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Four-dimensional respiratory correlated computed tomography (4D RCCT) has been widely used for studying organ motion. Most current algorithms use binning techniques which introduce artifacts that can seriously hamper quantitative motion analysis. In this paper, we develop an algorithm for tracking organ motion which uses raw time-stamped data and(More)
We develop a framework for polynomial regression on Riemannian manifolds. Unlike recently developed spline models on Riemannian manifolds, Riemannian polynomials offer the ability to model parametric polynomials of all integer orders, odd and even. An intrinsic adjoint method is employed to compute variations of the matching functional, and polynomial(More)
This paper presents a novel approach for diffeomorphic image regression and atlas estimation that results in improved convergence and numerical stability. We use a vector momenta representation of a diffeomorphism's initial conditions instead of the standard scalar momentum that is typically used. The corresponding variational problem results in a(More)
Parametric vs. Nonparametric Regression Nonparametric analysis includes kernel and spline-based curve fitting These result in a good fit, but number of parameters tied to amount of data Parametric regression (e.g. polynomial fitting) uses compact representation, resulting in more powerful statistical inference linear quadratic cubic spline Polynomials(More)
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. In this paper, we propose a novel hierarchical geodesic model (HGM), which generalizes HLMs to the manifold setting. Our proposed model explains(More)
Four-dimensional (4D) respiratory correlated computed tomography (RCCT) has been widely used for studying organ motion. Most current RCCT imaging algorithms use binning techniques that are susceptible to artifacts and challenge the quantitative analysis of organ motion. In this paper, we develop an algorithm for analyzing organ motion which uses the raw,(More)
State of the art radiation treatment methods such as hypo-fractionated stereotactic body radiation therapy (SBRT) can successfully destroy tumor cells and avoid damaging healthy tissue by delivering high-level radiation dose that precisely conforms to the tumor shape. Though these methods work well for stationary tumors, SBRT dose delivery is particularly(More)
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(More)
Cycle-to-cycle variations in respiratory motion can cause significant geometric and dosimetric errors in the administration of lung cancer radiation therapy. A common limitation of the current strategies for motion management is that they assume a constant, reproducible respiratory cycle. In this work, we investigate the feasibility of using rapid MRI for(More)