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We've been on a project that given us in Medical Imaging Systems class about that Computed Tomography Simulation on MATLAB for 3 months. We are still going on comprehensive research on these all of subjects. We've a little information about Radon Transform, Back-projection, Central Slice Theorem and Fourier Transform but project don't go ahead anymore. There a figure about our problem below.

We're stuck at one point which we have to solve to length of line that passing into inside of image pixel squares.

There is a variable(a_i) shown in Fig. 1. We can't calculate these lengths with equation shown below.

The teacher that gave this project to us don't want to that we to do interpolation on this subject. As the result of matrix of multiplying of attenuation coefficient and r(or rho), she's wanting to a matrix that storing this r lengths, as this problem's answer.

Would you help us, please?

Rushabh Mehta
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remidosol
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  • @CareyGregory I'm asking about an equation that shown in Fig.2. AB line equation. How can I describe this equation for 1-45 & 46-89 & 90-134 & 135-179 theta angles? There is a source and transducer(detector). Our attenuation coefficients are pixels' grayscale value, and angles' are theta. I'm asking the line equation that passing into inside of image pixels. So, it's look like y = ax+b or something like that. How can I solve this derivation and implement this to an image? –  Dec 01 '19 at 19:45
  • @CareyGregory Which are these line equations? I couldn't derive. –  Dec 01 '19 at 19:49
  • Thank you for the edits. I've reopened it. Now my question is in what way is this a medical question? It appears to be purely a math problem, which means it would get better answers on Match.SE. I can migrate it there for you if you agree. – Carey Gregory Dec 01 '19 at 21:57
  • @CareyGregory Sir, it's a math problem but it's a problem that depends on medical imaging in computed tomography. There are Radon Transform, Reconstruction Algorithms, Fourier Transform but this problem bears on CT. –  Dec 01 '19 at 22:03
  • @CareyGregory As your wish, sir. You can migrate. –  Dec 01 '19 at 22:07
  • Can you please explain a bit more about why you cannot do the calculation? Do you not have enough information about $x_1$ and $y_1$ etc? I hope this helps. – ad2004 Dec 01 '19 at 22:45
  • If you are looking for a form of the equation of the lines intersecting the image pixels, it would be something like $y=tan(\beta)x+\delta{x}/cos(\beta)*k$, I believe, where $\delta{x}$ is the spacing between the lines from the source, and k is some index to count the line number. I hope this helps. – ad2004 Dec 01 '19 at 22:57
  • @ad2004 Angle of incidence is changing between 0 and 180 degrees. By the way, the pixel state which beam's intersects are changing continously according to this angle of incidence. – remidosol Dec 01 '19 at 23:02
  • @ad2004 I will work on it sir. If any trouble appear, I'll back again. Even so thanks. – remidosol Dec 01 '19 at 23:12

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