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Bayesian Regression and Longitudinal Modeling of Manifold data: Applications to Time-varying Shape Analysis
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| 자료유형 | 학위논문 |
|---|---|
| 서명/저자사항 | Bayesian Regression and Longitudinal Modeling of Manifold data: Applications to Time-varying Shape Analysis. |
| 개인저자 | Muralidharan, Prasanna. |
| 단체저자명 | The University of Utah. School of Computing. |
| 발행사항 | [S.l.]: The University of Utah., 2017. |
| 발행사항 | Ann Arbor: ProQuest Dissertations & Theses, 2017. |
| 형태사항 | 141 p. |
| 기본자료 저록 | Dissertations Abstracts International 81-02B. Dissertation Abstract International |
| ISBN | 9781085575669 |
| 학위논문주기 | Thesis (Ph.D.)--The University of Utah, 2017. |
| 일반주기 |
Source: Dissertations Abstracts International, Volume: 81-02, Section: B.
Advisor: Fletcher, P. Thomas. |
| 이용제한사항 | This item must not be sold to any third party vendors. |
| 요약 | The statistical study of anatomical shape is crucial in many medical image analysis applications, specifically in the context of understanding healthy brain developmental processes and those with neurological disorders such as Alzheimer's and Huntington's disease. Shape is defined as the geometry of an object invariant to position, size, and orientation. Shape is nonlinear, and therefore, traditional Euclidean statistics for shape analysis are not appropriate. However, shape is better represented on nonlinear Riemannian manifolds. This dissertation develops novel statistical methodologies to analyze data that find a natural parameterization on Riemannian manifolds. These techniques are generalizations of methods developed for the Euclidean setting. The methods are then applied to study anatomical shape variability.First, a new statistical technique called geodesic mixed-effects models is developed to study longitudinal data variability parameterized on a nonlinear manifold. The recent emergence of large-scale longitudinal imaging studies necessitates development of such methods to study dynamic anatomical processes such as motion, growth, and degeneration. Geodesic mixed-effects models are natural generalizations of linear mixed-effects models, developed for Euclidean longitudinal data, to the manifold setting. This model was evaluated on example anatomical shape data to study age-related anatomical variability in healthy individuals and those who have Alzheimer's disease.Just as with geodesic mixed-effects models, existing longitudinal shape models, linear or manifold, have focused on modeling only age-related anatomical variability, but have not included the ability to handle multiple covariates, such as sex, disease diagnosis, IQ, etc. Unfortunately, covariate modeling is not straightforward to set up when anatomical shape is represented on a manifold. Instead, as a first step, this dissertation proposes a Bayesian mixed-effects model, for shape represented in a linear space, that incorporates simultaneous relationships between longitudinal shape data and multiple predictors or covariates to the model. The framework also automatically selects which covariates are most relevant to the shape evolution based on observed data.As a final contribution, in a step toward predictive modeling and uncertainty quantification, this dissertation proposes a Bayesian interpretation of the polynomial regression problem for data represented on a manifold. Just like Bayesian ridge regression for Euclidean data, the proposed manifold regression model penalizes higher order polynomial coefficients, resulting in simpler polynomials explaining trends in the observed manifold response data. A key feature of these methods is that they are entirely based on intrinsic properties of the underlying nonlinear manifold. Although the methods presented in this work are for polynomial models, the ideas are transferable to more general parametric regression models with alternate choices for regularization priors.The applications presented in this dissertation are in the fields of medical image analysis and shape analysis. That said, the methods and theory are widely applicable to many other scientific fields, including robotics, computer vision, and evolutionary biology. |
| 일반주제명 | Medical imaging. Statistics. Applied mathematics. |
| 언어 | 영어 |
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: 이 자료의 원문은 한국교육학술정보원에서 제공합니다. |
