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231224s2011 xx |||||o 00| ||eng c |
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|a 10.1109/TVCG.2011.171
|2 doi
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|a eng
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|a Zou, Guangyu
|e verfasserin
|4 aut
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|a Authalic parameterization of general surfaces using Lie advection
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|c 2011
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|a Text
|b txt
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|a ƒaComputermedien
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|a Date Completed 24.02.2012
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|a Date Revised 08.04.2022
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|a published: Print
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|a Citation Status MEDLINE
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|a © 2011 IEEE
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|a Parameterization of complex surfaces constitutes a major means of visualizing highly convoluted geometric structures as well as other properties associated with the surface. It also enables users with the ability to navigate, orient, and focus on regions of interest within a global view and overcome the occlusions to inner concavities. In this paper, we propose a novel area-preserving surface parameterization method which is rigorous in theory, moderate in computation, yet easily extendable to surfaces of non-disc and closed-boundary topologies. Starting from the distortion induced by an initial parameterization, an area restoring diffeomorphic flow is constructed as a Lie advection of differential 2-forms along the manifold, which yields equality of the area elements between the domain and the original surface at its final state. Existence and uniqueness of result are assured through an analytical derivation. Based upon a triangulated surface representation, we also present an efficient algorithm in line with discrete differential modeling. As an exemplar application, the utilization of this method for the effective visualization of brain cortical imaging modalities is presented. Compared with conformal methods, our method can reveal more subtle surface patterns in a quantitative manner. It, therefore, provides a competitive alternative to the existing parameterization techniques for better surface-based analysis in various scenarios
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|a Journal Article
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|a Research Support, N.I.H., Extramural
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|a Research Support, U.S. Gov't, Non-P.H.S.
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| 700 |
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|a Hu, Jiaxi
|e verfasserin
|4 aut
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| 700 |
1 |
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|a Gu, Xianfeng
|e verfasserin
|4 aut
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| 700 |
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|a Hua, Jing
|e verfasserin
|4 aut
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| 773 |
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|i Enthalten in
|t IEEE transactions on visualization and computer graphics
|d 1996
|g 17(2011), 12 vom: 01. Dez., Seite 2005-14
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|x 1941-0506
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|g volume:17
|g year:2011
|g number:12
|g day:01
|g month:12
|g pages:2005-14
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|u http://dx.doi.org/10.1109/TVCG.2011.171
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