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> Finally, in possibly his most ingenious invention, Hounsfield created an algorithm to reconstruct an image of the brain based on all these layers. By working

> Finally, in possibly his most ingenious invention, Hounsfield created an algorithm to reconstruct an image of the brain based on all these layers. By working backward and using one of the era’s fastest new computers, he could calculate the value for each little box of each brain layer. Eureka! And, of course, they glossed over the most interesting part by simply saying "an algorithm." I know that modern CT scans use Marching Cubes [1], which is what that particular algorithm was developed for, but that came later in the 80s. [1] https://en.wikipedia.org/wiki/Marching_cubes https://en.wikipedia.org/wiki/Marching_cubes

habi 5y ago
I don’t think they glossed over the marching cubes algorithm, but more over the theoretical work of Allan Cormack [0], which is crucial for CT reconstruction. (I work with (benchtop) microCT machines) [0]: https://en.wikipedia.org/wiki/Allan_MacLeod_Cormack https://en.wikipedia.org/wiki/Allan_MacLeod_Cormack
- alanbernstein 5y ago
  Wow, I didn't know there was such a thing. What do you image with them?
  - habi 5y ago
    Mostly biomedical samples. Recently a bunch of human teeth [1] or a few heads of zebrafishes [2]. I mostly deal with the data acquisition and then the image processing of the acquired tomographic data. [1]: https://habi.github.io/zmk-tooth-cohort-method-manuscript/ https://habi.github.io/zmk-tooth-cohort-method-manuscript/ [2]: https://doi.org/10.1371/journal.pone.0228333 https://doi.org/10.1371/journal.pone.0228333
geoduck14 5y ago
I was taught in school that the algorithm was an inverted 3d Fourier Transform. I'm not sure if I believe that now.
- throwaway81523 5y ago
  As I remember, Hounsfield originally used a much worse algorithm than that, although it was still workable and let him build usable machines. Later ones were more efficient due to using better math, but Hounsfield's got the job done.
- dreamcompiler 5y ago
  Sort of. https://en.wikipedia.org/wiki/Radon_transform#Relationship_with_the_Fourier_transform https://en.wikipedia.org/wiki/Radon_transform#Relationship_w...
dreamcompiler 5y ago
Marching Cubes is only the visualization mechanism after you have the voxels. The real work is in reconstructing the 3D data [voxels] from 1D scans, and that typically uses the Radon transform: https://en.wikipedia.org/wiki/Radon_transform https://en.wikipedia.org/wiki/Radon_transform
- AnimalMuppet 5y ago
  Don't they really use Feldkamp-Davis-Kress cone-beam algorithm? (https://pubmed.ncbi.nlm.nih.gov/15305448/ https://pubmed.ncbi.nlm.nih.gov/15305448/) Because the x-ray sources are point sources, or close, so you get a cone beam.
  - sandwall 5y ago
    Later, that was developed in 1984; CT's use collimated fan beams
    - AnimalMuppet 5y ago
      Use? You mean currently? I thought they used cone beams, but I never worked on them directly...
      - habi 5y ago
        A fan beam is ‘just’ a more collimated cone beam.
        sandwall 5y ago
        Yes, but this was only shown later -- The reconstruction algorithm for cone-beam was published in 1984 by research staff at Ford Motor Company. The Felkamp, Davis, and Kress algorithm was demonstrated as a natural extension of the fan-beam algorithm. -- first pencil beam, then fan-beam, finally cone-beam
  - habi 5y ago

habi 5y ago

I don’t think they glossed over the marching cubes algorithm, but more over the theoretical work of Allan Cormack [0], which is crucial for CT reconstruction. (I work with (benchtop) microCT machines) [0]: https://en.wikipedia.org/wiki/Allan_MacLeod_Cormack https://en.wikipedia.org/wiki/Allan_MacLeod_Cormack

alanbernstein 5y ago
Wow, I didn't know there was such a thing. What do you image with them?
- habi 5y ago
  Mostly biomedical samples. Recently a bunch of human teeth [1] or a few heads of zebrafishes [2]. I mostly deal with the data acquisition and then the image processing of the acquired tomographic data. [1]: https://habi.github.io/zmk-tooth-cohort-method-manuscript/ https://habi.github.io/zmk-tooth-cohort-method-manuscript/ [2]: https://doi.org/10.1371/journal.pone.0228333 https://doi.org/10.1371/journal.pone.0228333

geoduck14 5y ago

I was taught in school that the algorithm was an inverted 3d Fourier Transform. I'm not sure if I believe that now.

throwaway81523 5y ago
As I remember, Hounsfield originally used a much worse algorithm than that, although it was still workable and let him build usable machines. Later ones were more efficient due to using better math, but Hounsfield's got the job done.
dreamcompiler 5y ago
Sort of. https://en.wikipedia.org/wiki/Radon_transform#Relationship_with_the_Fourier_transform https://en.wikipedia.org/wiki/Radon_transform#Relationship_w...

dreamcompiler 5y ago

Marching Cubes is only the visualization mechanism after you have the voxels. The real work is in reconstructing the 3D data [voxels] from 1D scans, and that typically uses the Radon transform: https://en.wikipedia.org/wiki/Radon_transform https://en.wikipedia.org/wiki/Radon_transform

AnimalMuppet 5y ago
Don't they really use Feldkamp-Davis-Kress cone-beam algorithm? (https://pubmed.ncbi.nlm.nih.gov/15305448/ https://pubmed.ncbi.nlm.nih.gov/15305448/) Because the x-ray sources are point sources, or close, so you get a cone beam.
- sandwall 5y ago
  Later, that was developed in 1984; CT's use collimated fan beams
  - AnimalMuppet 5y ago
    Use? You mean currently? I thought they used cone beams, but I never worked on them directly...
    - habi 5y ago
      A fan beam is ‘just’ a more collimated cone beam.
      - sandwall 5y ago
        Yes, but this was only shown later -- The reconstruction algorithm for cone-beam was published in 1984 by research staff at Ford Motor Company. The Felkamp, Davis, and Kress algorithm was demonstrated as a natural extension of the fan-beam algorithm. -- first pencil beam, then fan-beam, finally cone-beam
- habi 5y ago