[Insight-users] Base question on derivative filters

[Oleksandr Dzyubak]

Maybe I am misreading the description.

 From the Class description:

RecursiveGaussianImageFilter 
<http://www.itk.org/Doxygen/html/classitk_1_1RecursiveGaussianImageFilter.html> 
is the base class for recursive filters that approximate convolution 
with the Gaussian kernel.

In this case, wouldn't the units from the RecursiveGaussian filter match 
those you would have
from the convolution?

Alex

Luis Ibanez wrote:
> The RecursiveGaussian filter doesn't use convolution.
>
> The value of sigma is set in physical coordinates.
>
> The output pixel values will have units of :
>
>        input intensity values /  physical coordinates
>
>     *IF* you use the FirstOrder setting.
>
> Note that there are also ZeroOrder and SecondOrder
> settings.
>
> In which case the intensity units of the output will be:
>
> ZeroOrder:      input intensity units
>
> Second Order :  input intensity units / (physical units)^2
>
>
>
>     Regards,
>
>
>          Luis
>
>
>
> -------------------------------------------------------------------------------
> On Wed, Sep 9, 2009 at 9:51 AM, Oleksandr Dzyubak <adzyubak at gmail.com 
> <mailto:adzyubak at gmail.com>> wrote:
>
>     Don't you change the units while convolving with the Gaussian?
>
>     Alex
>
>     Kishore Mosaliganti wrote:
>
>         The resulting units are in world coordinates. You will not
>         need to divide by spacing. The sigma is also in world coordinates.
>
>         Kishore
>
>         On Tue, Sep 8, 2009 at 11:49 AM, Gomez Herrero, Alberto
>         <alberto.gomez-herrero at philips.com
>         <mailto:alberto.gomez-herrero at philips.com>
>         <mailto:alberto.gomez-herrero at philips.com
>         <mailto:alberto.gomez-herrero at philips.com>>> wrote:
>
>            Hello all,
>
>            
>            this is a question regarding derivative filters in general
>         and the
>            RecursiveGaussianImageFilter  in particular.
>
>            
>            When we compute, say, the first order derivative of, say, a 2D
>             image “ I“ we get two images of the same size, “Ix”, and
>         “Iy”. My
>            question is,  the resulting value (i.e. the Ix and Iy gray
>         levels)
>            is expressed in what units?, I mean, if the gradient is
>         defined as
>            increment_of_gray_level /
>            increment_of_distance_in_world_coordinates, everything is
>         ok; but
>            if this filter works as a simple pixelwise convolution
>         mask, then
>            the gradient is in increment_of_gray_level /
>         increment_of_pixels.
>            In that case, I need to divide by the spacing to get the
>         right units.
>
>            
>            I guess this is a very basic question, but I really need to
>         make
>            sure that this filters work as the first definition. I
>         can’t find
>            it in the code, I only know that the sigma for the
>         smoothing is in
>            world coordinates though…
>
>            
>            Anyone can clarify this please?
>
>            
>            Thanks,
>
>            
>            Alberto
>
>
>          
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