isl-org / isl-org/Open3D

How to align points to another set of points with probabilities?

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Description

### Checklist

- [X] I have searched for [similar issues](https://github.com/isl-org/Open3D/issues).
- [X] For Python issues, I have tested with the [latest development wheel](http://www.open3d.org/docs/latest/getting_started.html#development-version-pip).
- [X] I have checked the [release documentation](http://www.open3d.org/docs/release/) and the [latest documentation](http://www.open3d.org/docs/latest/) (for `master` branch).

### My Question

The source set N has the shape of (n, 3), and the target set M has the shape of (m, 3). However, each point in the target set also has a probability assigned between [0, 1]. So there's an additional vector p with the shape of (m, 1).

I want to use a point-to-point alignment method in `open3d` to optimize $E(T)= \sum p(i)*\|\|m(i)-Corres_n(m(i))\|\|^{2}$. With `open3d.registration.registration_icp`, currently I already can optimize $E(T)= \sum \|\|m(i)-Corres_n(m(i))\|\|^{2}$, but I don't know how to incorporate probabilities or weights in the function.

Thank you for help in advance.

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