Gaussian blur

[cihat eldeniz]

Hello,

In matlab, if we do h = fspecial('gauss',3,1), we get:

h =

    0.0751    0.1238    0.0751
    0.1238    0.2042    0.1238
    0.0751    0.1238    0.0751

Then we use imfilter(ourImage,h) to get the blurred image.

If I copy and paste this 2D kernel into the convolver [using
Process>Filters>Convolve...], I get nearly the same result as matlab.
However, I would also like to learn how to do it by using imagej commands
only within a plugin.

If I use Gaussian Blur with sigma 1, then the image is convolved with a 6x6
window right? [Since the assumed accuracy is 2e-4 for an image which is not
Byte or Color, and the sidelength of the kernel is given by
ceil(sigma*sqrt(-2*log(accuracy)))+1]. To have a 3x3 window, I have to set
the accuracy to at least exp(-2) = 0.1353, which is well above the
recommended upper limit on the website [0.02].

How could I have imagej perform the filtering operation in exactly the same
way as matlab with the 3x3 h given above, or is it possible at all?

Thanks.

[Michael Schmid]

Hi Cihat,

the Gaussian Blur of ImageJ is a bit complicated:
- It does two successive filter operation, one in x, one in y. This  
is faster than a 2D kernel. (Gaussian Blur is a separable filter)
- The kernel size reaches out as far as required to have the edge  
values at roughly 2*10^-3 (8-bit, RGB) or 2*10^-4 (16-bit, float) of  
the center value; you have read this correctly from the source code.  
The equation that you have read from the makeGaussianKernel method is  
for the radius; the side length is 2*radius-1.
- At the edges, the kernel is smoothly tapered towards zero to avoid  
artifacts caused by the small step that one have would otherwise.  
This process will fail if you set an accuracy that is too low, thus  
the upper limit of 0.02 for the accuracy. So you can't have a 3x3  
kernel with sigma=1.
- For large values of sigma, the rows or columns are first  
downscaled, then the filter operation is performed with a smaller  
sigma (smaller kernel), afterwards they are upscaled to the original  
size. Otherwise, computing time would be prohibitive for large sigma.

The whole algorithm is a compromise between speed and accuracy.

If you only want a 3x3 kernel for sigma=1, you have to use the  
Convolver class.

An alternative would be taking the GaussianBlur code as an external  
plugin and eliminating the 'edge correction code' of  
makeGaussianKernel. For a small kernel size it won't be worth the  
effort - there the Convolver will be fast enough.

Hope this helps,

Michael
________________________________________________________________

On 4 Jun 2009, at 16:09, cihat eldeniz wrote:

> Hello,
>
> In matlab, if we do h = fspecial('gauss',3,1), we get:
>
> h =
>
>     0.0751    0.1238    0.0751
>     0.1238    0.2042    0.1238
>     0.0751    0.1238    0.0751
>
> Then we use imfilter(ourImage,h) to get the blurred image.
>
> If I copy and paste this 2D kernel into the convolver [using
> Process>Filters>Convolve...], I get nearly the same result as matlab.
> However, I would also like to learn how to do it by using imagej  
> commands
> only within a plugin.
>
> If I use Gaussian Blur with sigma 1, then the image is convolved  
> with a 6x6
> window right? [Since the assumed accuracy is 2e-4 for an image  
> which is not
> Byte or Color, and the sidelength of the kernel is given by
> ceil(sigma*sqrt(-2*log(accuracy)))+1]. To have a 3x3 window, I have  
> to set
> the accuracy to at least exp(-2) = 0.1353, which is well above the
> recommended upper limit on the website [0.02].
>
> How could I have imagej perform the filtering operation in exactly  
> the same
> way as matlab with the 3x3 h given above, or is it possible at all?
>
> Thanks.

[cihat eldeniz]

It definitely helps a lot. Thank you very much for the time and effort!

2009/6/4 Michael Schmid <[hidden email]>

> Hi Cihat,
>
> the Gaussian Blur of ImageJ is a bit complicated:
> - It does two successive filter operation, one in x, one in y. This is
> faster than a 2D kernel. (Gaussian Blur is a separable filter)
> - The kernel size reaches out as far as required to have the edge values at
> roughly 2*10^-3 (8-bit, RGB) or 2*10^-4 (16-bit, float) of the center value;
> you have read this correctly from the source code. The equation that you
> have read from the makeGaussianKernel method is for the radius; the side
> length is 2*radius-1.
> - At the edges, the kernel is smoothly tapered towards zero to avoid
> artifacts caused by the small step that one have would otherwise. This
> process will fail if you set an accuracy that is too low, thus the upper
> limit of 0.02 for the accuracy. So you can't have a 3x3 kernel with sigma=1.
> - For large values of sigma, the rows or columns are first downscaled, then
> the filter operation is performed with a smaller sigma (smaller kernel),
> afterwards they are upscaled to the original size. Otherwise, computing time
> would be prohibitive for large sigma.
>
> The whole algorithm is a compromise between speed and accuracy.
>
> If you only want a 3x3 kernel for sigma=1, you have to use the Convolver
> class.
>
> An alternative would be taking the GaussianBlur code as an external plugin
> and eliminating the 'edge correction code' of makeGaussianKernel. For a
> small kernel size it won't be worth the effort - there the Convolver will be
> fast enough.
>
> Hope this helps,
>
> Michael
> ________________________________________________________________
>
>
> On 4 Jun 2009, at 16:09, cihat eldeniz wrote:
>
>  Hello,
>>
>> In matlab, if we do h = fspecial('gauss',3,1), we get:
>>
>> h =
>>
>>    0.0751    0.1238    0.0751
>>    0.1238    0.2042    0.1238
>>    0.0751    0.1238    0.0751
>>
>> Then we use imfilter(ourImage,h) to get the blurred image.
>>
>> If I copy and paste this 2D kernel into the convolver [using
>> Process>Filters>Convolve...], I get nearly the same result as matlab.
>> However, I would also like to learn how to do it by using imagej commands
>> only within a plugin.
>>
>> If I use Gaussian Blur with sigma 1, then the image is convolved with a
>> 6x6
>> window right? [Since the assumed accuracy is 2e-4 for an image which is
>> not
>> Byte or Color, and the sidelength of the kernel is given by
>> ceil(sigma*sqrt(-2*log(accuracy)))+1]. To have a 3x3 window, I have to set
>> the accuracy to at least exp(-2) = 0.1353, which is well above the
>> recommended upper limit on the website [0.02].
>>
>> How could I have imagej perform the filtering operation in exactly the
>> same
>> way as matlab with the 3x3 h given above, or is it possible at all?
>>
>> Thanks.
>>
>