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In [[image analysis]], the '''generalized structure tensor (GST)''' is an extension of the Cartesian [[structure tensor]] to [[curvilinear coordinates]].<ref name="bigun04pami3">{{cite journal |last1=Bigun |first1=J. |last2=Bigun |first2=T. |last3=Nilsson |first3=K. |title=Recognition by symmetry derivatives and the generalized structure tensor |journal=IEEE Transactions on Pattern Analysis and Machine Intelligence |date=December 2004 |volume=26 |issue=12 |pages=1590–1605 |doi=10.1109/TPAMI.2004.126|pmid=15573820 |s2cid=602221 |url=http://urn.kb.se/resolve?urn=urn:nbn:se:hh:diva-237 }}</ref> It is mainly used to detect and to represent the "direction" parameters of curves, just as the Cartesian structure tensor detects and represents the direction in Cartesian coordinates. Curve families generated by pairs of locally orthogonal functions have been the best studied.
It is a widely known method in applications of image and video processing including computer vision, such as biometric identification by fingerprints,<ref name=fronthaler08tip>{{cite journal
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|url=http://urn.kb.se/resolve?urn=urn:nbn:se:hh:diva-1358
|citeseerx=10.1.1.160.6312
|s2cid=7119251
}}</ref> and studies of human tissue sections.<ref name=Schmitt>{{cite journal|author1=O. Schmitt |author2=H. Birkholz |
title=Improvement in cytoarchitectonic mapping by combining electrodynamic modeling with local orientation in high-resolution images of the cerebral cortex|
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pages= 225–243|
doi=10.1109/TIP.2007.916155
|pmid=18270124 |s2cid=7119251 |url=http://urn.kb.se/resolve?urn=urn:nbn:se:hh:diva-1358
}}</ref><ref name=Schmitt2>{{cite journal|author1=O. Schmitt |author2=M. Pakura |author3=T. Aach |author4=L. Homke |author5=M. Bohme |author6=S. Bock |author7=S. Preusse |
title=Analysis of nerve fibers and their distribution in histologic sections of the human brain|
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volume= 63|issue=4 |
year=2004|
pages= 220–243|doi=10.1002/jemt.20033 |pmid=14988920 |s2cid=28746142 |url=https://zenodo.org/record/3447120 }}</ref>
==GST in 2D and locally orthogonal bases==
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