Diffeomorphic density registration

In this book chapter we study the Riemannian Geometry of the density registration problem: Given two densities (not necessarily probability densities) defined on a smooth finite dimensional manifold find a diffeomorphism which transforms one to the other. This problem is motivated by the medical imaging application of tracking organ motion due to respiration in Thoracic CT imaging where the fundamental physical property of conservation of mass naturally leads to modeling CT attenuation as a density. We will study the intimate link between the Riemannian metrics on the space of diffeomorphisms and those on the space of densities. We finally develop novel computationally efficient algorithms and demonstrate there applicability for registering RCCT thoracic imaging.Comment: 23 pages, 6 Figures, Chapter for a Book on Medical Image Analysi

Weighted Diffeomorphic Density Matching with Applications to Thoracic Image Registration

In this article we study the problem of thoracic image registration, in particular the estimation of complex anatomical deformations associated with the breathing cycle. Using the intimate link between the Riemannian geometry of the space of diffeomorphisms and the space of densities, we develop an image registration framework that incorporates both the fundamental law of conservation of mass as well as spatially varying tissue compressibility properties. By exploiting the geometrical structure, the resulting algorithm is computationally efficient, yet widely general.Comment: Accepted in Proceedings of the 5th MICCAI workshop on Mathematical Foundations of Computational Anatomy, Munich, Germany, 2015 (http://www-sop.inria.fr/asclepios/events/MFCA15/

Doctor of Philosophy

dissertationX-ray computed tomography (CT) is a widely popular medical imaging technique that allows for viewing of in vivo anatomy and physiology. In order to produce high-quality images and provide reliable treatment, CT imaging requires the precise knowledge of t

A method for quantitative analysis of regional lung ventilation using deformable image registration of CT and hybrid hyperpolarized gas/H-1 MRI

Hyperpolarized gas magnetic resonance imaging (MRI) generates highly detailed maps of lung ventilation and physiological function while CT provides corresponding anatomical and structural information. Fusion of such complementary images enables quantitative analysis of pulmonary structure-function. However, direct image registration of hyperpolarized gas MRI to CT is problematic, particularly in lungs whose boundaries are difficult to delineate due to ventilation heterogeneity. This study presents a novel indirect method of registering hyperpolarized gas MRI to CT utilizing 1H-structural MR images that are acquired in the same breath-hold as the gas MRI. The feasibility of using this technique for regional quantification of ventilation of specific pulmonary structures is demonstrated for the lobes. The direct and indirect methods of hyperpolarized gas MRI to CT image registration were compared using lung images from 15 asthma patients. Both affine and diffeomorphic image transformations were implemented. Registration accuracy was evaluated using the target registration error (TRE) of anatomical landmarks identified on 1H MRI and CT. The Wilcoxon signed-rank test was used to test statistical significance. For the affine transformation, the indirect method of image registration was significantly more accurate than the direct method (TRE = 14.7  ±  3.2 versus 19.6  ±  12.7 mm, p = 0.036). Using a deformable transformation, the indirect method was also more accurate than the direct method (TRE = 13.5  ±  3.3 versus 20.4  ±  12.8 mm, p = 0.006). Accurate image registration is critical for quantification of regional lung ventilation with hyperpolarized gas MRI within the anatomy delineated by CT. Automatic deformable image registration of hyperpolarized gas MRI to CT via same breath-hold 1H MRI is more accurate than direct registration. Potential applications include improved multi-modality image fusion, functionally weighted radiotherapy planning, and quantification of lobar ventilation in obstructive airways disease