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Computational Differential Geometry ...

Lai, Rongjie.

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Computational Differential Geometry and Intrinsic Surface Processing.

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	Computational Differential Geometry and Intrinsic Surface Processing./
作者:	Lai, Rongjie.
面頁冊數:	122 p.
附註:	Source: Dissertation Abstracts International, Volume: 72-05, Section: B, page: .
Contained By:	Dissertation Abstracts International72-05B.
標題:	Applied Mathematics. -
電子資源:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3446862
ISBN:	9781124504421

Computational Differential Geometry and Intrinsic Surface Processing.
Lai, Rongjie.

Computational Differential Geometry and Intrinsic Surface Processing. - 122 p.

Source: Dissertation Abstracts International, Volume: 72-05, Section: B, page: .

Thesis (Ph.D.)--University of California, Los Angeles, 2010.

In this work, we focus on using the intrinsic geometric method to study variational problems and Laplace-Beltrami eigen-geometry on 3D triangulated surfaces and their applications to computational brain anatomy. Two classes of problems will be discussed in this dissertation. In the first part, we study how to tackle image processing problems on surfaces by using variational approaches. Starting from the proof for the suitability of total variation for image processing problems on surfaces, we generalize the well-known total variation related imaging models to study imaging problems on surfaces by using differential geometry techniques. As an advantage of this intrinsic method, popular algorithms for solving the total variation related problems can be adapted to solve the generalized models on surfaces. We also demonstrate that this intrinsic method provides us a robust and efficient way to solve imaging problems on surfaces. In the second part, we focus on studying surfaces' own geometry. Specifically, we will study how to detect local and global surface geometry and its applications to computational brain anatomy. The main tool we use is the Laplace-Beltrami (LB) operator and its eigen-systems, which provide us an intrinsic and robust tool to study surface geometry. We first propose to use LB nodal count sequences as a surface signature to characterize surface and demonstrate its applications to isospectral surfaces resolving and surface classification. Then, we provide a novel approach of computing skeletons of simply connected surfaces by constructing Reeb graphs from the eigenftmctions of an anisotropie Laplace-Beltrami operator. In the last topic about the LB eigen-geometry, we propose a general framework to define a mathematically rigorous distance between surfaces by using the eigen-system of the LB operator, and then we demonstrate one of its applications to tackle the challenging sulci region identification problem in computational brain anatomy.

ISBN: 9781124504421Subjects--Topical Terms:

1669109
Applied Mathematics.

Computational Differential Geometry and Intrinsic Surface Processing.
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