[Insight-users] discrete vs. recursive Gaussian derivatives image filter

[Iván Macía]

Hi Moti,

The Discrete Gaussian is normalized in order to have a standard Gaussian
with unit area under the curve. The  maximum error parameter is used in
order to calculate a kernel width such that approximates the unit area with
a given precision. For example if we want a maximum error of 0.02, we
calculate the kernel radius necessary to give an area of 0.98 or higher.
When spacing is exactly 1.0, this corresponds simply to the sum of the
values obtained in the kernel by the discrete Gaussian approximation. I
still have to check if the kernel is working well for values different than
one. The across-scale normalization should simply divide by the scale.

If we assume that estimated values for the discrete Gaussian are correct
(have you checked this? Are they correct for you?), then it may happen that
the recursive Gaussian approximation is not normalized in the same way (by
the unit area under the Gaussian curve) or that this normalization is not
correctly calculated or that there is an error in the implementation (a
multiplicative factor). In order to achieve a normalized unit area Gaussian,
one multiplies the exponential term by a factor of ( 1 / (
sqrt(2*pi*sigma^2) ) as can be seen in the standard normalized Gaussian
function formulation. Try to multiply the values of the recursive Gaussian
by this factor, to see if it gives the expected result.

Hope that helps

Iván
 

-----Mensaje original-----
De: insight-users-bounces at itk.org [mailto:insight-users-bounces at itk.org] En
nombre de Moti Freiman
Enviado el: domingo, 17 de enero de 2010 13:31
Para: insight-users at itk.org
Asunto: [Insight-users] discrete vs. recursive Gaussian derivatives image
filter

Hi all,
We tested the output of both discrete and recursive Gaussian
derivatives image filter on synthetic image including only
one pixle with value 1 in the center. All other pixels were set to
zero, expected to get almost similar results.
However, The output of the recursive filter was much higher than the
discrete one, almost in ten Gaussian sigma factor.
We used the normalizedacrossscale option, so we assumed that the
vlaues should be normalized and should get the same value.
Any ideas?
Many thanks.
Moti

-- 
__
Moti Freiman, Ph.D Student.
Medical Image Processing and Computer-Assisted Surgery Laboratory.
School of Computer Science and Engineering.
The Hebrew University of Jerusalem Givat Ram, Jerusalem 91904, Israel
Phone: +(972)-2-658-5371 (laboratory)
WWW site: http://www.cs.huji.ac.il/~freiman
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