Deformable models for volume feature tracking

Conventional three dimensional medical imaging devices have made possible the routine visualization of biological tissue acquired as a sequence of image volumes over time. Because biological tissue is rarely static, the accurate registration of features in two volumes from an image sequence is a common requirement for analysis of these data. This registration task can be difficult, since tissue can bend and stretch over time, and a motion description capturing the non-rigid deformation can be quite complex. One way to characterize the non-rigid deformation is by means of a vector field called a motion field, which describes the relative displacement of each voxel, and thus establishes a correspondence between any set of features in the two volumes. A field such as this can adequately describe any non-rigid deformation seen in biological tissue however, algorithms designed to estimate it are often confounded by the large dimensionality of the problem. Given the size of conventional medical imaging data sets, the total degrees of freedom represented by the number of independent vectors in the motion field is tremendously large.This dissertation focuses on incorporating elastic material models into a motion estimation algorithm so that the deformation of tissue in a medical imaging data set can be more accurately described. The research has been motivated by a problem seen in the acquisition of cardiac Positron Emission Tomography (PET). Because the heart moves during a PET acquisition, data are often distributed into different time frames, each capturing a specific phase of the cardiac cycle. This reduces motion-induced blur however, the individual time frames are quite noisy, and need to be recombined in some manner to improve image quality. Since the shape of the heart is different in each time frame, the data may not be simply added together, but first must be warped to match a common reference shape. Warping is achieved by using an optical flow-based motion algorithm to estimate the mapping between corresponding voxels in a source and a reference volume. The material model serves to reduce the large domain of possible motion fields, constraining the image data to deform as if it were a physical piece of elastic media undergoing stress from an external force.The main result of this dissertation is that by better modeling the material properties of tissue within the field of view in a dynamic cardiac PET acquisition, a better estimation of the motion field describing the deformation can be obtained. The motion estimation algorithm is unique from past approaches in that it uses a non-uniform model allowing large-displacement deformations to describe the elastic properties of a cardiac volume. It also uses a forward sampling scheme appropriate for recombination of voxels into a composite motion-corrected volume. Results indicate that this motion field can be used to produce a composite data set with less motion blur and improved contrast to noise characteristics.