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I am wondering if one can assume that a digital image has a tensor structure. I mean for example when we talk about isotropy in image processing, we are talking about the intensity arranged in a tensor like structure; having coordinates and values as opposed to a matrix which carries only information about values.

Why is this important ? because I would like to explain some processes in comparison with tensor functions. For example be able to explain isotropic operations

Thank you,

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  • $\begingroup$ see dsp.stackexchange.com/questions/13122/… $\endgroup$ – Jazzmaniac Mar 15 '15 at 21:42
  • $\begingroup$ @Jazzmaniac thanks but my question is how do they say isotropic when talking about kernels ? Isotropy for a kernel is what exactly ? isn't it the same definition of tensor isotropy ? I have switched to signal processing from continuum mechanics and isotropy for me stands for tensors $\endgroup$ – Engin007 Mar 15 '15 at 23:13
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An isotropic tensor is one invariant under rotations. An isotropic kernel is also invariant under rotations, but the way the rotation acts on the object is very different.

Tensors transform as linear forms, whereas images are just rotated like a scalar function of coordinates and the coordinates are rotated. So if you come from continuum mechanics, the image/kernel transforms like the pressure field.

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