How to extend the registration pipelines

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Checklist

• I have searched for similar issues.
• For Python issues, I have tested with the latest development wheel.
• I have checked the release documentation and the latest documentation (for main branch).

My Question

Hi,
I worked around this issue for a while, but I think I want to give it a try. I would love to be able to customize the registration pipelines in the open3d library (which I think are amazing and a very good point for using this library over others).

Idea

I want to change the registration so that it can be constrained (or the objective can be extended, but this could be a later step).
Personally, I am working with python and I am less proficient in C++, so I would love to be able to do this through the python bindings API without changing and writing C++ code. Once everything works, we can see how to translate/port it. I am willing to work on this.

Long Version

Background/Issues Check

I am also aware of these issues:

• [Feature request] Registration with constraints #409
  This is the most similar. The registration by constraining the rotation. Although the end of that discussion is that there is one implementation (this commit from this fork), it seems limited to setting the z-axis to zero, and it would be nice to be able to have some freedom on the constraints.
• How to set contraint on transformation matrix? Issue #5935
  This one is about stitching point cloud, so it is still a similar problem (constrained transformation), but did not reach any point
• Activate ICP on a subset of points based on a condition on angle between local normals of two point clouds for ICP, Issue #3139
  This is also interesting, as it would need a different constraint, pushing for a more flexible solution (not just setting some values to 0)
• How to stitch point clouds with no overlap? Issue #6995
  Again, in this case with static sensor it was solved, but could be seen as part of the same problem.

Question

So, to my question. Mostly, I thought about how to do it, and wanted to understand if I am in the right direction.

Checking the documentation, I see that a registration (for example, registration_icp) relies on a TransformationEstimation, which could be extended/customized. The TransformationEstimation only needs to implement 3 methods (__init__, compute_rmse and compute_transformation) as far as I understand, so it seems doable.

If I would just create a ConstrainedTransformationEstimation which accepts one axis as a parameter, and just ignore that axis (when doing compute_transformation, just use the other two axis?), would that be enough to actually perform a 2D registration on a pointcloud?
Should I use the pipelines as a reference, for example the doppler-icp-registration.py?

I am a bit afraid that the correspondences may cause some issues if the correct transformation would need the third dimension. But to me changing the TransformationEstimation seems the way to go (as it is changed between the standard ICP and the colored ICP for example in the tutorial).

Apart from this, I am not understanding where exactly the correspondences (point 1 of Understanding-ICP-Algorithm) are calculated (in each iteration of the ICP), could you point me out (so that can also be changed).

TL;DR

1. If I would just create a ConstrainedTransformationEstimation (extending TransformationEstimation) which accepts one axis as a parameter, and just ignore that axis (when doing compute_transformation, just use the other two axis?), would that be enough to actually perform a 2D registration on a pointcloud?
   Should I use the pipelines as a reference, for example the doppler-icp-registration.py?
2. could you point me out where exactly the correspondences are calculated (in each iteration of the ICP)