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Heart wall myofibers are arranged in minimal surfaces to optimize organ function
The generalized helicoid provides a unique foundation for analyzing the fibrous composite of the heart wall and should therefore find applications in heart tissue engineering and in the study of heart muscle diseases. Expand
Generalized Helicoids for Modeling Hair Geometry
This work presents a novel mathematical representation of hair based on a class of minimal surfaces called generalized helicoids that allows us to characterize the geometry of a single hair strand, as well as of those in its vicinity, by three intuitive curvature parameters and an elevation angle. Expand
Maurer-Cartan Forms for Fields on Surfaces: Application to Heart Fiber Geometry
Direct local measurements of the variation of the helix and transverse angles, of fiber fanning and twisting, and of the curvatures of the heart wall in which these fibers lie are obtained. Expand
Moving Frames for Heart Fiber Geometry
Using Diffusion MRI, it is demonstrated that one such specialization, the homeoid, constrains fibers to lie locally within ellipsoidal shells and yields improved fits in the rat, the dog and the human to those obtained using generalized helicoids. Expand
Atlases of Cardiac Fiber Differential Geometry
Improved consistency between GHM curvatures within a species and support a direct relation between myocardial shape and fiber curvature in the heart are demonstrated. Expand
Moving Frames for Heart Fiber Reconstruction
This work combines moving frame analysis with a diffusion inpainting scheme that incorporates rule-based priors for cardiac fibers, and demonstrates the superior performance of this approach in terms of error of fit when compared to alternate methods. Expand
Cardiac Fiber Inpainting Using Cartan Forms
Two complementary methods for fiber reconstruction from sparse orientation measurements derive from second-order properties related to fiber curvature as described by Maurer-Cartan connection forms are presented. Expand
School of Computer Science Phd Student Progress Report Form
Cerebral blood vessels can help differentiate normal from severely pathological anatomy. The identification of vessel lesions and malformations in medical images strongly correlates with risk factorsExpand
ECSE 626 Project Report Multimodality Image Registration by Maximization of Mutual Information
In 1997, Maes et al. [5] was one of the first papers to propose mutual information as a similarity metric for performing multimodal image registration. More than ten years later, mutual informationExpand
Generalized Helicoids for Hair Modeling Comp 558 -project Report
Recently, Savadjiev et al. introduced a generalized helicoid as an osculating object to characterize near parallel 3D curve patterns. This new model allows for patterns of different kinds to beExpand