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 means either a manual gizmo 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 nobody defines. We built splatreg, an open pure-PyTorch library, to find out what registering splats natively actually takes, and this paper reports the three things we learned. 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, 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; against the existing splat tools it is 2.9x more accurate in rotation (5.2 vs 15.3 degrees) and improves merge Chamfer 5.1x 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. MAC keeps a decisive edge exactly where its theory says it should, on contaminated correspondence sets (0.16 vs a 78 degree failure on a structured decoy). We argue published hypothesis-stage gains should be presumed pipeline-conditional until re-measured inside the receiving system. All numbers are reproducible from the released library and benchmarks: https://github.com/Archerkattri/splatreg