Finite element based tracking of deforming surfaces

Display Omitted We present a method to robustly track the geometry of an object that deforms over time.We fit a FEM-based model to the data leading to physically plausible results.We evaluate the performance of our method using synthetic and scanned data. We present an approach to robustly track the geometry of an object that deforms over time from a set of input point clouds captured from a single viewpoint. The deformations we consider are caused by applying forces to known locations on the object's surface. Our method combines the use of prior information on the geometry of the object modeled by a smooth template and the use of a linear finite element method to predict the deformation. This allows the accurate reconstruction of both the observed and the unobserved sides of the object. We present tracking results for noisy low-quality point clouds acquired by either a stereo camera or a depth camera, and simulations with point clouds corrupted by different error terms. We show that our method is also applicable to large non-linear deformations.

[1]  Hans-Peter Seidel,et al.  Animation cartography—intrinsic reconstruction of shape and motion , 2012, TOGS.

[2]  K. Mardia,et al.  Statistical Shape Analysis , 1998 .

[3]  Matthias Teschner,et al.  Robust and Efficient Estimation of Elasticity Parameters using the linear Finite Element Method , 2007, SimVis.

[4]  Huamin Wang,et al.  Modeling deformable objects from a single depth camera , 2009, 2009 IEEE 12th International Conference on Computer Vision.

[5]  Wojciech Matusik,et al.  Articulated mesh animation from multi-view silhouettes , 2008, ACM Trans. Graph..

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

[7]  Ming C. Lin,et al.  Simulation-Based Joint Estimation of Body Deformation and Elasticity Parameters for Medical Image Analysis , 2012, IEEE Transactions on Medical Imaging.

[8]  Takashi Matsuyama,et al.  Dynamic surface matching by geodesic mapping for 3D animation transfer , 2010, 2010 IEEE Computer Society Conference on Computer Vision and Pattern Recognition.

[9]  Samuel Boivin,et al.  Estimation of mechanical parameters of deformable solids from videos , 2008, The Visual Computer.

[10]  Dinesh K. Pai,et al.  Estimation of elastic constants from 3D range-flow , 2001, Proceedings Third International Conference on 3-D Digital Imaging and Modeling.

[11]  B. Boyce,et al.  An inverse finite element method for determining the anisotropic properties of the cornea , 2011, Biomechanics and modeling in mechanobiology.

[12]  Jaeil Choi,et al.  Fitting solid meshes to animated surfaces using linear elasticity , 2009, ACM Trans. Graph..

[13]  Masoom A Haider,et al.  Development of multiorgan finite element-based prostate deformation model enabling registration of endorectal coil magnetic resonance imaging for radiotherapy planning. , 2007, International journal of radiation oncology, biology, physics.

[14]  Jingfeng Jiang,et al.  A finite-element approach for Young's modulus reconstruction , 2003, IEEE Transactions on Medical Imaging.

[15]  Leonidas J. Guibas,et al.  Eurographics Symposium on Geometry Processing (2007) Reconstruction of Deforming Geometry from Time-varying Point Clouds , 2022 .

[16]  Jonathan H. Connell,et al.  A Statistical Approach for Real-time Robust Background Subtrac tion and Shadow Detection , 2014 .

[17]  Wojciech Matusik,et al.  Design and fabrication of materials with desired deformation behavior , 2010, ACM Trans. Graph..

[18]  Jean Ponce,et al.  Dense 3D motion capture from synchronized video streams , 2008, 2008 IEEE Conference on Computer Vision and Pattern Recognition.

[19]  Michael Garland,et al.  Surface simplification using quadric error metrics , 1997, SIGGRAPH.

[20]  M. Bro-Nielsen,et al.  Finite element modeling in surgery simulation , 1998, Proc. IEEE.

[21]  M. Otaduy,et al.  Capture and modeling of non-linear heterogeneous soft tissue , 2009, ACM Trans. Graph..

[22]  Demetri Terzopoulos.  Multi-Level Reconstruction of Visual Surfaces: Variational Principles and Finite Element Representations , 1982 .

[23]  Wolfgang Heidrich,et al.  Globally Consistent Space‐Time Reconstruction , 2010, Comput. Graph. Forum.

[24]  Leonidas J. Guibas,et al.  Dynamic geometry registration , 2007, Symposium on Geometry Processing.

[25]  Robert Rohling,et al.  Real-time solution of the finite element inverse problem of viscoelasticity , 2011 .

[26]  Zoran Popovic,et al.  The space of human body shapes: reconstruction and parameterization from range scans , 2003, ACM Trans. Graph..

[27]  Jorge Nocedal,et al.  On the limited memory BFGS method for large scale optimization , 1989, Math. Program..

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

[29]  K J Parker,et al.  Imaging of the elastic properties of tissue--a review. , 1996, Ultrasound in medicine & biology.

[30]  David J. Hawkes,et al.  Validation of nonrigid image registration using finite-element methods: application to breast MR images , 2003, IEEE Transactions on Medical Imaging.

[31]  Gary K. L. Tam,et al.  Registration of 3D Point Clouds and Meshes: A Survey from Rigid to Nonrigid , 2013, IEEE Transactions on Visualization and Computer Graphics.

[32]  Dan A. Alcantara,et al.  Space-time surface reconstruction using incompressible flow , 2008, SIGGRAPH 2008.

[33]  Slobodan Ilic,et al.  Probabilistic Deformable Surface Tracking from Multiple Videos , 2010, ECCV.

[34]  Daniel Cohen-Or,et al.  Consensus Skeleton for Non‐rigid Space‐time Registration , 2010, Comput. Graph. Forum.

[35]  Ghassan Hamarneh,et al.  A Survey on Shape Correspondence , 2011, Comput. Graph. Forum.

[36]  Hans-Peter Seidel,et al.  Performance capture from sparse multi-view video , 2008, ACM Trans. Graph..

[37]  Pieter Peers,et al.  Temporally coherent completion of dynamic shapes , 2012, TOGS.

[38]  Jochen Lang,et al.  Tracking Complete Deformable Objects with Finite Elements , 2012, 2012 Second International Conference on 3D Imaging, Modeling, Processing, Visualization & Transmission.

[39]  Leonidas J. Guibas,et al.  Robust single-view geometry and motion reconstruction , 2009, ACM Trans. Graph..

[40]  Slobodan Ilic,et al.  Free-form mesh tracking: A patch-based approach , 2010, 2010 IEEE Computer Society Conference on Computer Vision and Pattern Recognition.