[Insight-developers] Gaussian filter performance

[Karl Krissian]

The recursive Gaussian filter is an approximation of the discrete
Gaussian convolution (you can check INRIA Tech Report 1893 of Rachid
Deriche),
but its interest is than its computation time is not
depend on the kernel size.
However, you should not remove the discrete gaussian
which is in general more accurate (depending on the size of the support).

My experience when convolving with derivatives of the gaussian kernel is
that it is better to use discrete convolution for small kernel or when
high accuracy is needed (the recursive filter seems to create unwanted
zero-crossing for example when convolving with the second order
derivatives of the Gaussian).



Karl Krissian, PhD
Laboratory of Mathematics in Imaging (LMI)
Harvard Medical School, Brigham and Women's Hospital
Tel:617-278-0639, Fax:617-264-6887

On Fri, 9 May 2003, Mark Foskey wrote:

> Yes, I had noticed the same thing but I hadn't yet followed up.  I
> wasn't as systematic as you were, so I wasn't as confident of my
> results.  This means that the documentation I recently put in the
> comments may be false, as they advocate using the discrete gaussian
> filter for a small kernel.
>
> I also noticed, however, that the result of applying the discrete
> gaussian filter to a binary image looked more like my idea of a
> smoothed image than did the recursive gaussian.  So I'm also interested
> in knowing if there is wisdom out there on the accuracies of both methods.
>
> If it turns out that we can't say that the discrete gaussian is more
> accurate, it is questionable whether we should keep it.
>
> Paul Yushkevich wrote:
> > I have been trying to choose an appropriate Gaussian blurring filter to
> > use in the SnAP project.  While doing so, I tried to compare the
> > performance of three candidates from ITK and VTK on a sample image.  The
> > candidates were itk::DiscreteGaussianImageFilter,
> > itk::RecursiveGaussianImageFilter and vtkImageGaussianSmooth .  I ran
> > the filters with default parameters, only changing the standard deviation.
> >
> > Perhaps the result is useful to others, so I post it here.  For one
> > thing, it shows that the recursive gaussian filter seems to perform
> > better on even very small sigmas.  What is the error of the recursive
> > filter w.r.t to the true solution for subpixel values of sigma?
> >
> > The times listed below are for VC6 Release program running on a
> > two-month old machine.
> >
> > Loaded image     : image01.mha
> > Image size       : 7109137 bytes
> > Image dimensions : 181 x 217 x 181
> > Component count  : 1
> > File type        : Binary
> > File byte order  : Little Endian
> >
> > Standard Deviation: 0.5
> >   ITK Discrete Gaussian   : 3688ms.
> >   ITK Recursive Gaussian  : 515ms.
> >   VTK Gaussian            : 1907ms.
> >
> > Standard Deviation: 1.5
> >   ITK Discrete Gaussian   : 4578ms.
> >   ITK Recursive Gaussian  : 484ms.
> >   VTK Gaussian            : 2281ms.
> >
> > Standard Deviation: 2.5
> >   ITK Discrete Gaussian   : 5672ms.
> >   ITK Recursive Gaussian  : 485ms.
> >   VTK Gaussian            : 2406ms.
> >
> > Standard Deviation: 3.5
> >   ITK Discrete Gaussian   : 7079ms.
> >   ITK Recursive Gaussian  : 500ms.
> >   VTK Gaussian            : 2781ms.
> >
> > Standard Deviation: 4.5
> >   ITK Discrete Gaussian   : 8578ms.
> >   ITK Recursive Gaussian  : 484ms.
> >   VTK Gaussian            : 3078ms.
> >
> > Paul.
> >
> >
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>
> --
> Mark Foskey    (919) 843-5436  Computer-Aided Diagnosis and Display Lab
> mark_foskey@unc.edu            Department of Radiology, CB 7515, UNC
> http://www.cs.unc.edu/~foskey  Chapel Hill, NC  27599-7515
>
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