Shape and nonrigid motion estimation through physics-based synthesis

A physics-based framework for 3-D shape and nonrigid motion estimation for real-time computer vision systems is presented. 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. Applying continuous Kalman filtering theory, 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.