Affine Invariants of Vector Fields

0518086 - ÚTIA 2022 RIV US eng J - Journal Article
Kostková, Jitka - Suk, Tomáš - Flusser, Jan
Affine Invariants of Vector Fields.
IEEE Transactions on Pattern Analysis and Machine Intelligence. Roč. 43, č. 4 (2021), s. 1140-1155. ISSN 0162-8828. E-ISSN 1939-3539
R&D Projects: GA ČR GA18-07247S
Institutional support: RVO:67985556
Keywords : Vector field * total affine transformation * affine invariants
OECD category: Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)
Impact factor: 24.314, year: 2021
Method of publishing: Limited access
http://library.utia.cas.cz/separaty/2019/ZOI/kostkova-0518086.pdf https://ieeexplore.ieee.org/abstract/document/8892626

Vector fields are a special kind of multidimensional data, which are in a certain sense similar to digital color images, but are distinct from them in several aspects. In each pixel, the field is assigned to a vector that shows the direction and the magnitude of the quantity, which has been measured. To detect the patterns of interest in the field, special matching methods must be developed. In this paper, we propose a method for the description and matching of vector field patterns under an unknown affine transformation of the field. Unlike digital images, transformations of vector fields act not only on the spatial coordinates but also on the field values, which makes the detection different from the image case. To measure the similarity between the template and the field patch, we propose original invariants with respect to total affine transformation. They are designed from the vector field moments. It is demonstrated by experiments on real data from fluid mechanics that they perform significantly better than potential competitors.
Permanent Link: http://hdl.handle.net/11104/0303983