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

Don't they really use Feldkamp-Davis-Kress cone-beam algorithm? (https://pubmed.ncbi.nlm.nih.gov/15305448/)

Because the x-ray sources are point sources, or close, so you get a cone beam.

There’s a large amount of different reconstruction algorithms, some geared for speed, some geared for noisy data, some geared for quality. Wikipedia has a quick overview: https://en.wikipedia.org/wiki/Tomographic_reconstruction

Later, that was developed in 1984; CT's use collimated fan beams

Use? You mean currently? I thought they used cone beams, but I never worked on them directly...

A fan beam is ‘just’ a more collimated cone beam.

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

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

Wow, I didn't know there was such a thing. What do you image with them?

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/

[2]: https://doi.org/10.1371/journal.pone.0228333

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

Sort of.

https://en.wikipedia.org/wiki/Radon_transform#Relationship_w...

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.