In class, I very briefly mentioned that there's a connection to these images and something known as the Radon transform. The Radon transform is basically a continuous version of the Hough transform of lines expressed in normal form. It also has connections to the Fourier transform (and Fourier slice theorem) discussed last class.
And the Radon transform is used by CAT (computed axial tomography) scanners---a medical imaging device for non-invasively imaging into your body. In short, CAT scans capture measurements (known as sinograms) that look very much like those shown on this slide, and use an inverse Radon transform procedure to reconstruct the image of a line, rectangle, or circle from this result. The invention of the CAT scanner even won the Nobel prize in 1979 (though the Radon transform itself was introduced 80 years earlier).
In class, I very briefly mentioned that there's a connection to these images and something known as the Radon transform. The Radon transform is basically a continuous version of the Hough transform of lines expressed in normal form. It also has connections to the Fourier transform (and Fourier slice theorem) discussed last class.
And the Radon transform is used by CAT (computed axial tomography) scanners---a medical imaging device for non-invasively imaging into your body. In short, CAT scans capture measurements (known as sinograms) that look very much like those shown on this slide, and use an inverse Radon transform procedure to reconstruct the image of a line, rectangle, or circle from this result. The invention of the CAT scanner even won the Nobel prize in 1979 (though the Radon transform itself was introduced 80 years earlier).