what is the use of radon transform in image processing ?Can we convert 2D image to 1D signal by radon transform ?

we are doing a project on image processing.Automated Diagnosis of Glaucoma Using Texture and Higher Order Spectra Features.we have to do radon transform in preprocessing.is that needed for converting the image of eyes into signal ?

Answer 1

[Image Analyst]

The radon transform takes a projection of a 2D image along a direction to give the 1D profile. Kind of like if you stood the image on its edge and took an x-ray of it. In fact it's used in 3D medical imaging for CT reconstruction.

No, you do not need it to convert the image into the signal because the image is the signal. Or at least a signal. It's possible that you could generate tons of signals with various algorithms and radon() would also give a signal. However it sounds like you're trying to follow the algorithm in some very specific paper, and if that paper uses radon() as one of the steps, then go ahead and use it. Just in advance, I'll mention the FAQ: http://matlab.wikia.com/wiki/FAQ#Can_you_program_up_the_algorithm_in_this_article_for_me_and_explain_it_to_me.3F

[Ashwini]

Need some more clarification on Radon transform and R transform.

I applied Radon transform on a 3x3 matrix and obtained the following values.

a = [8 1 6;3 5 7;4 9 2]

r=radon(a,1:30:180);

r=

         0         0         0         0         0         0
    1.8387    1.6390    1.9203    1.8561    1.1949    1.0942
   13.1951   12.6928   12.2494   13.1602   13.5809   13.9016
   15.0023   17.2811   16.9505   15.0023   17.2811   16.9505
   13.0555   10.8035   11.6696   13.0904    9.9153   10.0174
    1.9085    2.5836    2.2102    1.8910    3.0277    3.0363
         0         0         0         0         0         0

what does these values signify. Also i got R transform value by summing up the radon coefficients in each column as r1=sum(r.^2);

 r1=[576.6475  585.8208  582.1199  576.6384  591.9878  591.3391]

Does maximum value of r1 which is 591.9878 signify that my matrix a is oriented to 151 degrees since i computed Radon transform for 1 to 180 degree with 30 degree spacing.

[Image Analyst]

The values are the sum of "a" along the angles you gave, which are (in degrees) 1, 31, 61, 91, 121, and 151. Note, there are no perpendicular angles of 90 or 180 that you have passed to it, so that's why the values at the center are not exactly the sum along rows or columns. There is one column for each of those 6 angles.

For the number of rows, it basically has to calculate how many elements it needs. As you can imagine, if the projection is along 45 degrees, then it will need more elements to get the projection than if it went strictly along rows or columns. I mean the diagonal of a rectangle is longer than either side, isn't it? So that's why the number of rows is not exactly the same as either the rows or columns in the array.

[Ashwini]

"The values are the sum of "a" along the angles you gave, which are (in degrees) 1, 31, 61, 91, 121, and 151." Does this means sum(sum(imrotate(a,61))=sum(r(:,3)).

Also please give me some explanation on R transform that is obtained from radon transform. What does maximum value in r1 means??

[Image Analyst]

The radon transform is like the sum along an angle, just like as if you had done an x-ray along that angle. For a 2D image, it gives you a 1-D profile. It's not a bad analogy - the radon transform being the x-ray of the image along an angle. In fact radon transforms are used in CT and MRI reconstruction.

The max value of the profile will be the "ray" that passed through the densest (i.e. brightest) part of the image.