| Description |
Diffeomorphic models of image deformation are a mainstay of medical image registration due to both their advantageous mathematical properties, allowing the analysis of shape and giving rise to the field of computational anatomy, and their practical ability to accurately model the wide variety anatomical variability and physiological motion encountered in clinical practice. However, the price for these beneficial properties is a restriction on the types of motion that can be modeled, most notably the requirements of differentiability and topology preservation. In this work, we consider observed cases of nondiffeomorphic motion in medical imaging, and develop generative statistical models that accurately represent the observed motion while leveraging the useful diffeomorphic framework by representing nonsmooth motion via multiple diffeomorphic transformations. We focus on two motivating cases: nonsmooth motion in fluoroscopic imaging due to the overlapping 2D projections of 3D objects, and the nonsmooth sliding motion of the lower lungs against the thoracic wall in 4DCT imaging. In fluoroscopic imaging, we represent the observed motion as the additive combination of smoothly deforming layers, investigate the effect of layer image priors (regularization), and show applications to denoising, frame interpolation, and digital subtraction angiography. Motivated by challenges encountered in temporal registration of contrast-enhanced vessels, a novel discrete registration technique is developed for estimating smooth, nonlinear motion of small or repetitive features. Applications of this technique on slice-to-slice microscopy registration are presented. To model discontinuous motion in 4DCT imaging, we propose a framework for representing and estimating globally invertible and piecewise-smooth transformations. This formulation explicitly represents the location of discontinuities in the deformation field. Based on a novel representation of the invertibility constraint, our formulation allows us to automatically estimate the discontinuous motion, including the location of discontinuities, from the image data. Finally, we extend this invertible and piecewise-smooth model to represent spatially localized topological image changes as a separation between smooth segments in the composite deformation. Initial results are presented modeling the physical tearing of 2D histological sections, automatically estimating both the deformation and tearing region. |
