uisng peaks on linescan of image as locations for polyfits.

I take a horizontal linescan through an image of what should be regular spaced fluorescent beads. However due to optical distortion, at large distances from the centre, their location is different to what it should be - This is what I'm trying to measure.

So I take the linescan (red line) using the centre coordinates of the image (i.e. rows/2 and cols/2)

I then plot these and use the peakdet.m file to find the peaks. (This just finds the brightest pixel in each peak,with no fitting or interpolation)

[maxtab, mintab] = peakdet(yth_row, level);

where level is a threshold (which I just take as the mean/4, and yth_row is my linescan thru the image.

So my linescan with the found peaks are:

What I need to do is to use the peaks found by peakdet (i.e. maxtab) and perform some sort of fit (polynomial of order 5) around each peaks and include say 3 pixels each side of this peak. Then use the max in this fit to give the "real" locations of the each peak with sub-pixel resolution.

This is where I am stuck.

(maxtab(:,1) is the vector of x locations of the peaks, and maxtab(:,2) is the actual y value of them.

Any help would be appreciated.

Answer 1

[Image Analyst]

Actually I'm not seeing any noticeable distortion in that image. Is there any? Pincushion or barrel? Anyway, see my attached demos of polyfit() and spline().

[Jason]

This is only a small portion of my total field of view. My full fov is 16x larger and then u start to see distortion.

[Jason]

I need to perform the polyfit on all the peaks and then get a new vector of peak positions

[Image Analyst]

But not all at once. You're best off extracting one peak at a time and fitting only that one peak with a quadratic or 4th order or something.

[Rehan]

Hi Dear Image analyst, i want your help, i know this topic is little different,but you are all in all, so please help me. Let's say we have a periodic pattern (1D) with black and white stripes. The period is p. We can move the pattern along the pattern direction. Each time we move only p/3. Can we write the Fourier transform of this pattern and what happens when we move the pattern?

[Image Analyst]

Rehan - it's easy enough to try it and see, and you'll learn more. See my attached fft demos.

[Rehan]

ok i try, thank you very much.. :)

[Rehan]

Dear Sir, I tried but couldn't,can you please give me some hint. thankks

[Image Analyst]

Rehan, rather than hijack Jason's thread, why don't you start your own question?

[Jason]

Hi IA. I managed to perform the fit over all the peaks sequentially - but whilst it works well for most the peaks, there are quite a few where it doesn't.

On a previous thread, you asked for the data, I have included it here (linescan.txt is my raw linescan across the image, and peaks.txt is the peaks found by the peakDet.m file (which only has unit pixel resolution)

A typical problem of my polynomial fits to each peak is highlighted below. The black dots are the actual peak intensity found by peakDet.m and the blue crosses are the peaks found by fitting each peak to a polynomial (assuming black dot is the centre of the fits and allowing 3 pixels either side of this).

I have no idea why the cross circled in green has been found? Would you have any recomendations to improve this?

Thanks Jason

[Image Analyst]

I would not take this line scan approach at all. I would use a 2D approach. I'd use imregionmax() to find the peaks, then I'd probably use voronoi() to segment the image into a bunch of little zones. Then I'd use regionprops to get the weighted centroid location of each little zone. Consider my approach - I think you might agree it's more accurate and less dependent on where you draw some line.

[Jason]

Ok i will take a look at your suggestion - it sounds very interesting. Using your method, would i first generate the raw linescan data?

How do I apply voroni():

img=getimage(handles.axes1);
[rMiddle,cMiddle,r,c]=GetImageCentre(handles,img)  %my function
yth_row=img(rMiddle,:)+img(rMiddle-1,:)+img(rMiddle+1,:);
yth_row=yth_row-min(yth_row(:));   %Remove background
regmax = imregionalmax(yth_row);
figure
plot(regmax,'r.')
voronoi(1,regmax)

[Image Analyst]

I don't know - I'd have to research it just like you. I don't use voronoi very often so I'm not sure about what all the input and output arguments are. Check the help. Also, post your original image, without the green and red lines in it, and maybe this weekend I can try something.

But no, you don't need to generate any line scans at all, you're just finding the peaks so that you know how to divide the image up into little zones around each peak, then getting the weighted centroid with regionprops() which I think would be pretty much like fitting each little mountain to a smooth curve.

[Rehan]

ok, Sorry for that. I have made new question http://www.mathworks.com/matlabcentral/answers/252930-fourier-transform-of-a-pattern-with-black-and-white-stripes

[Jason]

Here is the raw image, thanks for any help. Jason