Towards Topological Analysis of Non-symmetric Tensor Fields via Complexification
- 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.
| Author: | Bernhard Burgeth, Andreas KleefeldORCiD, Eugene Zhang, Yue Zhang |
|---|---|
| DOI: | https://doi.org/10.1007/978-3-031-19897-7_5 |
| ISBN: | 978-3-031-19897-7 |
| Parent Title (English): | Discrete Geometry and Mathematical Morphology |
| Publisher: | Springer |
| Place of publication: | Cham |
| Editor: | Étienne Baudrier, Benoît Naegel, Adrien Krähenbühl, Mohamed Tajine |
| Document Type: | Conference Proceeding |
| Language: | English |
| Year of Completion: | 2022 |
| Date of first Publication: | 2022/10/20 |
| Date of the Publication (Server): | 2024/07/10 |
| First Page: | 48 |
| Last Page: | 59 |
| Note: | Second International Joint Conference, DGMM 2022, Strasbourg, France, October 24–27, 2022 |
| Note: | Corresponding author: Andreas Kleefeld |
| Link: | https://doi.org/10.1007/978-3-031-19897-7_5 |
| Zugriffsart: | campus |
| Institutes: | FH Aachen / Fachbereich Medizintechnik und Technomathematik |
| collections: | Verlag / Springer |
| Licence (German): |  Urheberrechtlich geschützt |
