(Editor's note: this page was written with lots of help from Cat Scan (who is not a radiologist or a piece of X-ray equipment, but who often purrs like a CT scanner), and a few pawstrokes from Sniff, too.)
Computed tomography (CT, also known as computerized axial tomography, or CAT) is a method for taking pictures of cross-sectional slices of an object (like a patient) without actually having to slice the object.
A standard X-ray photograph is taken by placing a sheet of film on one side of a patient, and "shining" X-rays through the patient onto the film. This gives you a two-dimensional (flat) picture of all the structures between the X-ray tube and the film. Sometimes it's hard to figure out whether one object you see on a standard X-ray is in front of or behind another object, even if you take another picture at a different angle to the first picture.
A CT scan, sometimes called a CAT scan,
Once we have the 180 different line pictures, we can "assemble" them mathematically into a single picture of the "slice" through which all of the line pictures were taken. We call this process reconstruction. This has to be done with a computer, thus the "computed" in CT. (A tomograph is a cross-sectional image; the term "axial" in computerized axial tomography refers to the axis around which all of the "line pictures" are taken.) We also can't start the reconstruction until all of the line pictures are taken, since every pixel (picture element) in the final picture of the slice depends on all 180 of the line pictures.
An example may help you to see how reconstruction works. Let's take a 2 pixel by 2 pixel CT scan, and take only 2 sets of line pictures: one horizontally and one vertically, and therefore at a 90-degree angle to each other. (Think of Cat Scan looking at a birdie from one window and Sniff looking at the same birdie from another window, with their views at right angles to each other.) We first take the horizontal line pictures, then we take the vertical line pictures. Each line picture is actually a number which indicates the density of the line (how light or dark all of the pixels in the line are). In CT lingo, these densities are called ray sums (a ray is a line through the slice being scanned, and the ray sum is the sum of the densities of the pixels included in that particular ray). In our example, the two horizontal lines (rows) have ray sums of 7 and 11, and the two vertical lines (columns) have ray sums of 8 and 10.
Row ray sums | |||
---|---|---|---|
? | ? | 7 | |
? | ? | 11 | |
Column ray sums | 8 | 10 |
To back-project, we first take the row ray sums and divide them evenly by the number of pixels in the row.
Row ray sums | |||
---|---|---|---|
3.5 | 3.5 | 7 | |
5.5 | 5.5 | 11 | |
Column ray sums | 8 | 10 |
Now, we take the column ray sums and divide them evenly among the number of pixels in the column.
Row ray sums | |||
---|---|---|---|
3.5 + 4 | 3.5 + 5 | 7 | |
5.5 + 4 | 5.5 + 5 | 11 | |
Column ray sums | 8 | 10 |
Adding the row and column contributions, we get:
Row ray sums | |||
---|---|---|---|
7.5 | 8.5 | 7 | |
9.5 | 10.5 | 11 | |
Column ray sums | 8 | 10 |
What we've done so far is simple back projection. In a real CT scanner, there are lots more line pictures, and since they are taken at many different angles we must adjust each line ray sum's contribution to the density of a pixel to account for the angle that that line makes with the row and column where that pixel lies. Even so, simple back projection is prone to errors in density calculation.
A simple way to correct for these errors is iterative back projection. Here, after doing the initial back projection, we go back to the first set of line pictures (in this case, the rows), add up the densities of each pixel in each row as calculated from the original back projection, and divide this sum by the number of pixels in the row.
Row ray sums | |||
---|---|---|---|
7.5 | 8.5 | 7 - 16 = -9 | |
9.5 | 10.5 | 11 - 20 = -9 | |
Column ray sums | 8 | 10 |
This correction is then "added" (actually subtracted, since the subtraction produces a negative difference) to each pixel in the row.
Row ray sums | |||
---|---|---|---|
7.5 - 4.5 = 3 | 8.5 - 4.5 = 4 | 7 - 16 = -9 | |
9.5 - 4.5 = 5 | 10.5 - 4.5 = 6 | 11 - 20 = -9 | |
Column ray sums | 8 | 10 |
Then we repeat the process using the sum of the calculated density of each column in the image and that column's original ray sum, applying the correction for each column to each pixel in that column.
Row ray sums | |||
---|---|---|---|
3 | 4 | 7 - 16 = -9 | |
5 | 6 | 11 - 20 = -9 | |
Column ray sums | 8 - 8 = 0 | 10 - 10 = 0 |
In this example, it turns out that the calculated ray sums for each column after the rows were corrected agree with the original column ray sums, so the column corrections are zero. If you look at the pixel densities by row and column, you'll see that each row adds up to the original row ray sum and that each column adds up to the original column ray sum -- which means that our reconstruction of the original "image" is perfect. (This doesn't happen a lot in real CT scans.)
Row ray sums | |||
---|---|---|---|
3 | 4 | 7 | |
5 | 6 | 11 | |
Column ray sums | 8 | 10 |
To see all of this in animated form, click the Start button in
the picture below. Cat Scan
scans the rows in the animation, while
Sniff scans the columns.
Click on the green flag to reset the "scanner".
Click here for information on the animation.
(NOTE: you must have Java enabled
in your browser to see the animation.)
Of course, the process is much more complex if you are scanning at 180 different angles. Real CT scanners also take several different line pictures at each of the 180 different positions of the X-ray tube, which complicates things even more -- and makes iterative back projection very slow. The original CT scanners neede 20 minutes or so to reconstruct a single image. Reconstruction in modern scanners uses special image processing algorithms to perform what is referred to as filtered back projection (the computer performs operations very similar to those used to process and filter sounds), and can reconstruct an image in seconds -- often while the next image is being scanned.
(Note, by the way, that although "CT scanners" use X-rays the line pictures don't have to be X-ray pictures. Magnetic resonance imaging scanners use the phenomenon of nuclear magnetic resonance (NMR) for their line pictures, while positron emission tomography scanners, or PET scanners, use positrons (the antimatter version of electrons) to take the line pictures.)