Recursive estimation of shape and nonrigid motion

This paper presents an approach for recursively estimating 3D object shape and general nonrigid motion, which makes use of physically based dynamic models. The models provide global deformation parameters which represent the salient shape features of natural parts, and local deformation parameters which capture shape details. The equations of motion governing the models, augmented by point-to-point constraints, make them responsive to externally applied forces. We extend this system of differential equations to formulate a shape and nonrigid motion estimator, a nonlinear Kalman filter, that recursively transforms the discrepancy between the data and the estimated model state into generalized forces while formally accounting for uncertainty in the observations. A Riccati update process maintains a covariance matrix that adjusts the forces in accordance with the system dynamics and the current and prior observations. The estimator applies the transformed forces to adjust the translational, rotational, and deformational degrees of freedom such that the model evolves as consistently as possible with the noisy data. We present model fitting and motion tracking experiments of articulated flexible objects from real and synthetic noise-corrupted 3D data.