Kinematic behaviors of deformable objects have been extensively investigated. A number of strategies attempt to recover the motion and deformation properties from image sequences, by employing various data constraints and spatial, temporal, and spatio-temporal modelling of the object structure and dynamics. The structural models, however, often lack plausible physical meanings. Further, while the stochastic temporal filtering paradigm, such as the Kalman filtering framework, is popular in motion estimation, it makes restrictive assumptions about the statistical properties of the external disturbances that corrupt the true data. ^∞...[ Read more ]

Kinematic behaviors of deformable objects have been extensively investigated. A number of strategies attempt to recover the motion and deformation properties from image sequences, by employing various data constraints and spatial, temporal, and spatio-temporal modelling of the object structure and dynamics. The structural models, however, often lack plausible physical meanings. Further, while the stochastic temporal filtering paradigm, such as the Kalman filtering framework, is popular in motion estimation, it makes restrictive assumptions about the statistical properties of the external disturbances that corrupt the true data.

We present a physically-constrained, robust H^∞ filtering framework for the estimation of object kinematics from image sequences, with specific applications to the study of the left ventricle (LV) of the heart. Through the use of the sparsely distributed LV boundary features and the magnetic resonance (MR) phase contrast or tagging signals of the LV mid-wall as input data, the system dynamics of the heart is constructed as a set of partial differential equations by applying the biomechanical models of the myocardium within the finite element framework. It is then transformed into a state-space representation, and with weak assumptions of finite energy on the external disturbances, the robust H^∞ filter is adopted to achieve the optimal min-max estimates against any variety of noises.

Accuracy and robustness of the framework is assessed, and compared to the Kalman filtering results, using simulation data sets with known motion/deformation and various noises. Experiments are conducted with canine MR image sequences, including both MR tagging and MR phase contrast data, for the analysis of the myocardial kinematic properties, and physiologically sensible results are achieved.