Group-Valued Regularization for Analysis of Articulated Motion

We present a novel method for estimation of articulated motion in depth scans. The method is based on a framework for regularization of vector- and matrix- valued functions on parametric surfaces. We extend augmented-Lagrangian total variation regularization to smooth rigid motion cues on the scanned 3D surface obtained from a range scanner. We demonstrate the resulting smoothed motion maps to be a powerful tool in articulated scene understanding, providing a basis for rigid parts segmentation, with little prior assumptions on the scene, despite the noisy depth measurements that often appear in commodity depth scanners.

[1]  Hao Li,et al.  Global Correspondence Optimization for Non‐Rigid Registration of Depth Scans , 2008, Comput. Graph. Forum.

[2]  E. Celledoni,et al.  Lie group methods for rigid body dynamics and time integration on manifolds , 2003 .

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

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

[5]  Larry S. Davis,et al.  Learned Models for Estimation of Rigid and Articulated Human Motion from Stationary or Moving Camera , 2004, International Journal of Computer Vision.

[6]  Hui Chen,et al.  3D free-form object recognition in range images using local surface patches , 2004, Proceedings of the 17th International Conference on Pattern Recognition, 2004. ICPR 2004..

[7]  Gérard G. Medioni,et al.  Object modelling by registration of multiple range images , 1992, Image Vis. Comput..

[8]  Alessio Del Bue,et al.  Optimal Metric Projections for Deformable and Articulated Structure-from-Motion , 2011, International Journal of Computer Vision.

[9]  Dorin Comaniciu,et al.  Mean Shift: A Robust Approach Toward Feature Space Analysis , 2002, IEEE Trans. Pattern Anal. Mach. Intell..

[10]  Gérard G. Medioni,et al.  3D object recognition in range images using visibility context , 2011, 2011 IEEE/RSJ International Conference on Intelligent Robots and Systems.

[11]  Helmut Pottmann,et al.  Geometry of the Squared Distance Function to Curves and Surfaces , 2002, VisMath.

[12]  Frank Chongwoo Park,et al.  A Lie Group Formulation of Robot Dynamics , 1995, Int. J. Robotics Res..

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

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

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

[16]  T. Banchoff,et al.  Differential Geometry of Curves and Surfaces , 2010 .

[17]  R. Kimmel,et al.  An efficient solution to the eikonal equation on parametric manifolds , 2004 .

[18]  Berthold K. P. Horn,et al.  Determining Optical Flow , 1981, Other Conferences.

[19]  Ye Zhang,et al.  Integrated 3D scene flow and structure recovery from multiview image sequences , 2000, Proceedings IEEE Conference on Computer Vision and Pattern Recognition. CVPR 2000 (Cat. No.PR00662).

[20]  Guillaume Lavoué,et al.  Learning Boundary Edges for 3D‐Mesh Segmentation , 2011, Comput. Graph. Forum.

[21]  Xue-Cheng Tai,et al.  Augmented Lagrangian Method for Total Variation Based Image Restoration and Segmentation Over Triangulated Surfaces , 2012, J. Sci. Comput..

[22]  Rachid Deriche,et al.  Universität Des Saarlandes Fachrichtung 6.1 – Mathematik Colour, Texture, and Motion in Level Set Based Segmentation and Tracking Colour, Texture, and Motion in Level Set Based Segmentation and Tracking , 2022 .

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

[24]  Sunil Arya,et al.  An optimal algorithm for approximate nearest neighbor searching fixed dimensions , 1998, JACM.

[25]  M. J. D. Powell,et al.  A method for nonlinear constraints in minimization problems , 1969 .

[26]  Junfeng Yang,et al.  A New Alternating Minimization Algorithm for Total Variation Image Reconstruction , 2008, SIAM J. Imaging Sci..

[27]  Thomas Brox,et al.  High Accuracy Optical Flow Estimation Based on a Theory for Warping , 2004, ECCV.

[28]  J. Paul Siebert,et al.  Local feature extraction and matching on range images: 2.5D SIFT , 2009, Comput. Vis. Image Underst..

[29]  Lourdes Agapito,et al.  Automated articulated structure and 3D shape recovery from point correspondences , 2011, 2011 International Conference on Computer Vision.

[30]  Andrew W. Fitzgibbon,et al.  Real-time human pose recognition in parts from single depth images , 2011, CVPR 2011.

[31]  Tony F. Chan,et al.  A framework for intrinsic image processing on surfaces , 2011, Comput. Vis. Image Underst..

[32]  M. Hestenes Multiplier and gradient methods , 1969 .

[33]  Hédy Attouch,et al.  Proximal Alternating Minimization and Projection Methods for Nonconvex Problems: An Approach Based on the Kurdyka-Lojasiewicz Inequality , 2008, Math. Oper. Res..

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

[35]  Mikhail Belkin,et al.  Constructing Laplace operator from point clouds in Rd , 2009, SODA.

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

[37]  Marc Levoy,et al.  Efficient variants of the ICP algorithm , 2001, Proceedings Third International Conference on 3-D Digital Imaging and Modeling.

[38]  Ron Kimmel,et al.  Geometric curve flows on parametric manifolds , 2007, J. Comput. Phys..

[39]  Patrick L. Combettes,et al.  Proximal Splitting Methods in Signal Processing , 2009, Fixed-Point Algorithms for Inverse Problems in Science and Engineering.

[40]  Xue-Cheng Tai,et al.  Augmented Lagrangian Method, Dual Methods and Split Bregman Iteration for ROF Model , 2009, SSVM.

[41]  Yu Wang,et al.  Fast Regularization of Matrix-Valued Images , 2012, Efficient Algorithms for Global Optimization Methods in Computer Vision.

[42]  Alexander M. Bronstein,et al.  Articulated Motion Segmentation of Point Clouds by Group-Valued Regularization , 2012, 3DOR@Eurographics.

[43]  Andrew P. Murray,et al.  A Distance Metric for Finite Sets of Rigid-Body Displacements via the Polar Decomposition , 2007 .

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

[45]  LoTsz-Wai Rachel,et al.  Local feature extraction and matching on range images , 2009 .

[46]  Alfred M. Bruckstein,et al.  Over-Parameterized Variational Optical Flow , 2007, International Journal of Computer Vision.

[47]  Alfred M. Bruckstein,et al.  Over-Parameterized Optical Flow Using a Stereoscopic Constraint , 2011, SSVM.

[48]  Gilad Adiv,et al.  Determining Three-Dimensional Motion and Structure from Optical Flow Generated by Several Moving Objects , 1985, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[49]  Andriy Myronenko,et al.  Point Set Registration: Coherent Point Drift , 2009, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[50]  BlakeAndrew,et al.  Real-time human pose recognition in parts from single depth images , 2013 .

[51]  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.

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

[53]  Vijay Kumar,et al.  On the generation of smooth three-dimensional rigid body motions , 1998, IEEE Trans. Robotics Autom..

[54]  W. Eric L. Grimson,et al.  Learning visual flows: A Lie algebraic approach , 2009, CVPR.