Image Reconstruction from Projections

The Radon transform is presented, which is important in computerized tomography in medical and industrial applications. This transform enables to produce the image of an object, without intrusion, using its projections at various directions. As this transform uses the normal form of a line, it is presented first. Then, the Radon transform and its properties are described next. The Fourier-slice theorem and the filtered back-projection of the images are presented. Finally, line detection using the Hough transform is given. Examples are included to illustrate the various concepts.