| In this thesis, we develop probabilistic approaches for the analysis of cardiac tagged magnetic resonance (MR) images based upon deformable B-spline models. The major contributions of this thesis include 3D/4D automatic tag detection, motion and strain field measurement as well as 2D displacement field reconstruction.; We propose a Maximum A Posteriori (MAP) estimation framework for automatically tracking tag features in an image sequence, which includes multiple short-axis (SA) and long-axis (LA) images for each frame. This method models the locations of cardiac material points as Markov Random Fields (MRF) on a parameterized B-spline solid. The MAP estimation problem leads to a log likelihood, which is then optimized to find the optimal B-spline model fitting the present tag features. Also, we show that 4D analysis of tagged MR images, adjustment of the deformable B-spline model's parameters (number of knots and spline order), and user's revision to the tag tracking results may all be unified within this framework. The algorithms are all validated with images, and cardiac deformation fields and strains from both simulated and data are reported.; For 2D dense displacement reconstruction, analysis of SA tagged images is undertaken. In 2D, the deformation field reconstruction is based upon the constrained thin-plate splinereconstruction of deformation subject to smoothness, intersection registration, and tag line correspondence constraints. The algorithm is validated with simulated images, and myocardial strains based upon reconstructed dense displacement fields are reported. |
