Rotation invariants of vector fields from orthogonal moments
Vector field images are a type of new multidimensional data that appear in many engineering areas. Although the vector fields can be visualized as images, they differ from graylevel and color images in several aspects. In order to analyze them, special methods and algorithms must be originally developed or substantially adapted from the traditional image processing area. Here, we propose a method for the description and matching of vector field patterns under an unknown rotation of the field. Rotation of a vector field is socalled total rotation, where the action is applied not only on the spatial coordinates but also on the field values. Invariants of vector fields with respect to total rotation constructed from orthogonal Gaussian–Hermite moments and Zernike moments are introduced. Their numerical stability is shown to be better than that of the invariants published so far. We demonstrate their usefulness in a real world template matching application of rotated vector fields.
 Authors:

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 Northwestern Univ., Evanston, IL (United States). School of Automation
 Inst. of Information Theory and Automation of the CAS, Praha (Czech Republic)
 Los Alamos National Lab. (LANL), Los Alamos, NM (United States). Data Science at Scale Team
 Publication Date:
 Report Number(s):
 LAUR1726797
Journal ID: ISSN 00313203
 Grant/Contract Number:
 AC5206NA25396
 Type:
 Accepted Manuscript
 Journal Name:
 Pattern Recognition
 Additional Journal Information:
 Journal Volume: 74; Journal Issue: C; Journal ID: ISSN 00313203
 Publisher:
 Elsevier
 Research Org:
 Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
 Sponsoring Org:
 USDOE Office of Science (SC). Advanced Scientific Computing Research (ASCR) (SC21); USDOE National Nuclear Security Administration (NNSA)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 97 MATHEMATICS AND COMPUTING; Vector field; Total rotation; Invariants; Gaussian–Hermite moments; Zernike moments; Numerical stability
 OSTI Identifier:
 1392885
Yang, Bo, Kostková, Jitka, Flusser, Jan, Suk, Tomáš, and Bujack, Roxana. Rotation invariants of vector fields from orthogonal moments. United States: N. p.,
Web. doi:10.1016/j.patcog.2017.09.004.
Yang, Bo, Kostková, Jitka, Flusser, Jan, Suk, Tomáš, & Bujack, Roxana. Rotation invariants of vector fields from orthogonal moments. United States. doi:10.1016/j.patcog.2017.09.004.
Yang, Bo, Kostková, Jitka, Flusser, Jan, Suk, Tomáš, and Bujack, Roxana. 2017.
"Rotation invariants of vector fields from orthogonal moments". United States.
doi:10.1016/j.patcog.2017.09.004. https://www.osti.gov/servlets/purl/1392885.
@article{osti_1392885,
title = {Rotation invariants of vector fields from orthogonal moments},
author = {Yang, Bo and Kostková, Jitka and Flusser, Jan and Suk, Tomáš and Bujack, Roxana},
abstractNote = {Vector field images are a type of new multidimensional data that appear in many engineering areas. Although the vector fields can be visualized as images, they differ from graylevel and color images in several aspects. In order to analyze them, special methods and algorithms must be originally developed or substantially adapted from the traditional image processing area. Here, we propose a method for the description and matching of vector field patterns under an unknown rotation of the field. Rotation of a vector field is socalled total rotation, where the action is applied not only on the spatial coordinates but also on the field values. Invariants of vector fields with respect to total rotation constructed from orthogonal Gaussian–Hermite moments and Zernike moments are introduced. Their numerical stability is shown to be better than that of the invariants published so far. We demonstrate their usefulness in a real world template matching application of rotated vector fields.},
doi = {10.1016/j.patcog.2017.09.004},
journal = {Pattern Recognition},
number = C,
volume = 74,
place = {United States},
year = {2017},
month = {9}
}