Structure tensor: Difference between revisions

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{{cite conference|author1=I. Laptev |author2=T. Lindeberg |name-list-style=amp |chapter=Space–time interest points
|title=International Conference on Computer Vision ICCV'03|chapter-url=http://kth.diva-portal.org/smash/record.jsf?pid=diva2%3A442088&dswid=2038 |doi=10.1109/ICCV.2003.1238378|pages=432–439|volume=I|year=2003}}
</ref><ref>
{{cite conference|author=B. Triggs|chapter=Detecting Keypoints with Stable Position, Orientation, and Scale under Illumination Changes
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:<math> \begin{bmatrix} x' \\ y' \\ t' \end{bmatrix} = G \begin{bmatrix} x \\ y \\ t \end{bmatrix} = \begin{bmatrix} x - v_x \, t \\ y - v_y \, t \\ t \end{bmatrix} </math>,
it is, however, from a computational viewpoint preferable to parameterize the components in the structure tensor/second-moment matrix <math>S</math> using the notion of ''Galilean diagonalization''<ref name=lin04icpr>
{{cite conference|author1=T. Lindeberg |author2=A. Akbarzadeh |author3=I. Laptev |name-list-style=amp |chapter=Galilean-corrected spatio-temporal interest operators|title=International Conference on Pattern Recognition ICPR'04|chapter-url=http://kth.diva-portal.org/smash/record.jsf?pid=diva2%3A441205&dswid=-545 |doi=10.1109/ICPR.2004.1334004|date=August 2004|volume=I| pages=57–62}}
</ref>
:<math> S' = R_\text{space}^{-\text{T}} \, G^{-\text{T}} \, S \, G^{-1} \, R_\text{space}^{-1} = \begin{bmatrix} \nu_1 & \, & \, \\ \, & \nu_2 & \, \\ \, & \, & \nu_3 \end{bmatrix} </math>
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these concepts together allow for Galilean invariant recognition of spatio-temporal events.<ref>
{{cite conference|author1=I. Laptev |author2=B. Caputo |author3=C. Schuldt |author4=T. Lindeberg |name-list-style=amp |chapter=Local velocity-adapted motion events for spatio-temporal recognition |title=Computer Vision and Image Understanding|chapter-url=http://kth.diva-portal.org/smash/record.jsf?pid=diva2%3A335153&dswid=7950 |doi=10.1016/j.cviu.2006.11.023|year=2007|volume=108| pages= 207–229}}</ref>
 
==See also==