Towards Topological Analysis of Non-symmetric Tensor Fields via Complexification

Burgeth, Bernhard; Kleefeld, Andreas; Zhang, Eugene; Zhang, Yue

doi:10.1007/978-3-031-19897-7_5

Contribution to a conference proceedings/Contribution to a book

FZJ-2022-03760

Towards Topological Analysis of Non-symmetric Tensor Fields via Complexification

Burgeth, B.Extern* ; Kleefeld, A. (Corresponding author)FZJ* ; Zhang, E.Extern* ; Zhang, Y.Extern*

2022
Springer International Publishing Cham
ISBN: 978-3-031-19896-0 (print), 978-3-031-19897-7 (electronic)

Discrete Geometry and Mathematical Morphology, DGMM 2022, Strasbourg, France, 24 Oct 2022 - 27 Oct 2022 Cham : Springer International Publishing, Lecture Notes in Computer Science 13493, 48 - 59 (2022) [10.1007/978-3-031-19897-7_5]

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Please use a persistent id in citations: http://hdl.handle.net/2128/32098 doi:10.1007/978-3-031-19897-7_5

Abstract: 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.

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