Generalized structure tensor: Difference between revisions

Revision as of 17:54, 7 January 2014

Revision as of 18:05, 7 January 2014

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Generalized Structure Tensor is an extension of the Cartesian [[Structure Tensor]] to [[Curvilinear coordinates]]. It finds the direction along which an image can undergo a translation with minimal error, measured in [[L2 norm]] amounting to [[total least squares]] sense, where the translation is along the curvilinear coordinates (instead of Cartesian).

Among the curvilinear coordinates, locally orthogonal coordinates, are best studied.

<ref name=bigun86>

@inproceedings{bigun1988pattern,

title="Pattern recognition by detection of local symmetries",

author={Bigun, Josef},

booktitle={Proceedings of Pattern Recognition in Practice III},

year={1988}

}</ref>

The Generalized structure tensor can be used as an alternative to [[Hough Transform]] in [[image processing]] and [[computer vision]]. The main differences comprise:

*Complex voting

*Not only positive voting but also negative voting is allowed

*With one template multiple patterns belonging to the same family can be detected

==See also==

*[[Hough Transform]]

*[[Tensor]]

*[[Directional derivative]]

*[[Gaussian]]

*[[Corner detection]]

*[[Edge detection]]

*[[Lucas Kanade method|Lucas-Kanade method]]

*[[Affine shape adaptation]]

==References==

<references/>

==Resources==

{{DEFAULTSORT:Generalized Structure Tensor}}

[[Category:Tensors]]

[[Category:Feature detection]]

== Request review at [[WP:AFC]] ==

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Generalized Structure Tensor:

Generalized Structure Tensor is an extension of the Cartesian [[Structure Tensor]] to [[Curvilinear coordinates]]. It finds the direction along which an image can undergo a translation with minimal error, measured in [[L2 norm]] amounting to [[total least squares]] sense, where the translation is along the curvilinear coordinates (instead of Cartesian).

Among the curvilinear coordinates, locally orthogonal coordinates, are best studied.

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The Generalized structure tensor can be used as an alternative to [[Hough Transform]] in [[image processing]] and [[computer vision]]. The main differences comprise:

*Negative voting is allowed

*With one template multiple patterns belonging to the same family can be detected, because not nonly negative but also Complex Voting is allowed.

*Complex voting

*Not only positive voting but also negative voting is allowed

*With one template multiple patterns belonging to the same family can be detected