[Insight-users] 2D Gaussian Kernel?

[Christian Lackas]

* David Doria <daviddoria at gmail.com> [111017 19:54]:

Hi David,

> It seems that all of the ITK filters that use Gaussian kernels use 1D
> Gaussian kernels in each dimension. Am I missing an operator that
> actually creates a 2D Gaussian kernel?

applying a multi-D Gaussian kernel is a linearily separable function, so
you get the same result if you use a 2D Gaussian as when you use 2x 1D
in x/y direction. That said, the latter one is more efficient to
calculate (complexity 2*n vs n^2). This also extends to the third (and
further dimensions).

See for instance http://en.wikipedia.org/wiki/Linearly_separable and
http://en.wikipedia.org/wiki/Gaussian_blur for details.

So a true 2D Gaussian kernel is not required and would be inefficient.

Christian

-- 
Dr. Christian Lackas, Managing Partner
inviCRO, LLC -- In Imaging Yours
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