Structure tensor: Difference between revisions

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Revision as of 08:38, 10 July 2021

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{{FeatureDetectionCompVisNavbox}}{{Use American English|date = March 2019}}

{{Short description|Tensor related to gradients}}

In mathematics, the '''structure [[tensor]]''', also referred to as the '''second-moment matrix''', is a [[matrix (mathematics)|matrix]] derived from the [[gradient]] of a [[function (mathematics)|function]]. It summarizesdescribes the predominant directionsdistribution of the gradient in a specified neighborhood ofaround a point, and makes the degreeinformation toinvariant whichrespect thosethe observing coordinates<!-- Example: if you have a 2D image with two components storing the gradient direction and a Gaussian blur is performed separately on each component, the result will be ill-formed (specially for the directions arewere [[Coherencevector orientations flip). On the other hand if the blur is performed component-wise on a 2x2 structure tensor the main eigenvector (physicsscaled by its eigenvalue)|coherent]] will properly represent the gradient. -->. The structure tensor is often used in [[image processing]] and [[computer vision]].<ref name=bigun86>

J. Bigun and G. Granlund (1986), ''Optimal Orientation Detection of Linear Symmetry''. Tech. Report LiTH-ISY-I-0828, Computer Vision Laboratory, Linkoping University, Sweden 1986; Thesis Report, Linkoping studies in science and technology No. 85, 1986.

</ref><ref name=bigun87>