Let us now return to the concept of the sinogram. To help us understand this a little bit better, Jacob will go in a bit more detail with a somewhat simple object and describe how the connection is between the sinogram and the projections. I have another example here where I have two squares as the example image. The resulting data from taking the Radon transform is oftentimes called a sinogram. How you get to the sinogram is basically from taking all the projections and putting them as columns of another array. So, if we take the first projection to be going vertically, you'll see the two squares, there's some space in between them which is what shows up in the first column over here. We see some space in between in the data. As we rotate, the two squares will overlap in the projections. That's what you see once you get to this yellow bit. As you keep rotating in the projections, they'll move away from each other again to this point where they're furthest away and then you keep rotating and then eventually they will be starting to move toward each other again in the projection space. So, taking all of those projections, that's going to give you a sinogram which is really the output of the Radon transform. Jacob mentions here the Radon transform and as he explains, really the sinogram is the output of the so-called Radon transform which goes all the way back to the first formulation of the 3D reconstruction problem. The Radon transform is really the name for this operation of doing the actual 3D reconstruction. Now, you have before heard that, many of the data that would take, they are taking only between zero and 180 degrees. There's a reason for this and here Jacob has an explanation. So, in the parallel beam case, we need to do only a 180 degrees because if we keep going beyond 180 degrees, we're actually just going to be getting mirror images, mirror projections that we already have. So, 180 degrees is enough for the parallel beam geometry. What Jakob is saying is that once we reach 180 degrees, we are basically taking the same data again from the opposite direction. So, 180 degrees corresponds exactly to the projection we got at zero degrees, and if we go then above 180 degrees, we will just take redundant data that we have from the opposite direction. So, that's why for parallel beam geometry, we will stop at 180 degrees with our scanning. Now, you have heard how the projections relates to the sinogram, and what will happen in the next video is that we will start to look at how we then get from the sinogram to the actual 3D reconstruction of the object.
