Rubix: Global Correspondence-Free Point Set Alignment through Assignment Geometry

arXiv:2610.10408 · cs.CV, cs.CG, cs.LG, cs.RO, math.OC · Submitted 2026-10-07 · Read on arXiv

cs.CV, cs.CG, cs.LG, cs.RO, math.OC

Submitted: 2026-10-07

Updated: 2026-10-07

Code: https://github.com/url-kaist/Quatro

Terminology

• Alignment — 55× in this paper · explained in 1 episode
• Accuracy — 36× in this paper · explained in 1 episode
• Core — 13× in this paper · explained in 2 episodes
• Clustering — 10× in this paper · explained in 2 episodes
• Pruning — 7× in this paper · explained in 4 episodes
• Verification — 6× in this paper · explained in 2 episodes
• APEX — 5× in this paper · explained in 1 episode
• Adaptation — 5× in this paper · explained in 1 episode
• Trace — 5× in this paper · explained in 2 episodes
• Alternating Minimization — 4× in this paper · explained in 1 episode
• Wasserstein Distance — 4× in this paper · explained in 4 episodes
• Alternation — 3× in this paper · explained in 1 episode
• Optimal Transport — 3× in this paper · explained in 5 episodes
• Point Clouds — 3× in this paper · explained in 2 episodes
• Embeddings — 2× in this paper · explained in 2 episodes
• Register Any Point — 2× in this paper
• 2-Wasserstein Distance — 1× in this paper · explained in 1 episode
• Adam — 1× in this paper · explained in 2 episodes
• Adaptive Selection — 1× in this paper · explained in 1 episode
• Calibration — 1× in this paper · explained in 7 episodes
• Decoupling — 1× in this paper · explained in 2 episodes
• Degeneracy — 1× in this paper · explained in 3 episodes
• Failure Modes — 1× in this paper · explained in 3 episodes
• Graph Construction — 1× in this paper · explained in 3 episodes
• International Conference on Computer Vision — 1× in this paper
• Regularization — 1× in this paper · explained in 3 episodes
• Riemannian optimization — 1× in this paper · explained in 2 episodes
• Robustness — 1× in this paper · explained in 5 episodes
• Transformer — 1× in this paper · explained in 2 episodes

Sources

• A Second-Order Lower Bound for Globally Optimal 2D Registration
• Fast globally optimal Truncated Least Squares point cloud registration with fixed rotation axis
• DC-Reg: Globally Optimal Point Cloud Registration via Tight Bounding with Difference of Convex Programming
• Beyond Procrustes distances: a multilinear Gromov-Wasserstein distance capturing chirality

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