TY  - CHAP
A1  - Burgeth, Bernhard
A1  - Kleefeld, Andreas
A1  - Zhang, Eugene
A1  - Zhang, Yue
ED  - Baudrier, Étienne
ED  - Naegel, Benoît
ED  - Krähenbühl, Adrien
ED  - Tajine, Mohamed
T1  - Towards Topological Analysis of Non-symmetric Tensor Fields via Complexification
T2  - Discrete Geometry and Mathematical Morphology
N2  - 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 2x2 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.
Y1  - 2022
SN  - 978-3-031-19897-7
U6  - https://doi.org/10.1007/978-3-031-19897-7_5
N1  - Second International Joint Conference, DGMM 2022, Strasbourg, France, October 24–27, 2022
N1  - Corresponding author: Andreas Kleefeld
SP  - 48
EP  - 59
PB  - Springer
CY  - Cham
ER  -