Radon Transform

Hi does anybody know how to compute the Radon transform of an ellipse?

Answer 1

[Michael]

If the ellipse has a uniform value the integral becomes the product between that value and the length of each beam through the ellipse. It should be possible to get an analytic expression for this length in terms of the ellipse parameters and the line parameters, although it might take some work to get this.

Alternatively if you have sufficient memory you can use the radon.m with an extremely high resolution phantom to get a good approximation.

It is linear, so the sum of the transforms of the individual ellipses should equal the transform of the sum of the ellipses (ie. the transform of your Shepp-Logan phantom).

[Vera]

Yes I know the first way is possible but too long thats why I was thinking that there might be a shorter way and yes i am using another function (ex. radon.m) for radon transform of one ellipse and then summing the transforms and it does work but the code I have found for this radon transform of the ellipses its not so understandable to me (the angle of the ellipse is also used in the radon transform), its the one I wrote in the comment of the previous question, so I wanted to find another way ..

And I dont get why you say I can use radon.m with extremely high resolution phantom?(I am actually using the modified Shepp- Logan phantom if that's what you wanted to say)

Answer 2

[Ryan]

http://www.mathworks.com/help/toolbox/images/ref/radon.html ?

Answer 3

[Vera]

Yes but I was thinking an analytical formula is what I need

[Ryan]

You can comment on an answer to continue discussing it. What form is your data expressed in? The Radon transform is for images. You could plot the ellipse and then use getframe() and crop the image out if needed or use a phantom of an ellipse made outside of Matlab. I am unaware of any good method to create a matrix (image) from two vectors.