Re: 1-D Gaussian multiplier/convolution function around line in image.

Posted by Michael Schmid on Jan 26, 2019; 3:02pm
URL: http://imagej.273.s1.nabble.com/1-D-Gaussian-multiplier-convolution-function-around-line-in-image-tp5021719p5021721.html

Hi Ethan,

is it right that you want the weighted *sum* over the pixels at fixed x?

Then, even if you don't need a convolution, the easiest might be doing
the 1D convolution and then selecting the value at the y position of
choice.

ImageJ has the possibility to do a 1D Gaussian blur (because 2D Gaussian
blur is done by blurring successively in x and y), but there is
currently no function in the user interface for it.

You can access it via Java or JavaScript:

   ip = IJ.getImage().getProcessor();
   g = new GaussianBlur();
   g.blurGaussian(ip, 0.0, 6.37, 0.001);
   IJ.getImage().updateAndDraw();

The four parameters of blurGaussian are the ImageProcessor, the sigma in
x, the sigma in y, and the accuracy of the kernel (the latter must be
less than 0.02; recommended values are 0.002 for 8-bit or RGB and and
0.00001 - 0.0002 for 16-bit or floating-point images.

Sigma is the length in pixels where the kernel decays from the maximum
(1) to 1/sqrt(e); the value of 6.37 gives you a FWHM (full width at half
maximum) of 15.

Note that the convolution is scaled such that if you have a constant
pixel value, his value is preserved after the convolution. In your
suggested equation, the sum would increase with the width of the
Gaussian, which is proportional to 1/sqrt(b).

Of course, you can also write a macro for it, or use Herbie's
Process>Math>macro and then add up all the pixels along a vertical line
(e.g., 'select all' and 'plot profile' will give you the average over
the pixel columns; multiply them with the image height to get the sum.)


Michael
________________________________________________________________




On 2019-01-26 02:36, Cohen, Ethan D wrote:

> I have an image, where I want to vertically weight the intensity the
> pixels, by a 1-D Gaussian function around a horizontal line ROI in the
> image, so that the peak is 3X the original intensity, with a Gaussian
> ½ bandwidth of say 15 pixels in the Y direction.
>
> Something like, v=3v* exp (-b*(y-y0)^2  -1*(y-y0));?
>
> Or maybe ImageJ already has a feature for 1-D Gaussian weighting (not
> blur)?   I guess this is sort of a 1-D convolution.
>
> Is there a function already in ImageJ to do this?
> I suppose I could make some sort of weighting matrix, but it seems
> rather painful.
>
> Ethan.
>
>
> Ethan Cohen, Ph.D.
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