The real question is how detailed must be the reconstructed bone. The grade of discretization depends on the purpose of desired model. For example, if you want to study the mechanical stress on the bone, the graphic resolution should go down to the level at sponge structure. If you want to study the external shape only, you need less graphic resolution than previous. IMHO you need two steps discretization:

1) Smoothing procedure for scalar 3D-image, where you can set the degree of fineness. If different degrees of fineness are needed for different regions, then you can mask the the regions and run the smoothing for every single single ROI at its unique smoothing degree.

2) density gradient based surface detection, where you can set the threshold value

Both steps can be done with Matlab with little knowledge in programing.

Also there is a possibility to use FEM method and discretize to 3D by using tetrahedrons instead of 2D method using polygons.

I use a good tool from Unity 3D and this tool have the possibility to export the new low poly mesh generated.

https://assetstore.unity.com/packages/tools/modeling/mesh-simplify-43658

You might be able to delete the inner data and then fill the holes this creates? This should be pretty straight forward using slicer and then whichever 3D modelling software you usually use. That's if you want to retain the detail- otherwise, a lot of smoothing, or changing the file format would also help. I have the same sort of issues with 3D models of teeth created using microCT and then loaded onto sketchfab, but they're nowhere near as complicated as bone. 

You can choose surface polygons in some editors (eg, Geomagic or Avizo), then invert to choose all the inner structures, then delete and fill any holes that may have formed.

Removing the inside as Rita and Justin suggested may be the best way to remove unnecessary data. Sadly I don't have access to Avizo or Geomagic. I do have Slicer, but I was not aware of a way to delete the inner data. I will look into it and report back; thanks!

Once I have a model of the outside only I can think about smoothing/decimating steps

As it seems you are eager to keep mesh data, and only need small file-sizes to transmit such data over network, I highly recommend taking a look at some 3D mesh compression and decompression libs such as:

• Google's Draco Library - https://github.com/google/draco
• Corto Library - https://github.com/cnr-isti-vclab/corto

Both Libs work in C++ and JS and are meant to be used for web-based 3D rendering.

Wish you the best!

https://github.com/google/draco

https://github.com/cnr-isti-vclab/corto

Answers will depend on the software platform and the pipeline you are using to do the CT to 3D model conversion. It appears that you are using 3D Slicer, as such you will find better answer to your inquiries on their discussion site (discourse.slicer.org).

Short answer is: you need to edit the segmentation such that there is not internal structure, but a solid a geometry.

Here is a thread that can be helpful.

https://discourse.slicer.org/t/how-to-edit-stl-file/960/21

Thanks for all the answers!

It was indeed possible to do some advanced data segmentation in Slicer. However, as I am dealing with with a bone segment (spongeous bone visible on 4 sides of the scan) and a hole in the middle, removing the inner parts was tricky and did not yield that much in terms of polygon reduction.

What eventually worked for me was (obviously) cropping unncessary parts and, most importantly running ambient occlusion coloring in meshlab and using this quality model as input for quadric edge collapse decimation, i.e. applying most of the simplification on the least visible (black/d. grey areas) and the least/no simplification on the light grey/white areas.

One on the proper solution for these kind of problems is using coreset. Regarding to the computational geometry, coreset is a small set of points that includes the best representative points of the original point set with regard to a geometric objective function. It seems you should define an optimization problem based on your application, firstly. Then you can approximate the solutions by using coreset idea. The following paper is one the attractive studies that uses coreset in computer vision.

Coresets for Triangulation https://ieeexplore.ieee.org/abstract/document/8031058