%0 Conference Paper
%A Burgeth, Bernhard
%A Kleefeld, Andreas
%A Zhang, Eugene
%A Zhang, Yue
%T Towards Topological Analysis of Non-symmetric Tensor Fields via Complexification
%V 13493
%C Cham
%I Springer International Publishing
%M FZJ-2022-03760
%@ 978-3-031-19896-0 (print)
%B Lecture Notes in Computer Science
%P 48 - 59
%D 2022
%X Fields of asymmetric tensors play an important role in many applications such as medical imaging (diffusion tensor magnetic resonance imaging), physics, and civil engineering (for example Cauchy-Green-deformation tensor, strain tensor with local rotations, etc.). However, such asymmetric tensors are usually symmetrized and then further processed. Using this procedure results in a loss of information. A new method for the processing of asymmetric tensor fields is proposed restricting our attention to tensors of second-order given by a 2 × 2 array or matrix with real entries. This is achieved by a transformation resulting in Hermitian matrices that have an eigendecomposition similar to symmetric matrices. With this new idea numerical results for real-world data arising from a deformation of an object by external forces are given. It is shown that the asymmetric part indeed contains valuable information.
%B Discrete Geometry and Mathematical Morphology
%C 24 Oct 2022 - 27 Oct 2022, Strasbourg (France)
Y2 24 Oct 2022 - 27 Oct 2022
M2 Strasbourg, France
%F PUB:(DE-HGF)8 ; PUB:(DE-HGF)7
%9 Contribution to a conference proceedingsContribution to a book
%U <Go to ISI:>//WOS:001286406100005
%R 10.1007/978-3-031-19897-7_5
%U https://juser.fz-juelich.de/record/910341