| Research shows that cardiac health may be determined from cardiac motion, particularly the motion of the primary pumping chamber, the left ventricle. For this reason, a primary goal in medical image processing is to extract left ventricular motion from image sequences in order to diagnose and assess cardiovascular disease. Magnetic resonance imaging provides a valuable tool for this purpose---known as tagging---in which sheets of tissue are magnetically altered, prior to imaging, by applying external electromagnetic fields. In subsequent image sequences, the altered tissue is clearly identifiable and provides a visual motion cue. To assess heart health, the visual cue provided by tagging must be translated into an accurate, quantitative reconstruction of three-dimensional left ventricular motion---the motivation for this dissertation.; We demonstrate that three-dimensional left ventricular motion may be directly determined from the deformation of the tagged sheets of tissue. We therefore propose an algorithm for tracking the deformation of the sheets using magnetic resonance image sequences. The algorithm employs a physically-motivated, stochastic model and optimal estimation theory. We also construct a method that converts the tracked deformation of the tagged sheets into estimates of three-dimensional point motion.; In developing these methods for extracting left ventricular motion from tagged images, we have also made two contributions of a more general nature. First, the motion model, upon which the tracking algorithm is based, combines aspects of kriging---a spatial interpolation method---and Kalman filtering---an efficient temporal estimation method. Accordingly, we devised a new space-time estimation method that combines kriging and Kalman filtering. Second, our analysis of the process of tagging led to a new interpretation of the physics of tagging, which can be used to design and analyze the electromagnetic fields used in tagging. |
