Group-Valued Regularization Framework for Motion Segmentation of Dynamic Non-rigid Shapes

Understanding of articulated shape motion plays an important role in many applications in the mechanical engineering, movie industry, graphics, and vision communities. In this paper, we study motion-based segmentation of articulated 3D shapes into rigid parts. We pose the problem as finding a group-valued map between the shapes describing the motion, forcing it to favor piecewise rigid motions. Our computation follows the spirit of the Ambrosio-Tortorelli scheme for Mumford-Shah segmentation, with a diffusion component suited for the group nature of the motion model. Experimental results demonstrate the effectiveness of the proposed method in non-rigid motion segmentation.

[1]  Ariel Shamir,et al.  A survey on Mesh Segmentation Techniques , 2008, Comput. Graph. Forum.

[2]  Franck Hétroy,et al.  A Framework for motion-based mesh sequence segmentation , 2010 .

[3]  Christoph Bregler,et al.  Non-Rigid Modeling of Body Segments for Improved Skeletal Motion Estimation , 2003 .

[4]  Knut-Andreas Lie,et al.  Scale Space and Variational Methods in Computer Vision, Second International Conference, SSVM 2009, Voss, Norway, June 1-5, 2009. Proceedings , 2009, SSVM.

[5]  Nir A. Sochen,et al.  Regularizing Flows over Lie Groups , 2009, Journal of Mathematical Imaging and Vision.

[6]  David A. Forsyth,et al.  Generalizing motion edits with Gaussian processes , 2009, ACM Trans. Graph..

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

[8]  Tong-Yee Lee,et al.  Segmenting a deforming mesh into near-rigid components , 2006, The Visual Computer.

[9]  Ron Kimmel,et al.  Generalized multidimensional scaling: A framework for isometry-invariant partial surface matching , 2006, Proceedings of the National Academy of Sciences of the United States of America.

[10]  Teofilo F. GONZALEZ,et al.  Clustering to Minimize the Maximum Intercluster Distance , 1985, Theor. Comput. Sci..

[11]  Daniel Cremers,et al.  Motion Competition: A variational framework for piecewise parametric motion segmentation , 2005 .

[12]  W. Marsden.  I and J , 2012 .

[13]  D. Hochbaum,et al.  A best possible approximation algorithm for the k--center problem , 1985 .

[14]  Paul J. Besl,et al.  A Method for Registration of 3-D Shapes , 1992, IEEE Trans. Pattern Anal. Mach. Intell..

[15]  Helmut Leopold,et al.  Multimedia Applications, Services and Techniques — ECMAST’99 , 2000, Lecture Notes in Computer Science.

[16]  Mark Meyer,et al.  Implicit fairing of irregular meshes using diffusion and curvature flow , 1999, SIGGRAPH.

[17]  D. Mumford,et al.  Optimal approximations by piecewise smooth functions and associated variational problems , 1989 .

[18]  Alan Brunton,et al.  Segmenting animated objects into near-rigid components , 2010, The Visual Computer.

[19]  Radu Horaud,et al.  Articulated shape matching using Laplacian eigenfunctions and unsupervised point registration , 2008, 2008 IEEE Conference on Computer Vision and Pattern Recognition.

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

[21]  Alexander M. Bronstein,et al.  Numerical Geometry of Non-Rigid Shapes , 2009, Monographs in Computer Science.

[22]  Martin Rumpf,et al.  An image processing approach to surface matching , 2005, SGP '05.

[23]  B. Hall.  Lie Groups, Lie Algebras, and Representations: An Elementary Introduction , 2004 .

[24]  A. Iserles,et al.  Lie-group methods , 2000, Acta Numerica.

[25]  Hao Zhang,et al.  Robust 3D Shape Correspondence in the Spectral Domain , 2006, IEEE International Conference on Shape Modeling and Applications 2006 (SMI'06).

[26]  Fatih Murat Porikli,et al.  Learning on lie groups for invariant detection and tracking , 2008, 2008 IEEE Conference on Computer Vision and Pattern Recognition.

[27]  Ron Kimmel,et al.  Hierarchical Matching of Non-rigid Shapes , 2011, SSVM.

[28]  Mauro R. Ruggeri,et al.  Spectral-Driven Isometry-Invariant Matching of 3D Shapes , 2010, International Journal of Computer Vision.

[29]  Keenan Crane,et al.  Lie group integrators for animation and control of vehicles , 2009, TOGS.

[30]  I. Holopainen.  Riemannian Geometry , 1927, Nature.

[31]  Peter Meer,et al.  Nonlinear Mean Shift over Riemannian Manifolds , 2009, International Journal of Computer Vision.

[32]  Mohamed Daoudi,et al.  Fast and precise kinematic skeleton extraction of 3D dynamic meshes , 2008, 2008 19th International Conference on Pattern Recognition.

[33]  Bernhard Burgeth,et al.  Scale Spaces on Lie Groups , 2007, SSVM.

[34]  Michael G. Strintzis,et al.  Object Articulation Based on Local 3D Motion Estimation , 1999, ECMAST.

[35]  Thomas A. Funkhouser,et al.  A benchmark for 3D mesh segmentation , 2009, ACM Trans. Graph..

[36]  Michael Damsgaard,et al.  Do kinematic models reduce the effects of soft tissue artefacts in skin marker-based motion analysis? An in vivo study of knee kinematics. , 2010, Journal of biomechanics.

[37]  L. Ambrosio,et al.  Approximation of functional depending on jumps by elliptic functional via t-convergence , 1990 .

[38]  J. Eells,et al.  Harmonic Mappings of Riemannian Manifolds , 1964 .

[39]  David B. Shmoys,et al.  A Best Possible Heuristic for the k-Center Problem , 1985, Math. Oper. Res..

[40]  Nahum Kiryati,et al.  Piecewise-Smooth Dense Optical Flow via Level Sets , 2006, International Journal of Computer Vision.

[41]  J. Weickert,et al.  Lucas/Kanade meets Horn/Schunck: combining local and global optic flow methods , 2005 .

[42]  Marco Attene,et al.  Mesh Segmentation - A Comparative Study , 2006, IEEE International Conference on Shape Modeling and Applications 2006 (SMI'06).

[43]  Daniel Cremers,et al.  Motion Competition: A Variational Approach to Piecewise Parametric Motion Segmentation , 2005, International Journal of Computer Vision.

[44]  Søren Hauberg,et al.  Gaussian-Like Spatial Priors for Articulated Tracking , 2010, ECCV.

[45]  Sebastian Thrun,et al.  Recovering Articulated Object Models from 3D Range Data , 2004, UAI.

[46]  Kiyoharu Aizawa,et al.  Motion Segmentation for Time-Varying Mesh Sequences Based on Spherical Registration , 2009, EURASIP J. Adv. Signal Process..

[47]  Andreas Müller,et al.  Differential-Geometric Modelling and Dynamic Simulation of Multibody Systems , 2009 .

[48]  N. N. Yanenko,et al.  The Method of Fractional Steps , 1971 .

[49]  Ben Taskar,et al.  Cascaded Models for Articulated Pose Estimation , 2010, ECCV.

[50]  L. Rudin,et al.  Nonlinear total variation based noise removal algorithms , 1992 .

[51]  Aaron Hertzmann,et al.  Learning 3D mesh segmentation and labeling , 2010, SIGGRAPH 2010.