Explore projection space
X-ray images look at the shadow of an object, which is also called a projection. Since bone absorbs X-rays much more than the surrounding tissue, they are very good at producing high-contrast images of fractures.
However, one picture doesn’t tell the whole story, and if we were to rotate the arm 90°, we’d obviously see something else:
Combining the information in these two images tells us about the break and how to fix it. So rotating gives us more information.
What if we were to rotate by lots of little steps and take lots of pictures? If we stack them all together, we can see how the image changes as we rotate. This produces an image called a sinogram.
Below is a simulator that shows a simple object on the left (e.g. a sturdy bone), and below it a picture of what you’d see if you took an x-ray image from the top. Using your mouse, rotate the image slowly, and build up a collection of projections, to produce a sinogram on the right. Experiment with different objects to see how the sinogram changes.
Did you notice?
We don’t actually need a full 360 degree rotation. Because x-rays go through things easily we can get away with only 180 degrees: the rest is a mirror image!
The downside to producing incredibly detailed images is that every exposure irradiates your patient. You therefore face an important tradeoff between getting the detail you need while doing as little damage to the patient as possible. It’s also impossible to create a perfect image, which produces noise.
Below is a simulator that lets you select how many exposures (projections) to take, and see what the effect is on the reconstructed image.
Try uploading your own image and have a look at the sinogram, and how well it reconstructs
Each time you get a projection, you irradiate your patient! Therefore you need to figure out what the scans show using as little details as possible.
Mr. Potato Head has arrived in your emergency room in pieces. It looks like he’s fallen from a great height and it’s not clear where the injuries are. You pick several spots that appear concern you and order some immediate scans. You suspect he’s already been subjected to high radiation dosage so it’s important to limit his exposure.