GMP.

[48]  S. Yau,et al.  Global conformal surface parameterization , 2003 .

[49]  Marc Alexa,et al.  Context-based surface completion , 2004, ACM Trans. Graph..