SHAPE AND NONRIGID MOTION ESTIMATION THROUGH PHYSICS-BASED SYNTHESIS

This paper presents a physics-based framework for 3-D shape and nonrig id 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. Thr ough the efficient numerical simulation of Lagrange equations of motio n, the models can synthesize physically correct behaviors in response to applied forces and imposed constraints. We exploit the shape and mo tion synthesis capabilities of our models for the purposes of visual e stimation. Applying continuous nonlinear Kalman filtering theory, we c onstruct a recursive shape and motion estimator that employs the Lagra nge equations as a system model. We interpret the continuous Kalman fi lter physically: The system model continually synthesizes nonrigid mot ion in response to generalized forces that arise from the inconsistenc y between the incoming observations and the estimated model state. The observation forces also account formally for instantaneous uncertaint ies and incomplete information. A Riccati procedure updates a covarian ce matrix that transforms the forces in accordance with the system dyn amics and prior observation history. The transformed forces modify the translational, rotational, and deformational state variables of the s ystem model to reduce inconsistency, thus producing nonstationary shap e and motion estimates from the time-varying visual data. We demonstra te the dynamic estimator in experiments involving model fitting and tr acking of articulated and flexible objects from noisy 3-D data.