Analysis of Velocity Encoded Images --- With Applications in Cardiac MRI

The topic of the thesis is the analysis of velocity encoded medical images, acquired using magnetic resonance imaging or other means. The application in mind is to use such data to determine the motion and deformation of the human heart, which is of clinical and physiological interest. As the velocity measurements are noisy and degraded, an important issue is the regularization of the measurements to obtain reliable estimates of the motion and deformation of the heart. Several methods for motion tracking are proposed and evaluated in the thesis. The methods can be classified either as Lagrangian, where the spatiotemporal deformation is explicitly constructed and adapted to measured data, or as Eulerian, where the velocity data is regularized as a pre-processing step before temporal integration of the data is made. The methods are constructed using tools such as Fourier analysis, spline mappings and filtering using partial differential equations. It is concluded that Lagrangian methods are preferable due to better performance and flexibility. Another topic of the thesis is the generation of spatiotemporal models of the shape and motion of an object. A method that generates models that are physically admissible is presented.