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

Key points

• Rubix solves the equally weighted planar problem globally under squared Euclidean loss.1
• Each matching $σ$ of two centered $n$-point sets defines a complex correlation $zσ=\sumi\bar xi y{σ(i)}$.1
• We prove the sharp bound of $n(n-1)$ vertices for $n\ge2$, answering Rote's rotation-assignment open problem.1
• Assignment-based bounds extend the approach to three-dimensional rotations and partial matching at a supplied translation through branch-and-bound.1

Sources (1)

• [1]Rubix: Global Correspondence-Free Point Set Alignment through Assignment Geometry
  arXiv (AI, ML, NLP, CV, robotics, multi-agent) · Oct 7, 04:55 PM

  Procrustes-Wasserstein alignment jointly estimates a matching and rotation without supplied correspondences, but alternating minimization can stop at suboptimal solutions.

  Rubix solves the equally weighted planar problem globally under squared Euclidean loss.

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