Re: Help with computing correlations along z in stacks.

Posted by Michael Schmid on Feb 26, 2015; 4:37pm
URL: http://imagej.273.s1.nabble.com/Help-with-computing-correlations-along-z-in-stacks-tp5011785p5011788.html

Hi Thomas,

unfortunately I don't know matlab, but it seems to my that you can it in ImageJ without very much programming, i.e., in a macro:
- Image>Stacks>Reslice to have the z direction run in x or y.
- Convert to float and subtract the background value, so that the background gets a value of 0
- Pad the canvas size to a square that is a power of 2.
- Create a 32-bit image of the same size with you function centered in the middle, running in the same x or y direction as the original z direction, only in the middle line.
- For all stack slices, run Process>Math>FD Math and correlate (with inverse transform) the images of the resliced stack with the image having the function.
- Combine the output images to a stack, and reslice to the original orientation if desired.

If you want to do programming in Java, you could also use the built-in 1D FHT (fast Hartley transform) of ImageJ.
  https://github.com/imagej/imagej1/blob/master/ij/process/FHT.java
Correlation is simply multiplying the FHT arrays index by index, then transform back (inverseTransform1D).


Michael
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On Feb 26, 2015, at 12:14, Thomas Julou wrote:

> Hello,
>
> I hope this list is the right place to ask my question.
> In order to achieve robust segmentation of bacteria from white light pictures, we use a "correlation" image. The principle is to acquire a z-stack of bright field pictures, and to correlate the intensity along z with an « expected" intensity profile. So far, we wrote the code in Matlab only.
>
> However for several purpose, I’d be interested in having the code written for imageJ (among other, doing the acquisition with micro-manager and processing images on the fly; though I know I could call MM from Matlab). Since I'm new to plug-in programming (but anticipate that speed will matter in this case), I'd really appreciate getting pointers to appropriate libraries / examples.
>
> Here are a few specific questions:
> - is it better to run a FFT per (x, y) intensity profile or is there any kind of "vectorized syntax"?
> - which fft library do you recommend? fftw? imglib2?
> - is it realistic to write this for cuda / opencl already? (to me it looks like a good task for a gpu)?
>
> Below is the code I wrote for matlab since it might help to answer.
> Thank you in advance for your help. Best,
>
> Thomas
>
> --
> Thomas Julou  |  Computational & Systems Biology  |  Biozentrum – University of Basel  |  Klingelbergstrasse 50/70 CH-4056 Basel  |  [phone]
>
>
>> function IM_CORREL = correlImg(IM, sigma)
>> [ny, nx, nz] = size(IM);
>> z = (1:nz)';
>> center = round(nz/2);
>>
>> zProfile = - (z-center) .* exp(- (z-center).^2 / (2*sigma^2));
>> zProfileFFT = fft(zProfile);
>> zProfileFFT(1) = 0;
>>
>> zProfileFFTc = conj(zProfileFFT);
>> Z_PROFILE_FFT_C(1,1,:) = zProfileFFTc;
>> Z_PROFILE_FFT_C = repmat(Z_PROFILE_FFT_C, [ny nx]);
>>
>> IM_Z_FFT = fft(IM, [], 3);
>> IM_Z_FFT(:,:,1) = 0;
>> CORREL = real(ifft(IM_Z_FFT.*Z_PROFILE_FFT_C, [], 3));
>>
>> idx = [center+1:nz 1:center];
>> IM_CORREL = CORREL(:,:,idx);
>
> --
> ImageJ mailing list: http://imagej.nih.gov/ij/list.html

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