Closed-Form Solution to Non-rigid 3D Surface Registration

We present a closed-form solution to the problem of recovering the 3D shape of a non-rigid inelastic surface from 3D-to-2D correspondences. This lets us detect and reconstruct such a surface by matching individual images against a reference configuration, which is in contrast to all existing approaches that require initial shape estimates and track deformations from image to image.

[1]  Katsushi Ikeuchi,et al.  Deformable surfaces: a free-form shape representation , 1991, Optics & Photonics.

[2]  Dimitris N. Metaxas,et al.  Constrained deformable superquadrics and nonrigid motion tracking , 1991, Proceedings. 1991 IEEE Computer Society Conference on Computer Vision and Pattern Recognition.

[3]  Baba C. Vemuri,et al.  Geometric Methods in Computer Vision , 1991 .

[4]  Laurent D. Cohen,et al.  Deformable models for 3-D medical images using finite elements and balloons , 1992, Proceedings 1992 IEEE Computer Society Conference on Computer Vision and Pattern Recognition.

[5]  Demetri Terzopoulos,et al.  A finite element model for 3D shape reconstruction and nonrigid motion tracking , 1993, 1993 (4th) International Conference on Computer Vision.

[6]  Dimitris N. Metaxas,et al.  Shape and Nonrigid Motion Estimation Through Physics-Based Synthesis , 1993, IEEE Trans. Pattern Anal. Mach. Intell..

[7]  Bernd Neumann,et al.  Computer Vision — ECCV’98 , 1998, Lecture Notes in Computer Science.

[8]  Long Quan,et al.  Linear N-Point Camera Pose Determination , 1999, IEEE Trans. Pattern Anal. Mach. Intell..

[9]  Matthew Turk,et al.  A Morphable Model For The Synthesis Of 3D Faces , 1999, SIGGRAPH.

[10]  Thomas Vetter,et al.  A morphable model for the synthesis of 3D faces , 1999, SIGGRAPH.

[11]  N. Courtois,et al.  Efficient Algorithms for Solving Overdefined Systems of Multivariate Polynomial Equations , 2000, EUROCRYPT.

[12]  Bart Preneel,et al.  Advances in cryptology - EUROCRYPT 2000 : International Conference on the Theory and Application of Cryptographic Techniques, Bruges, Belgium, May 14-18, 2000 : proceedings , 2000 .

[13]  Paul D. Fiore,et al.  Efficient Linear Solution of Exterior Orientation , 2001, IEEE Trans. Pattern Anal. Mach. Intell..

[14]  Timothy F. Cootes,et al.  Active Appearance Models , 2001, IEEE Trans. Pattern Anal. Mach. Intell..

[15]  Kostas Daniilidis,et al.  Linear Pose Estimation from Points or Lines , 2002, ECCV.

[16]  Aaron Hertzmann,et al.  Learning Non-Rigid 3D Shape from 2D Motion , 2003, NIPS.

[17]  Adrien Bartoli,et al.  Direct Estimation of Non-Rigid Registration , 2004, BMVC.

[18]  Demetri Terzopoulos,et al.  Symmetry-seeking models and 3D object reconstruction , 1988, International Journal of Computer Vision.

[19]  G LoweDavid,et al.  Distinctive Image Features from Scale-Invariant Keypoints , 2004 .

[20]  Demetri Terzopoulos,et al.  Snakes: Active contour models , 2004, International Journal of Computer Vision.

[21]  Simon Baker,et al.  Active Appearance Models Revisited , 2004, International Journal of Computer Vision.

[22]  Alex Pentland,et al.  Automatic extraction of deformable part models , 1990, International Journal of Computer Vision.

[23]  Vincent Lepetit,et al.  Real-time nonrigid surface detection , 2005, 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR'05).

[24]  Alessio Del Bue,et al.  Non-rigid 3D Factorization for Projective Reconstruction , 2005, BMVC.

[25]  David A. Forsyth,et al.  Combining Cues: Shape from Shading and Texture , 2006, 2006 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR'06).

[26]  Vincent Lepetit,et al.  Accurate Non-Iterative O(n) Solution to the PnP Problem , 2007, 2007 IEEE 11th International Conference on Computer Vision.

[27]  Michael R. Lyu,et al.  Progressive Finite Newton Approach To Real-time Nonrigid Surface Detection , 2007, 2007 IEEE Conference on Computer Vision and Pattern Recognition.

[28]  Vincent Lepetit,et al.  Deformable Surface Tracking Ambiguities , 2007, 2007 IEEE Conference on Computer Vision and Pattern Recognition.

[29]  Pascal Fua,et al.  Convex Optimization for Deformable Surface 3-D Tracking , 2007, 2007 IEEE 11th International Conference on Computer Vision.

[30]  Pascal Fua,et al.  Surface Deformation Models for Nonrigid 3D Shape Recovery , 2007, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[31]  Vincent Gay-Bellile,et al.  Direct Estimation of Nonrigid Registrations with Image-Based Self-Occlusion Reasoning , 2010, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[32]  Adrien Bartoli,et al.  Monocular Template-based Reconstruction of Inextensible Surfaces , 2011, International Journal of Computer Vision.