Shape and Nonrigid Motion Estimation through Physics-Based Synthesis

Dimitri Metaxas, Demetri Terzopoulos

Research output: Contribution to journalArticlepeer-review

247 Scopus citations


This paper presents a physics-based framework for 3-D shape and nonrigid motion estimation aimed at real-time computer vision. The framework features dynamic models that incorporate the mechanical principles of rigid and nonrigid bodies into conventional geometric primitives. Through the efficient numerical simulation of Lagrange equations of motion, the models can synthesize physically correct behaviors in response to applied forces and imposed constraints. We exploit the shape and motion synthesis capabilities of our models for the purposes of visual estimation. Applying continuous nonlinear Kalman filtering theory, we construct a recursive shape and motion estimator that employs the Lagrange equations as a system model. We interpret the continuous Kalman filter physically: The system model continually synthesizes nonrigid motion in response to generalized forces that arise from the inconsistency between the incoming observations and the estimated model state. The observation forces also account formally for instantaneous uncertainties and incomplete information. A Riccati procedure updates a covariance matrix that transforms the forces in accordance with the system dynamics and prior observation history. The transformed forces modify the translational, rotational, and deformational state variables of the system model to reduce inconsistency, thus producing nonstationary shape and motion estimates from the time-varying visual data. We demonstrate the dynamic estimator in experiments involving model fitting and tracking of articulated and flexible objects from noisy 3-D data.

Original languageEnglish (US)
Pages (from-to)580-591
Number of pages12
JournalIEEE Transactions on Pattern Analysis and Machine Intelligence
Issue number6
StatePublished - Jun 1993
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Software
  • Computer Vision and Pattern Recognition
  • Computational Theory and Mathematics
  • Artificial Intelligence
  • Applied Mathematics


  • Analysis by synthesis
  • Kalman filtering
  • computer vision
  • constraints
  • deformable models
  • nonrigid motion estimation
  • physics-based modeling


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