Add CorrespondenceCheckerBasedOnRotation for orientation-constrained RANSAC

[jGiltinan]

Type

• Bug fix (non-breaking change which fixes an issue): Fixes #
• New feature (non-breaking change which adds functionality).
• Breaking change (fix or feature that would cause existing functionality to not work as expected) Resolves #

Motivation and Context

In structured environments, such as an overhead laser profiler mounted on an X-Y gantry or fixed above a conveyor belt, objects rest on an approximately flat surface. Their rotation about the Z-axis is unknown, but their orientation about the X and Y axes is physically constrained to within a small tolerance by gravity and the surface they rest on.

Existing Open3D correspondence checkers operate purely on local point geometry (edge lengths, point-to-point distance, surface normals). They have no mechanism to encode this kind of global orientation prior. As a result, RANSAC wastes iterations validating physically impossible, tilted or inverted orientations, and can become trapped in catastrophically wrong local minima, producing correct-looking local geometry fits that are globally flipped or upside-down which causes ICP to diverge.

Checklist:

• I have run python util/check_style.py --apply to apply Open3D code style
  to my code.
• This PR changes Open3D behavior or adds new functionality.
  • Both C++ (Doxygen) and Python (Sphinx / Google style) documentation is
    updated accordingly.
  • I have added or updated C++ and / or Python unit tests OR included test
    results (e.g. screenshots or numbers) here.
• I will follow up and update the code if CI fails.
• For fork PRs, I have selected Allow edits from maintainers.

Description

This PR introduces CorrespondenceCheckerBasedOnRotation, a new correspondence checker that allows developers to independently constrain the allowed rotation of a RANSAC hypothesis about any of the three Cartesian axes (X, Y, Z). Each axis is configured with a tolerance in radians. A value of -1 (the default) disables the check for that axis, making the checker flexible for a wide variety of structured scanning applications.
Example use:

checker = o3d.pipelines.registration.CorrespondenceCheckerBasedOnRotation(
   [np.pi * 10 / 180, # x-axis constrained to +/- 10 degrees
    np.pi * 10 / 180, # x-axis constrained to +/- 10 degrees
    1  # z-axis is unconstrained
    ]
)

The motivating case, along with sample results is summarized in a video: https://youtu.be/VuRbrNXATr8

For the benchmark results, the checker was tested on 3DBenchy registered against a synthetic laser scan, over 5 deterministic random seeds, single-threaded for determinism.

Configuration	Mean Total Time	Std Dev	Registration Failures
Current Open3D (EdgeLength + Distance + Normal)	139s	±157s	1 in 5
CorrespondenceCheckerBasedOnRotation only	603s	±55s	0 in 5
Combined (Rotation first, then EdgeLength + Distance + Normal)	90s	±19s	0 in 5

Key observations:

• Current checkers alone are fast per iteration but fail on symmetric/ambiguous geometry by converging to a physically impossible (inverted) alignment (Seed 43).
• The rotation checker alone is perfectly robust but slow, as it does not constrain translation, allowing RANSAC to waste expensive validation steps on bad-translation hypotheses.
• Combined, the rotation checker cheaply eliminates impossible global orientations early (fail-fast), and the vanilla checkers constrain local geometry. The result is both faster and perfectly robust across all seeds.

The code for the benchmark results is located at: https://github.com/jGiltinan/Open3D-Demonstrations

[update-docs]

Thanks for submitting this pull request! The maintainers of this repository would appreciate if you could update the CHANGELOG.md based on your changes.