[cola1917]

Type

• Bug fix (non-breaking change which fixes an issue): Fixes Wrong check for identity transformation as a result of registration #6153

Motivation and Context

A rigid transformation's trace depends on rotation, not translation. The existing trace() == 4.0 check rejects successful pure-translation registrations. Replacing it with an exact identity comparison would still reject valid identity alignments.

Description / plan summary

The goal is to distinguish missing correspondences from a valid zero-rotation alignment without changing registration algorithms, public APIs, or benchmark output formats.

• Use zero fitness to reject missing correspondences in fragment registration, retaining the existing information-matrix overlap threshold.
• Use positive fitness for the RANSAC benchmark's alignment selection.
• Remove the unused trace-based success variable in the FGR benchmark, preserving its existing unconditional recording behavior.
• Explain the acceptance rule in the reconstruction tutorial and add deterministic regression coverage for both registration routes.

Validation

Tested the current-main Python examples (base b6c5e196384ad71e75b6e6f9c5da22d046221f1d) on Linux, CPython 3.12.15, NumPy 2.5.4, and the official open3d-cpu==0.20.0 wheel. This was not a fresh C++ source build.

• New focused regressions: 10 failed / 20 passed before; 30 passed after. They evaluate real RegistrationResult objects from synthetic geometry and inject the results into example decision paths to avoid stochastic matching obscuring the acceptance check.
• python -m pytest python/test/pipelines -q: 36 passed.
• Additional smoke validation with actual CPU FGR and RANSAC optimizers (not mocked): identity, translation, and rotation on 32 synthetic points with known matching descriptors, 6/6 passed, maximum transform error below 6e-16. Four valid results had trace exactly four and were rejected by the old check. This does not benchmark FPFH matching quality.
• Repository changed-file style check, compileall, and git diff --check passed.

No GPU run, full C++ build, full test suite, real-data reconstruction, or complete documentation build was performed.

Checklist

• Applied repository code style with the pinned tools and checked changed files.
• Updated Python example behavior and the corresponding tutorial. No C++ API changes.
• Added Python regression tests and included test evidence above.
• I will follow up and update the code if CI fails.
• Allow edits from maintainers.

AI assistance was used for implementation and validation; the commands and results reported above were executed locally.

[update-docs]

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