[Insight-users] Base question on derivative filters
Luis Ibanez
luis.ibanez at kitware.com
Wed Sep 9 11:13:44 EDT 2009
Hi Alex,
1) ITK, (just as VTK and OpenGL) does not specify units.
The meaning of spacing units is up to you to define.
People in Optical Microscopy will probably specify
spacing in microns.
While Electron Microscopy will probably use nanometers.
People in Astronomy will probably use parsecs or
light years.
and most people in radiology will use millimeters.
Again, the actual unit is up to you to decide.
Just make sure that you use the same units
consistently.
Nobody wants to see another $125 M gone
to waste like in the Mars lander crash where
engineers mixed centimeters with inches....
http://www.cnn.com/TECH/space/9909/30/mars.metric/
2) The use of NormalizationAcrossSpace flag
comes down to neutralizing the use of the
spacing. This should only be done if you are
actually performing scale-space analysis.
That is, running filters at multiple scales to
then consolidate their results across scales.
Most mortals do not need to use this flag :-)
So, in general, Sigma does have units
equal to the image spacing units.
Regards,
Luis
---------------------------------------------------------------------
On Wed, Sep 9, 2009 at 11:03 AM, Oleksandr Dzyubak <adzyubak at gmail.com>wrote:
> Hi Luis,
>
> Thanks for your clarification.
> Using power of OpenSource, I looked over the templates you recommended
> and particular the ::SetUp method.
>
> Couple questions.
>
> 1) const ScalarRealType spacingTolerance = 1e-8;
>
> Is it 0.01 micron?
>
> 2) ::SetNormalizeAcrossScale method.
> You have to use Sigma which is not dimensionless.
> Do you use sigma renormalization in such a way that it becomes
> dimensionless
> and afterward you work with only dimensionless variables?
>
>
> Alex
>
>
> Luis Ibanez wrote:
>
>>
>> Hi Alex,
>>
>> The RecursiveGaussianImageFilter "approximates" convolution,
>> but it doesn't "perform" convolution.
>>
>> This filter implements an IIR filter.
>> For details, please see:
>>
>> "Fast Algorithms for Low-Level Vision"
>> R.Deriche in IEEE-PAMI Vol.12, No.1, January 1990, pp 78-87,
>>
>> "Recursively Implementing The Gaussian and Its Derivatives",
>> R. Deriche,
>> INRIA, 1993, ftp://ftp.inria.fr/INRIA/tech-reports/RR/RR-1893.ps.gz
>>
>>
>> Note that "convolution" by itself doesn't really
>> set units, *unless* you take unit conversion into
>> account in the computation of the convolution
>> kernel coefficients.
>>
>>
>> Using the power of Open Source, things will be
>> a lot clearer if you look at the internals of the code. :-)
>>
>>
>> For example, look at lines 56-69 of
>> Insight/Code/BasicFilters/itkDiscreteGaussianImageFilter.txx
>>
>> Which actually performs a convolution with a truncated
>> approximation of the Gaussian kernel.
>>
>> Note the use of the "m_UseImageSpacing" variable.
>>
>> On the other hand, look at the
>>
>> itkRecursiveSeparableImageFilter which is the parent
>> class of the itkRecursiveGaussianImageFilter. In particular
>> look at lines 264-267 of itkRecursiveSeparableImageFilter.txx:
>>
>> const typename InputImageType::SpacingType & pixelSize
>> = inputImage->GetSpacing();
>> this->SetUp( pixelSize[m_Direction] );
>> and their effect on
>> lines 79-256 in itkRecursiveGaussianImageFilter.txx
>>
>>
>>
>>
>> Regards,
>>
>>
>> Luis
>>
>>
>>
>> -----------------------------------------------------------------------------------------------------------------------
>> On Wed, Sep 9, 2009 at 10:22 AM, Oleksandr Dzyubak <adzyubak at gmail.com<mailto:
>> adzyubak at gmail.com>> wrote:
>>
>>
>> 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>
>> <mailto: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>>
>> <mailto: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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