Doctor of Philosophy

dissertationThe statistical study of anatomy is one of the primary focuses of medical image analysis. It is well-established that the appropriate mathematical settings for such analyses are Riemannian manifolds and Lie group actions. Statistically defined atlases, in which a mean anatomical image is computed from a collection of static three-dimensional (3D) scans, have become commonplace. Within the past few decades, these efforts, which constitute the field of computational anatomy, have seen great success in enabling quantitative analysis. However, most of the analysis within computational anatomy has focused on collections of static images in population studies. The recent emergence of large-scale longitudinal imaging studies and four-dimensional (4D) imaging technology presents new opportunities for studying dynamic anatomical processes such as motion, growth, and degeneration. In order to make use of this new data, it is imperative that computational anatomy be extended with methods for the statistical analysis of longitudinal and dynamic medical imaging. In this dissertation, the deformable template framework is used for the development of 4D statistical shape analysis, with applications in motion analysis for individualized medicine and the study of growth and disease progression. A new method for estimating organ motion directly from raw imaging data is introduced and tested extensively. Polynomial regression, the staple of curve regression in Euclidean spaces, is extended to the setting of Riemannian manifolds. This polynomial regression framework enables rigorous statistical analysis of longitudinal imaging data. Finally, a new diffeomorphic model of irrotational shape change is presented. This new model presents striking practical advantages over standard diffeomorphic methods, while the study of this new space promises to illuminate aspects of the structure of the diffeomorphism group

Challenges in Markov chain Monte Carlo for Bayesian neural networks

Markov chain Monte Carlo (MCMC) methods have not been broadly adopted in Bayesian neural networks (BNNs). This paper initially reviews the main challenges in sampling from the parameter posterior of a neural network via MCMC. Such challenges culminate to lack of convergence to the parameter posterior. Nevertheless, this paper shows that a non-converged Markov chain, generated via MCMC sampling from the parameter space of a neural network, can yield via Bayesian marginalization a valuable predictive posterior of the output of the neural network. Classification examples based on multilayer perceptrons showcase highly accurate predictive posteriors. The postulate of limited scope for MCMC developments in BNNs is partially valid; an asymptotically exact parameter posterior seems less plausible, yet an accurate predictive posterior is a tenable research avenue

Hierarchical Geodesic Models in Diffeomorphisms

Hierarchical linear models (HLMs) are a standard approach for analyzing data where individuals are measured repeatedly over time. However, such models are only applicable to longitudinal studies of Euclidean data. This paper develops the theory of hierarchical geodesic models (HGMs), which generalize HLMs to the manifold setting. Our proposed model quantifies longitudinal trends in shapes as a hierarchy of geodesics in the group of diffeomorphisms. First, individual-level geodesics represent the trajectory of shape changes within individuals. Second, a group-level geodesic represents the average trajectory of shape changes for the population. Our proposed HGM is applicable to longitudinal data from unbalanced designs, i.e., varying numbers of timepoints for individuals, which is typical in medical studies. We derive the solution of HGMs on diffeomorphisms to estimate individual-level geodesics, the group geodesic, and the residual diffeomorphisms. We also propose an efficient parallel algorithm that easily scales to solve HGMs on a large collection of 3D images of several individuals. Finally, we present an effective model selection procedure based on cross validation. We demonstrate the effectiveness of HGMs for longitudinal analysis of synthetically generated shapes and 3D MRI brain scans

Thermal stability of plasma-nitrided aluminum oxide films on Si

The effect of post-deposition rapid thermal annealing in vacuum and in dry O2 on the stability of remote plasma-assisted nitrided aluminum oxide films on silicon is investigated. The areal densities of Al, O, N, and Si were determined by nuclear reaction analysis and their concentration versus depth distributions by narrow nuclear reaction resonance profiling, with subnanometric depth resolution. Annealing in both vacuum and O2 atmospheres produced partial loss of N from the near-surface regions of the films and its transport into near-interface regions of the Si substrate. Oxygen from the gas phase was incorporated in the AlON films in exchange for O and N previously existing therein, as well as in the near-interface regions of the Si substrate, leading to oxynitridation of the substrate. Al and Si remained essentially immobile under rapid thermal processing, confirming that the presence of nitrogen improves the thermal stability characteristics of the AlON/ Si structures in comparison with non-nitrided Al2O3 /Si

The mid-infrared diameter of W Hydrae

Mid-infrared (8-13 microns) interferometric data of W Hya were obtained with MIDI/VLTI between April 2007 and September 2009, covering nearly three pulsation cycles. The spectrally dispersed visibility data of all 75 observations were analyzed by fitting a circular fully limb-darkened disk (FDD) model to all data and individual pulsation phases. Asymmetries were studied with an elliptical FDD. Modeling results in an apparent angular FDD diameter of W Hya of about (80 +/- 1.2) mas (7.8 AU) between 8 and 10 microns, which corresponds to an about 1.9 times larger diameter than the photospheric one. The diameter gradually increases up to (105 +/- 1.2) mas (10.3 AU) at 12 microns. In contrast, the FDD relative flux fraction decreases from (0.85 +/- 0.02) to (0.77 +/- 0.02), reflecting the increased flux contribution from a fully resolved surrounding silicate dust shell. The asymmetric character of the extended structure could be confirmed. An elliptical FDD yields a position angle of (11 +/- 20) deg and an axis ratio of (0.87 +/- 0.07). A weak pulsation dependency is revealed with a diameter increase of (5.4 +/- 1.8) mas between visual minimum and maximum, while detected cycle-to-cycle variations are smaller. W Hya's diameter shows a behavior that is very similar to the Mira stars RR Sco and S Ori and can be described by an analogous model. The constant diameter part results from a partially resolved stellar disk, including a close molecular layer of H2O, while the increase beyond 10 microns can most likely be attributed to the contribution of a spatially resolved nearby Al2O3 dust shell.Comment: 18 pages, 16 figure

Voice Activated Display of American Sign Language for Airport Security

Conference proceedings from the Technology and Persons with Disabilities Conference-2003. California State University at Northridge, Los Angeles, CA March 17-22, 2003