Registering Gaussian Splats Without the Point-Cloud Detour: Accuracy, Representation Semantics, and a Negative Result on Hypothesis-Stage Transfer

Abstract

Aligning two Gaussian splats of the same scene today requires either manual alignment in an editor or a detour through point clouds: export the Gaussian means, register those, and re-import a transform whose effect on anisotropy, opacity, and view-dependent color is left undefined. We built splatreg, an open pure-PyTorch library, to establish what registering splats natively actually requires, and this paper reports the result. First, accuracy costs nothing. A signed-distance field derived in closed form from the frozen target Gaussians, with a numerically audited Jacobian over SE(3) and Sim(3) and a Levenberg–Marquardt core under interchangeable seeds (FPFH, learned, zero-shot, global, maximal-clique), reaches 91.5% mean / 93.5% pooled registration recall on official 3DMatch and 72.5% / 74.4% on 3DLoMatch, matching the GeoTransformer local-to-global baseline it refines while adding Sim(3) scale and pose covariance; a drop-in zero-shot seed (BUFFER-X, ICCV 2025), which we ported to a modern CUDA stack, lifts a classical FPFH front-end from 0.630 to 0.962 registration recall on the official 3DMatch pairs and from 0.122 to 0.777 on 3DLoMatch through the identical refine; against the existing splat tools it is 2.9× more accurate in rotation (5.2◦ vs 15.3◦) and improves merge Chamfer 5.1× over naive concatenation. Second, the genuinely new work is semantic, not numeric. A splat is not closed under rigid motion the way a point cloud is: view-dependent color must be Wigner-rotated (real-basis SH rotation, verified to 2.4e-15; none of the splat tools we surveyed rotate SH), scale conventions must be normalized before fusion (mixed log/linear scales corrupt merges silently), and a baked transform must update means, quaternions, scales, and SH together. Each requirement is pinned by a released test, and we propose the checklist as the correctness bar for future splat registrars. Third, a negative result we did not expect. MAC, the maximal-clique estimator that lifts GeoTransformer by 3.7 and 3.9 recall points in its own evaluation, engages on 100% of pairs inside our pipeline yet moves both official splits by at most 4 pairs while costing 50% more runtime: native-voxel learned correspondences are already 60–80% inliers, and a residual-gated refine absorbs whatever seed differences remain. Fourth, an honest study of the pose covariance the library exposes: raw LM/Laplace covariance is grossly over-confident on real data (nominal-90% coverage 0.005) but split-conformal recalibration restores it at strong 𝑛 (0.900 / 0.905), and yet covariance-gated fusion is a second negative result — every uncertainty gate collapses to blanket abstention because the covariance does not rank registration failures (AUC 0.578, chance) while the LM residual does (AUC 0.773). We argue published hypothesis-stage gains should be presumed pipeline-conditional until re-measured, and we report the covariance as a calibratable diagnostic rather than a selective fusion signal. All numbers are reproducible from the released library and benchmarks.