Motion Estimation and Compensation in Medical Imaging

This dissertation presents a framework for estimation of motion fields in 2D images, 3D volumes and multi-dimensional signal registration. The primary application is motion compensation for sequences of medical images and volumes with contrast agents. The framework implies motion estimation in two steps where the intermediate result is constraints on the local motion vectors. One algorithm generates constraints and a second algorithm computes motion vector fields. We present two methods for generation of local motion constraints. The first method is based on phase from quadrature filters. The second method is based on canonical correlation and scalar products of quadrature filters. In both methods, a local confidence measure produced to increase accuracy and robustness. A mathematical result is a novel method for maximizing canonical correlation. The novel method can handle covariance matrices that are complex and singular. Parametric models, such as affine or finite elements, are used to estimate motion fields from local motion constraints and confidence measures. In order to control smoothness, the model is extended to incorporate stiffness and cost of deformations. Multiple layers of motion fields are estimated using implicit or explicit clustering of motion constraints. We also discuss some philosophical issues in the analysis of multiple motions. An extension of the known EM algorithm is presented together with experimental results on multiple layers for 2D images and 3D volumes. As an alternative to the EM algorithm, this thesis also introduces a method based on higher order outer products. In addition, we present a back projection algorithm for reconstruction of transparent layers. Clinical evaluation shows good results for 2D X-ray angiography images. Experimental results also show accurate motion estimates for 3D MRI mammograms and simulated images in 3D angiography.