How to filter/smooth an image that has circular symmetry?

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Aurelien Gregor
Aurelien Gregor 2021-2-5
编辑： Matt J 2021-2-5
Hello,
I have a set of 2d data with circular symmetry stored as matrices. I wish to use the symmetry in order to smooth my image by using the other points that are at a comparable distance from the center. This would be in contrast to a filter that uses local neighbouring points to smooth the data, which tends to distort this data.
The image presented here is quite smooth but I have many images with noise.
Thanks, Aurélien

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Matt J
Matt J 2021-2-5
编辑：Matt J 2021-2-5
Ran in:
One approach would be to use radon and iradon,
noisyImage= (1+sqrt((-100:100).^2 + (-100:100).'.^2));
noisyImage=noisyImage.*(noisyImage<=100) + 5*randn(size(noisyImage));
theta=0:0.25:180;
R=mean( radon(noisyImage,theta) ,2);
smoothImage=iradon( repmat(R,1,numel(theta)) ,theta );
imshowpair(noisyImage,smoothImage,'montage')
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Matt J
Matt J 2021-2-5
编辑：Matt J 2021-2-5
For those that don't understand the code, this is my understanding ... then "radon(yourImage,theta)" creates a 2d matrix by taking "slices" of your image that pass through the center of your image at each theta value.
Not slices. Projections.
https://www.mathworks.com/help/images/ref/radon.html#f6-466342
Basically, what you would see if you took an x-ray image through the object at each angle theta.
Do you not have any problems using theta=0:0.25:180
As you can see from my example output, I do not, but if you attach a.mat file containing your "noisyImage" variable, we can examine it.
Aurelien Gregor
Aurelien Gregor 2021-2-5
Thank you for your answers. Indeed it seems to work fine for you so there must be a subtle difference in our data that creates these issues.
I couldn't find a way to get rid of artifacts at both north and south pole, so I found theta vectors where the North pole didn't have any artifacts, and same thing for south pole, then combined both halves to make an image without artifacts. Not the most elegant method but it works !

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