In addition to its technical merits as a challenging non-rigid motion and structural integrity analysis problem, quantitative estimation of cardiac regional functions and material characteristics has significant physiological and clinical values. We have earlier developed a stochastic finite element framework for the simultaneous estimation of myocardial motion and material parameters from medical image sequences with an extended Kalman filter approach. In this paper, we present a new computational strategy for the framework based upon the maximum a posteriori estimation principles, realized through the extended Kalman smoother, that produce a sequence of kinematics state and material parameter estimates from the entire sequence of observations. The system dynamics equations of the heart is constructed using a biomechanical model with stochastic parameters, and the tissue material and deformation parameters are jointly estimated from the periodic imaging data. Experiments with canine ...