This Article 
 Bibliographic References 
 Add to: 
Recovery of Nonrigid Motion and Structure
July 1991 (vol. 13 no. 7)
pp. 730-742

The authors introduce a physically correct model of elastic nonrigid motion. This model is based on the finite element method, but decouples the degrees of freedom by breaking down object motion into rigid and nonrigid vibration or deformation modes. The result is an accurate representation for both rigid and nonrigid motion that has greatly reduced dimensionality, capturing the intuition that nonrigid motion is normally coherent and not chaotic. Because of the small number of parameters involved, this representation is used to obtain accurate overstrained estimates of both rigid and nonrigid global motion. It is also shown that these estimates can be integrated over time by use of an extended Kalman filter, resulting in stable and accurate estimates of both three-dimensional shape and three-dimensional velocity. The formulation is then extended to include constrained nonrigid motion. Examples of tracking single nonrigid objects and multiple constrained objects are presented.

[1] M. Aoki,Optimization of Stochastic Systems: Topics in Discrete-Time Dynamics, 2nd ed. New York: Academic, 1989.
[2] N. Ayache, O. D. Faugeras, "Maintaining representations of the environment of a mobile robot,"IEEE Trans. Robot. Automation, vol. 5, no. 6, pp. 804-819, 1989.
[3] K.-J. Bathe,Finite Element Procedures in Engineering Analysis, Englewood Cliffs, NJ: Prentice-Hall, 1982.
[4] T. Broida and R. Chellappa, "Estimation of object motion parameters from noisy images,"IEEE Trans. Pattern Anal. Machine Intell, vol. PAMI-8, no. 1, Jan. 1986.
[5] I. Essa, "Contact detection, collision forces and friction for physically-based virtual world modeling," M. S. thesis, Dep. Civil Eng., M.I.T., Cambridge, MA, 1990.
[6] O. D. Faugeras, N. Ayache, B. Faverjon, and F. Lutsman, "Building visual maps by combining noisy stereo measurements," inProc. IEEE Conf. Robotics Automat.pp. 1433-1438, 1987.
[7] B. Friedland,Control System Design, New York: McGraw-Hill, 1986.
[8] J. J. Gibson,The Senses Considered as Perceptual Systems, New York: Houghton Mifflin, 1966.
[9] R.E. Kalman, "A new approach to linear filtering and prediction problems,"Trans. ASME, J. Basic Eng., vol. 82D no. 1, pp. 35-45, 1960.
[10] R. E. Kalman and R. S. Bucy, "New results in linear filtering and prediction theory,"Trans. ASME, J. Basic Eng., vol. 83D, no. 1, pp. 95-108, 1961.
[11] P. Werkhoven, A. Toet, and J. J. Koenderink, "Displacement estimates through adaptive affinities,"IEEE Trans. Patt. Anal. Mach. Intell., vol. 12, no. 7, pp. 658-662, July 1990.
[12] A. Pentland and J. Williams, "The perception of non-rigid motion: Inference of material properties and force," inProc. Int. Joint Conf. Artificial Intell., Aug. 1989.
[13] A. Pentland and J. Williams, "Good vibrations: Modal dynamics for graphics and animation,"Comput. Graphics, vol. 23, no. 4, pp. 215-222, 1989.
[14] A. Pentland, I. Essa, M. Freidmann, B. Horowitz, and S. Sclaroff, "The thingworld modeling system: Virtual sculpting by modal forces,"Comput. Graphics, vol. 24, no. 2, pp. 143-144, 1990.
[15] A. Pentland, "Automatic extraction of deformable part models,"Int. J. Comput. Vision, vol. 4, pp. 107-126, 1990.
[16] L. J. Segerlind,Applied Finite Element Analysis, New York: Wiley, 1984.
[17] M. Subbarro, Interpretation of Image Flow: A Spatio-Temporal Approach,"IEEE Trans. Patt. Anal. Mach. Intell., vol. 11, no. 3, pp. 266-278, Mar. 1989.
[18] D. Terzopoulos, A. Witkin, and M. Kass, "Symmetry-seeking models for 3-D object reconstruction,"Int. J. Comput. Vision, vol. 1. no. 3, pp. 211-221, 1987.
[19] S. Ullman, "Maximizing the rigidity: The incremental recovery of 3-D structure from rigid and rubbery motion,"Perception, vol. 13, pp. 255-274, 1984.
[20] A. Pentland and S. Scarloff, "Closed form solutions to physically based shape modeling and recognition,"IEEE Trans. Patt. Anal. Machine Intell., this issue, pp. 715-729.
[21] D. Terzopoulos, A. Witkin, and M. Kass, "Constraints on deformable models: Recovering 3D shape and nonrigid motion,"Artificial Intell., vol. 36, pp. 91-123, 1988.

Index Terms:
nonrigid motion recovery; 3D shape; nonrigid structure recovery; 3D velocity; picture processing; finite element method; deformation modes; Kalman filter; filtering and prediction theory; finite element analysis; Kalman filters; picture processing
A. Pentland, B. Horowitz, "Recovery of Nonrigid Motion and Structure," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 13, no. 7, pp. 730-742, July 1991, doi:10.1109/34.85661
Usage of this product signifies your acceptance of the Terms of Use.