Symmetric positive-definite matrices: From geometry to applications and visualization

被引:101
作者
Moakher, M [1 ]
Batchelor, PG
机构
[1] ENIT, LAMSIN, Lab Math & Numer Modeling Engn Sci, Natl Engn Sch Tunis, BP 37, Tunis 1002, Tunisia
[2] Guys Hosp, Kings Coll London, Div Imaging Sci, London SE1 9RT, England
来源
VISUALIZATION AND PROCESSING OF TENSOR FIELDS | 2006年
关键词
D O I
10.1007/3-540-31272-2_17
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
In many engineering applications that use tensor analysis, such as tensor imaging, the underlying tensors have the characteristic of being positive definite. It might therefore be more appropriate to use techniques specially adapted to such tensors. We will describe the geometry and calculus on the Riemannian symmetric space of positive-definite tensors. First, we will explain why the geometry; constructed by Emile Cartan, is a natural geometry on that space. Then, we will use this framework to present formulas for means and interpolations specific to positive-definite tensors.
引用
收藏
页码:285 / +
页数:4
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