Homework 4: Computed Tomography

8 thoughts on “Homework 4: Computed Tomography

  1. Following the request to document *one* way to export a printable image.

    Often, your image analysis results are 16-bit integer or even floating-point values. Typical word-processing software cannot import those images, and you need to supply an 8-bit RGB image. The “cheap” way is to take a screenhot (use the PrtScr key), but there is a more elegant way:

    Select View -> Colormaps. Adjust the image to your liking with brightness, contrast, or even false colors (*). Then press the “Create” button in the colormaps dialog. A second window pops up, which looks like the first, but isn’t. The first image is unchanged, just displayed differently — in line with the idea of quantitative image analysis. The second image is the RGB representation of what you *see*. The second window has its own save button. Save the image (use a .png suffix!), and the PNG image can be imported into OpenOffice or similar.

    (*) For printing, it is often a good idea to apply a bit of gamma to counteract low contrast in the dark tones typically seen in printers.

  2. I received several questions regarding #4, the defects. Let me give you a hint — the detector problems (and these occur in the real world!) are covered in the third paragraph of Section 3.4 in the book, p. 52.

    When you try to explain the problems you see in the sinogram, try to explain them in terms of those described in Section 3.4. Also, the reconstructed image, when corrected properly, is sharp and does not show any blur, ring artifacts, or halos.

  3. For task 3, I was able to determine the SD for each of the reconstructed images to help decide which has the least amount of noise, but when I used the macro to compute the RMSE values for each, they all resulted in the same values. I tried deleting the macro and reloading it again, but it had the same results. Is there a way that I can correct this, or is just including the standard deviation values for each reconstruction sufficient proof?

    Thanks!

  4. You actually had me concerned for a moment that some of the new functions that I added for the CT in my lab would mess with the reconstruction results, but this is not the case. Pixel calibration and similar features are disabled as long as “real-world data” is not checked.

    So I went over the task myself, to the point of freshly downloading the sinogram and the macro. I reconstructed the sinogram with all three methods, and the macro gives me RMSE values of 1.95, 2.4, and 1.2, respectively.

    Is it possible that you didn’t reconstruct the image? You can try this: Go to Special -> Generate -> Shepp-Logan Head phantom. Check “increase contrast” and add weak noise (2 or 3). You should see the Head Phantom. Apply the macro — for a noise component of 2 it should give you a RMSE of 0.017.

  5. For #2, what do you mean when you say, “Select enhanced contrast to make the features more visible. Create projections (sinograms) with angular increments of 1, 2, 5, 10, and 20 degrees (360, 180, 72, and 36 projections, respectively).”?

    I can create the projections, however I don’t understand what the (360, 180, 72, and 36) refer to. My Erms values for angular increments of 1, 2, and 5 produce values in the range you specified, however for 20 it shoots up to 15 or so and is obviously incorrect.

  6. * Select enhanced contrast to make the features more visible: This refers to the checkbox in the window for the features of the Shepp-Logan phantom (Special->Generate)

    * Create projections (sinograms) with angular increments of 1, 2, 5, 10, and 20 degrees: This refers to the angular increment that you can select in the “make sinogram” function.

    Is it possible that you made some form of mistake for the 20 degree increment? It certainly looks awful, but the RMSE should not be totally off.

    • I apparently was doing it correct, however I would not ensure the correct image was loaded before moving onto the next photo. Loading the correct image each time and running it again fixed the problem.

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