[Insight-developers] Re: User's guide, DiscreteGaussian

[Luis Ibanez]

Hi Jim,

Thanks for bringing this up, to be honest I wasn't aware
that the method was so interesting. It is definetly worth
to add these details. We can even add the link to the URL
where the paper is.

Would you like to add this text ?

The Software guide may be robust at this point,...
If you want to give it a try, that will be great.

Otherwise I can make the changes and ask for your help
in proof reading later, just to make sure that we are
now honoring the method.

The content of the section is taken from:

   Examples/Filtering/DiscreteGaussianImageFilter.cxx



    Thanks


      Luis


-------------------------------------------


Miller, James V (Research) wrote:


Luis,

In the section of the user's guide that discusses the Discrete Gaussian, 
I think we should say more about the importance of the technique. It is 
more that just a traditional convolution with a Gaussian.  It convolves 
with a slightly different kernel such that you can use finite 
differences to approximate the derivatives of the smoothed image and get 
exactly the same answer as the convolving with the derivative of the 
Gaussian.  So if you need to take multiple derivatives (1st, 2nd, cross, 
etc.) you can smooth the image once and use finite differences for all 
the derivatives (as opposed to smoothing with various Gaussian 
derivative images).  Basically, Lindeberg figured out how to construct 
the smoothing kernels so that the smoothing and derivative operators 
commute after discretization (they usually commute before discretization 
but not afterwards).

I bring this up for two reasons.  One is that it is important enough to 
say.  It doesn't need to be anything in depth, just something akin to 
what you said for the RecursiveGaussian (and IIR).  The other reason I 
bring it up is that if you look at the plots of the kernel in the 
original paper,

Lindeberg: ``Discrete derivative approximations with scale-space 
properties: A basis for low-level feature detection'', 
<http://www.nada.kth.se/~tony/abstracts/Lin93-JMIV.html>J. of 
Mathematical Imaging and Vision, 3(4), pp. 349--376, 1993. (1.3Mb) 
<ftp://ftp.nada.kth.se/CVAP/scsp/papers/disc-der-approx-Njet.jmiv93.ps.Z>

the plots of the kernel tend to over shoot the peak of the true 
Gaussian.  So the plot in the user guide might be a little misleading.

The downside to the current implementation (and some of the derivative 
operators (especially the Laplacian)) is that it does not take into 
account the spacing of the data.

Lindeberg's papers can be accessed at:

http://www.nada.kth.se/~tony/earlyvision.html



*Jim Miller*
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