Generalized structure tensor: Difference between revisions

Revision as of 20:29, 4 January 2016

Revision as of 20:56, 4 January 2016

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{{sections|date=January 2016}}

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*Image binarization is not required.

==Physical and mathemical interpretation==

The curvilinear coordinates of GST can explain physical processes applied to images. Two of the most known such processes consist in rotation, and zooming. The first process is related to the transformation <math>\xi=\log(\sqrt{x^2+y^2})</math>. If an image <math>f</math> consists in iso-curves that can be explained by such a transformation, i.e. its iso-curves consist in circles <math>f(\xi,\eta)=g(\xi)</math>, where <math>g </math> is any real valued function defined on 1D, the image is invariant to rotations (around the origin).

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Generally, the estimated <math>\theta</math> represents the direction (in <math>\xi,\eta</math> coordinates) along which infinitisemal translations leave the image invariant, in practice least variant.

With every curvilinear coordinate basis pair, there is thus a pair of infinitesimal translators, a linear combination of which is a [[Differential operator]]. The latter are related to [[Lie algebra]].

This is connected to [[Lie operators]].

==Miscelenous==

Image in the context of the GST means both an ordinary image and an image neighborhood therein (local image), the context determining. For example, a photograph as well as any neighborhood of it are images.

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== See also ==

*[[Lie operators]]

*[[Structure tensor]]

*[[Hough transform]]

*[[Tensor]]

*[[Directional derivative]]

*[[Gaussian]]

*[[Corner detection]]

*[[Edge detection]]

*[[Affine shape adaptation]]

*[[Directional derivative]]

*[[Differential operator]]

*[[Lie operatorsalgebra]]

== References ==