Trajectory space: A dual representation for nonrigid structure from motion

IEEE Transactions on Pattern Analysis and Machine Intelligence

Volumn 33, Issue 7, 2011, Pages 1442-1456

  Akhter, Ijaz ^a   Sheikh, Yaser ^b   Khan, Sohaib ^a   Kanade, Takeo ^b  

^a LAHORE UNIVERSITY OF MANAGEMENT SCIENCES   (Pakistan)

^b CARNEGIE MELLON UNIVERSITY   (United States)

Author keywords

3D reconstruction; motion and tracking; Nonrigid structure from motion

Indexed keywords

DEFORMATION; DISCRETE COSINE TRANSFORMS; TRAJECTORIES; VIDEO RECORDING;

3D RECONSTRUCTION; DISCRETE COSINE TRANSFORM(DCT); DUAL REPRESENTATION; FACIAL EXPRESSIONS; LINEAR COMBINATIONS; MOTION AND TRACKING; MOTION CAPTURE DATA; STRUCTURE FROM MOTION;

PRINCIPAL COMPONENT ANALYSIS;

ALGORITHM; AUTOMATED PATTERN RECOGNITION; BIOLOGICAL MODEL; COMPUTER ASSISTED DIAGNOSIS; COMPUTER SIMULATION; HUMAN; IMAGE ENHANCEMENT; IMAGE SUBTRACTION; MOVEMENT (PHYSIOLOGY); PHOTOGRAPHY; PHYSIOLOGY; PROCEDURES; REPRODUCIBILITY; SENSITIVITY AND SPECIFICITY; SIGNAL PROCESSING; THREE DIMENSIONAL IMAGING; WHOLE BODY IMAGING;

ALGORITHMS; COMPUTER SIMULATION; HUMANS; IMAGE ENHANCEMENT; IMAGE INTERPRETATION, COMPUTER-ASSISTED; IMAGING, THREE-DIMENSIONAL; MODELS, BIOLOGICAL; MOVEMENT; PATTERN RECOGNITION, AUTOMATED; PHOTOGRAPHY; REPRODUCIBILITY OF RESULTS; SENSITIVITY AND SPECIFICITY; SIGNAL PROCESSING, COMPUTER-ASSISTED; SUBTRACTION TECHNIQUE; WHOLE BODY IMAGING;

EID: 79957472896     PISSN: 01628828     EISSN: None     Source Type: Journal    
DOI: 10.1109/TPAMI.2010.201     Document Type: Article

References (54)

1. G. Johansson, "Visual Perception of Biological Motion and a Model for Its Analysis," Perception and Psychophysics, vol. 14, pp. 201-211, 1973.
2. C. Bregler, A. Hertzmann, and H. Biermann, "Recovering Non-Rigid 3D Shape from Image Streams," Proc. IEEE Conf. Computer Vision and Pattern Recognition, vol. 2, pp. 690-696, 2000.
3. A.K. Jain, Fundamentals of Digital Image Processing. Prentice Hall, 1989.
4. K. Rao and P. Yip, Discrete Cosine Transform: Algorithms, Advantages, Applications. Academic, 1990.
5. J. Xiao, J. Chai, and T. Kanade, "A Closed Form Solution to Non-Rigid Shape and Motion Recovery," Int'l J. Computer Vision, vol. 67, pp. 233-246, 2006.
6. L. Torresani, A. Hertzmann, and C. Bregler, "Nonrigid Structure-from-Motion: Estimating Shape and Motion with Hierarchical Priors," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 30, no. 5, pp. 878-892, May 2008. (Pubitemid 351486755)
7. L. Torresani, A. Hertzmann, and C. Bregler, "Learning Non-Rigid 3D Shape from 2D Motion," Proc. 19th Ann. Conf. Neural Information Processing Systems, 2005.
8. M. Brand, "A Direct Method for 3D Factorization of Nonrigid Motion Observed in 2D," Proc. IEEE CS Conf. Computer Vision and Pattern Recognition, vol. 2, 2005.
9. A.D. Bue, F. Smeraldi, and L. Agapito, "Non-Rigid Structure from Motion Using Ranklet-Based Tracking and Non-Linear Optimization," Image and Vision Computing, vol. 25, pp. 297-310, 2007. (Pubitemid 44880516)
10. L. Torresani, D. Yang, E. Alexander, and C. Bregler, "Tracking and Modeling Non-Rigid Objects with Rank Constraints," Proc. IEEE CS Conf. Computer Vision and Pattern Recognition, vol. 1, pp. 493-500, 2001.
11. M. Brand, "Morphable 3D Models from Video," Proc. IEEE CS Conf. Computer Vision and Pattern Recognition, vol. 2, 2001.
12. H. Longuet-Higgins, "A Computer Algorithm for Reconstructing a Scene from Two Projections," Nature, vol. 293, pp. 133-135,1981.
13. R. Hartley and A. Zisserman, Multiple View Geometry in Computer Vision, second ed. Cambridge Univ. Press, 2004.
14. O. Faugeras and Q.T. Luong, The Geometry of Multiple Images. MIT Press, 2001.
15. Y. Ma, S. Soatto, J. Kosecka, and S.S. Sastry, An Invitation to 3-D Vision: From Images to Geomatric Models. Springer, 2003.
16. C. Tomasi and T. Kanade, "Shape and Motion from Image Streams under Orthography: A Factorization Method," Int'l J. Computer Vision, vol. 9, pp. 137-154, 1992. (Pubitemid 23621943)
17. L. Kontsevich, M. Kontsevich, and A. Shen, "Two Algorithms for Reconstructing Shapes," Optoelectronics, Instrumentation and Data Processing, vol. 5, pp. 76-81, 1987.
18. S. Ullman, "Maximizing Rigidity: The Incremental Recovery of 3-D Structure from Rigid and Rubbery Motion," Perception, vol. 13, pp. 255-274, 1984.
19. S. Chen, "Structure from Motion without the Rigidity Assumption," Proc. IEEE CS Workshop Computer Vision, pp. 105-112, 1985.
20. S. Chen Penna, "Shape and Motion of Non-Rigid Bodies," Computer Vision, Graphics, and Image Processing, vol. 36, pp. 175- 207, 1986.
21. D. Shulman and J.Y. Aloimonos, "(Non-)Rigid Motion Interpretation: A Regularized Approach," Proc. Royal Soc. London Series B, vol. 233, pp. 217-234, 1988. (Pubitemid 18084019)
22. J. Costeira and T. Kanade, "A Multibody Factorization Method for Independently Moving Objects," Int'l J. Computer Vision, vol. 49, pp. 159-179, 1998. (Pubitemid 128517909)
23. 2, k = 3;.; 6, and Their Application in Computer Vision," Int'l J. Computer Vision, vol. 48, pp. 53-67, 2002. (Pubitemid 34491075)
24. M. Han and T. Kanade, "Reconstruction of a Scene with Multiple Linearly Moving Objects," Int'l J. Computer Vision, vol. 59, pp. 285- 300, 2004.
25. A. Gruber and Y. Weiss, "Multibody Factorization with Uncertainty and Missing Data Using the EM Algorithm," Proc. IEEE CS Conf. Computer Vision and Pattern Recognition, vol. 1, pp. 707- 714, 2004.
26. R. Vidal and R. Hartley, "Motion Segementaion with Missing Data Using PowerFactorization and GPCA," Proc. IEEE CS Conf. Computer Vision and Pattern Recognition, vol. 2, pp. 310-316, 2004.
27. A.D. Bue, X. Llado, and L. Agapito, "Non-Rigid Metric Shape and Motion Recovery from Uncalibrated Images Using Priors," Proc. IEEE CS Conf. Computer Vision and Pattern Recognition, 2006.
28. A.D. Bue, "A Factorization Approach to Structure from Motion with Shape Priors," Proc. IEEE CS Conf. Computer Vision and Pattern Recognition, 2008.
29. A. Bartoli, V. Gay-Bellile, U. Castellani, J. Peyras, S. Olsen, and P. Sayd, "Coarse-to-Fine Low-Rank Structure-from-Motion," Proc. IEEE CS Conf. Computer Vision and Pattern Recognition, 2008.
30. J. Yan and M. Pollefeys, "A Factorization-Based Approach to Articulated Motion Recovery," Proc. IEEE CS Conf. Computer Vision and Pattern Recognition, vol. 2, pp. 815-821, 2005.
31. J. Yan and M. Pollefeys, "Automatic Kinematic Chain Building from Feature Trajectories of Articulated Objects," Proc. IEEE CS Conf. Computer Vision and Pattern Recognition, vol. 2, 2006.
32. P. Tresadern and I. Reid, "Articulated Structure from Motion by Factorization," Proc. IEEE CS Conf. Computer Vision and Pattern Recognition, 2005.
33. M. Paladini, A.D. Bue, M. Stosic, M. Dodig, J. Xavier, and L. Agapito, "Factorization for Non-Rigid and Articulated Structure Using Metric Projections," Proc. IEEE CS Conf. Computer Vision and Pattern Recognition, 2009.
34. V. Rabaud and S. Belongie, "Linear Embeddings in Non-Rigid Structure from Motion," Proc. IEEE CS Conf. Computer Vision and Pattern Recognition, 2009.
35. I. Akhter, Y. Sheikh, and S. Khan, "In Defense of Orthonormality Constraints for Nonrigid Structure from Motion," Proc. IEEE CS Conf. Computer Vision and Pattern Recognition, 2009.
36. J. Xiao and T. Kanade, "Uncalibrated Perspective Reconstruction of Deformable Structures," Proc. 10th IEEE Int'l Conf. Computer Vision, vol. 2, pp. 1075-1082, 2005. (Pubitemid 44042300)
37. R. Vidal and D. Abretske, "Nonrigid Shape and Motion from Multiple Perspective Views," Proc. European Conf. Computer Vision, 2006.
38. R. Hartley and R. Vidal, "Perspective Nonrigid Shape and Motion Recovery," Proc. 10th European Conf. Computer Vision, 2008.
39. V. Rabaud and S. Belongie, "Rethinking Non-Rigid Structure from Motion," Proc. IEEE CS Conf. Computer Vision and Pattern Recognition, 2008.
40. I. Akhter, Y. Sheikh, S. Khan, and T. Kanade, "Nonrigid Structure from Motion in Trajectory Space," Proc. Neural Information Processing Systems, 2008.
41. S. Carlsson and D. Weinshall, "Dual Computation of Projective Shape and Camera Positions from Multiple Images," Int'l J. Computer Vision, vol. 27, no. 3, pp. 227-241, 1998. (Pubitemid 128523361)
42. A. Shashua, "Trilinear Tensor: The Fundamental Construct of Multiple-View Geometry and Its Applications," Proc. Int'l Workshop Algebraic Frames for the Perception-Action Cycle, 1997.
43. L. Zelnik-Manor and M. Irani, "Temporal Factorization vs. Spatial Factorization," Proc. Eighth European Conf. Computer Vision, 2004.
44. S. Olsen and A. Bartoli, "Implicit Non-Rigid Structure-from-Motion with Priors," J. Math. Imaging and Vision, vol. 31, nos. 2/3, pp. 233-244, 2008.
45. G. Golub and W. Kahan, "Calculating the Singular Values and Pseudo-Inverse of a Matrix," J. SIAM: Series B, Numerical Analysis, vol. 2, pp. 205-224, 1965.
46. R. Zelinski and P. Noll, "Adaptive Transfrom Coding of Speech Signals," IEEE Trans. Acoustics, Speech, and Signal Processing, vol. 25, no. 4, pp. 299-309, Aug. 1977. (Pubitemid 8228866)
47. J. Huang and Y. Zhao, "A DCT-Based Fast Signal Subspace Technique for Robust Speech Recognition," IEEE Trans. Speech and Audio Processing, vol. 8, no. 6, pp. 747-751, Nov. 2000.
48. L.A. Park, M. Palaniswami, and K. Ramamohanarao, "A Novel Document Ranking Method Using the Discrete Cosine Transform," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 27, no. 1, pp. 130-135, Jan. 2005. (Pubitemid 40195903)
49. Z.M. Hafed and N.D. Levine, "Face Recognition Using the Discrete Cosine Transform," Int'l J. Computer Vision, vol. 43, no. 3, pp. 167-188, 2001. (Pubitemid 32897611)
50. H. Yan Li and T. Wang, "Motion Texture: A Two-Level Statistical Model for Character Motion Synthesis," ACM Trans. Graphics, vol. 21, no. 3, pp. 465-472, 2002.
51. Carnegie-Mellon Mocap Database, http://mocap.cs.cmu.edu/, 2003.
52. J. Xiao and T. Kanade, "Non-Rigid Shape and Motion Recovery: Degenerate Deformations," Proc. IEEE CS Conf. Computer Vision and Pattern Recognition, vol. 1, pp. 668-675, 2004.
53. R. White, K. Crane, and D. Forsyth, "Capturing and Animating Occluded Cloth," Proc. ACM SIGGRAPH, 2007.
54. A. Datta, Y. Sheikh, and T. Kanade, "Linear Motion Estimation for Systems of Articulated Planes," Proc. IEEE CS Conf. Computer Vision and Pattern Recognition, 2008.