Heavier refactoring

[thimotedupuch]

Please do not force push this PR until I open another PR for JuliaRobotics/RoME.jl that adds compatibility with this branch.

So I continued making changes to the source code. I added JuliaGeometry/GeometryBasics for the 2D/3D vectors and points, instead of the custom types previously defined and exported.

I removed a lot of legacy code, that was here for compatibility purposes, which I understand, but is really worth removing.

At some point, we will need to delete Project.toml and Manifest.toml and regenerate them with Julia 1.12 or never. But I plan to remove Rotations and LoopVectorization dependencies before that.

All tests pass, but a lot of them are not very relevant, I'll have to work on that as well.

I am still not very familiar with the Lie algebra computations and the ArrayPartition type.

Finally I did some diagrams with Mathcha.io with is very convenient for this kind of visualization. The README.md file hasn't been updated for 2 years, a lot of things in it are no longer relevant (broken links, etc...).

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Thank you very much,
I know this PR might be difficult to review

[dehann]

HI @thimotedupuch ,

Thanks for the contributions, I did not see this PR until now - sorry!

I think we should merge as much of the clean up code as soon as we can.

Most of the discussion is likely to be around JuliaGeometry vs Manifold universe data representations. Cameras are naturally projective machines and therefore well suited to manifold based descriptions, albeit that is newer and less well know. Geometry basics might be better embedded in the Images.jl universe but we'd have to look at that closely.

My first reaction is to push closer to JuliaManifolds representation and functions, but that will mostly likely require some kind of shim to accomodate JuliaGeometry representations.

[thimotedupuch]

Thanks for the feedback! I had actually forgotten about this contribution myself. A few months ago, I had plenty of free time, but I started my PhD a few weeks back. I should be able to work on this during the weekends. I'll try to review what can be merged this coming weekend.

Regarding my background, my computer vision knowledge mostly comes from university courses and Szeliski’s book, which provide a more 'geometric' perspective on camera models and scenes.

However, I agree that approaching the problem from a manifold perspective would be best; it is mathematically consistent and would perhaps bring a novel element to this package compared to other tools of the CV ecosystem.

Thanks again!

Thimoté D.