Re: Question about Gaussian Blur

Posted by Michael Schmid on Jan 31, 2015; 7:21pm
URL: http://imagej.273.s1.nabble.com/Question-about-Gaussian-Blur-tp5011393p5011396.html

Hi Ting,

in theory the kernel size of a Gaussian is infinite, because the function
never reaches exactly zero. In practice, the Gaussian decays rather
quickly so one can have a finite kernel of about 3-4 standard deviations
(approx. 3-4 sigma) in radius, and the error is already very low. This
finite kernel size used for the calculation is sometimes called "support
size".

In ImageJ, the size of the kernel actually used depends on the accuracy
needed:  With sigma=1, for 16-bit and float images the kernel is 9 pixels
wide (which gives 9x9 for a 2D image), but for 8-bit or RGB images is is
only 7 pixels wide because there is no need for a very high accuracy if
there are only 256 different values.

For large values of sigma, the situation is more complex: For sigma >=8,
the data are first downscaled, then the Gaussian Blur is applied, and
interpolation is used for upscaling to the original number of data points.
The downscaling and interpolation algorithms are specially designed for
best accuracy.
E.g. for a 32-bit (floating-point) image and sigma=8.1, the kernel is
essentially exact within the floating-point accuracy in a width of 63
pixels up to a distance of 31 pixels). The largest deviation from the
exact value of the Gaussian is at a distance of 34 pixels; it is roughly
10^-4 of the peak value.

For practical purposes, don't care about the size of the kernel; the
result that ImageJ delivers is almost the same as you would get with the
full accuracy of an infinite kernel.

Just care about the standard deviation sigma.

As a rule of thumb, if you blur an image with a standard deviation of
sigma, two small separate features of equal brightness must have a
distance of 2 sigma or more to remain discernible as separate features
after blurring.

Michael

____________________________________________________________________

On Sat, January 31, 2015 10:26, Ting Xu wrote:

>  Hi,
> I do not kown how to set the parameter when I use the gaussian blur filter
> in Figi(Image J 1.49m) . In the guide, it has said that “Sigma is the
> radius of decay to e − 0.5 (≈61%), i.e., the standard deviation
> (σ) of the Gaussian (this is the same as in Adobe®Photoshop®, but
> different from ImageJ versions till 1.38q, in which radius was
> 2.5 × σ “.  At the same time, I have found a letter, that you
> send to a user named Jarek in 4 May 2007, written that “With ImageJ
> 1.38r, you have to enter the standard deviation directly, and ImageJ will
> calculate an appropriate kernel size.”.So, is the kernelradius equal to
> sigma with the Image J 1.47m? i.e. if I enter 1 as the value ofthe
> standard deviation sigma,that the kernel radius is equal to 1 pixel
> too,and have a 3x3 kernel.
>
>
> How toset this parameter in the new version?
>
>
>  
> Please,any suggestions? Anything will be greatly appreciate.
>
> Thankyou very much. Warm regards,
>
> Ting Xu 
> School of stomatologyWuhan universityPR China
> Email: [hidden email]
>
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> ImageJ mailing list: http://imagej.nih.gov/ij/list.html
>

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