Lie Bodies: A Manifold Representation of 3D Human Shape

This technical report is complementary to [1] and contains proofs, formulas and additional plots. It is identical to the supplemental material submitted to European Conference on Computer Vision (ECCV 2012) on March 2012. References [1] Freifeld, O., Black, M.J.: Lie Bodies: A Manifold Representation of 3D Human Shape. European Conference on Computer Vision (2012) Lie Bodies: A Manifold Representation of 3D Human Shape Supplemental Material Oren Freifeld Division of Applied Mathematics, Brown University Michael J. Black Max Planck Institute for Intelligent Systems

[1]  Hans-Peter Seidel,et al.  A Statistical Model of Human Pose and Body Shape , 2009, Comput. Graph. Forum.

[2]  John M. Lee.  Introduction to Smooth Manifolds , 2002 .

[3]  Michael I. Miller,et al.  Pattern Theory: From Representation to Inference , 2007 .

[4]  Jovan Popovic,et al.  Deformation transfer for triangle meshes , 2004, ACM Trans. Graph..

[5]  Marc Alexa,et al.  Linear combination of transformations , 2002, ACM Trans. Graph..

[6]  K. Brown,et al.  Graduate Texts in Mathematics , 1982 .

[7]  P. Thomas Fletcher,et al.  Gaussian Distributions on Lie Groups and Their Application to Statistical Shape Analysis , 2003, IPMI.

[8]  Peter Schröder,et al.  A simple geometric model for elastic deformations , 2010, ACM Trans. Graph..

[9]  Pascal Fua,et al.  Linear Local Models for Monocular Reconstruction of Deformable Surfaces , 2011, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[10]  M. Kilian,et al.  Geometric modeling in shape space , 2007, SIGGRAPH 2007.

[11]  Michael I. Miller,et al.  REPRESENTATIONS OF KNOWLEDGE IN COMPLEX SYSTEMS , 1994 .

[12]  Sebastian Thrun,et al.  SCAPE: shape completion and animation of people , 2005, SIGGRAPH '05.

[13]  Søren Hauberg,et al.  Manifold Valued Statistics, Exact Principal Geodesic Analysis and the Effect of Linear Approximations , 2010, ECCV.

[14]  Kathleen M. Robinette,et al.  Civilian American and European Surface Anthropometry Resource (CAESAR), Final Report. Volume 1. Summary , 2002 .

[15]  Richard M. Murray,et al.  A Mathematical Introduction to Robotic Manipulation , 1994 .

[16]  Michael J. Black,et al.  Detailed Human Shape and Pose from Images , 2007, 2007 IEEE Conference on Computer Vision and Pattern Recognition.

[17]  Hans-Peter Seidel,et al.  Multilinear pose and body shape estimation of dressed subjects from image sets , 2010, 2010 IEEE Computer Society Conference on Computer Vision and Pattern Recognition.

[18]  M I Miller,et al.  Mathematical textbook of deformable neuroanatomies. , 1993, Proceedings of the National Academy of Sciences of the United States of America.

[19]  P. Thomas Fletcher,et al.  Statistics of shape via principal geodesic analysis on Lie groups , 2003, 2003 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, 2003. Proceedings..

[20]  U. Grenander,et al.  Computational anatomy: an emerging discipline , 1998 .

[21]  Nicholas J. Higham,et al.  The Scaling and Squaring Method for the Matrix Exponential Revisited , 2005, SIAM J. Matrix Anal. Appl..

[22]  H. Karcher.  Riemannian center of mass and mollifier smoothing , 1977 .

[23]  P. Thomas Fletcher,et al.  Principal Geodesic Analysis on Symmetric Spaces: Statistics of Diffusion Tensors , 2004, ECCV Workshops CVAMIA and MMBIA.

[24]  Michael J. Black,et al.  Home 3D body scans from noisy image and range data , 2011, 2011 International Conference on Computer Vision.

[25]  Michael J. Black,et al.  Contour people: A parameterized model of 2D articulated human shape , 2010, 2010 IEEE Computer Society Conference on Computer Vision and Pattern Recognition.

[26]  Hwee Tou Ng,et al.  Statistical lattice-based spoken document retrieval , 2010, TOIS.

[27]  Ioannis A. Kakadiaris,et al.  Computer Vision and Mathematical Methods in Medical and Biomedical Image Analysis , 2004, Lecture Notes in Computer Science.

[28]  D. Kendall.  SHAPE MANIFOLDS, PROCRUSTEAN METRICS, AND COMPLEX PROJECTIVE SPACES , 1984 .