Does the radon and iradon built in functions use the center as the reference for the projections?

For example in this image how can iradon function differentiate between P0(0)=3 and P0(1)=7 since both projections are taken horizontally?

Answer 1

[Image Analyst]

No it doesn't use the center. It's as if you had a whole army of those rays, all parallel to each other. The arrowheads land on a 1-D array. So essentially each pixel in the array is the sum of all pixel values along the ray perpendicular to that point in the array that passes through your "body".

The "3" and "7" rays are different because they each passed though a different "path" through the body and ended up on a different pixel in the 1-D array.

Real CT instruments no longer pass a 1-D set of rays through the body. They pass a 2-D set of rays through, like a pyramidal cone, so the radon transform (the projection) is also a 2-D image.

[oumi k]

Thank you for answering. So just to make sure I understood, the radon reconstruction is for a 2D set of rays and not 1D set? If so, how can we recosntruct an image from just a 1D set only?

[Image Analyst]

The radon transform function only works with 2-D images. It produces a 1-D projection (a list of numbers). If you pass in multiple angles, then you'll get multiple 1-D projections stitched together in the form of a 2-D image where one dimension represents distance and the other dimension is the angle (each angle gives you one column in the image). See the attached demo.

I don't know how to do the full CT reconstruction. I had a semester long graduate college course in it, but that was back in 1983, and I haven't done it since. Now, I just know the conceptual basics about filtered back projection. It's very complicated. They don't hand out Nobel Prizes for trivial stuff. https://en.wikipedia.org/wiki/Godfrey_Hounsfield

[oumi k]

Thank you for your answer.

[oumi k]

Reagrding the distance, what distance exactly? What is the start and end point for the distance ?

Answer 2

[Walter Roberson]

No, the center is not used; see the algorithm at https://www.mathworks.com/help/images/ref/radon.html#f6-466342 which has a diagram.