@inproceedings{BurgethKleefeldZhangetal.2022,
  author    = {Burgeth, Bernhard and Kleefeld, Andreas and Zhang, Eugene and Zhang, Yue},
  title     = {Towards Topological Analysis of Non-symmetric Tensor Fields via Complexification},
  series = {Discrete Geometry and Mathematical Morphology},
  booktitle = {Discrete Geometry and Mathematical Morphology},
  editor    = {Baudrier, {\´E}tienne and Naegel, Beno{\^i}t and Kr{\"a}henb{\"u}hl, Adrien and Tajine, Mohamed},
  publisher = {Springer},
  address   = {Cham},
  isbn      = {978-3-031-19897-7},
  doi       = {10.1007/978-3-031-19897-7_5},
  pages     = {48 -- 59},
  year      = {2022},
  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 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.},
  language  = {en}
}