الملخص
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. Each matching $σ$ of two centered $n$-point sets defines a complex correlation $z_σ=\sum_i\bar x_i y_{σ(i)}$. Their convex hull is the permutation polygon: supporting vertices give optimal matchings at fixed rotations, and the farthest vertex gives the global alignment. We prove the sharp bound of $n(n-1)$ vertices for $n\ge2$, answering Rote's rotation-assignment open problem. In exact arithmetic, assignment queries recover the polygon in $\mathcal O(n^5)$ operations. Assignment-based bounds extend the approach to three-dimensional rotations and partial matching at a supplied translation through branch-and-bound. On timed MPEG-7 shape pairs, Rubix attains every numerical reference value in 12 ms on average, 50 times faster than a rotation grid at the same accuracy. Its distances improve gravity-aligned matching of real 3D scans, shape retrieval and noisy crystal classification over alternating minimization.
الكلمات المفتاحية
الموضوع
بيانات النشر
- المجلة
- غير متاح
- وصول مفتوح
- وصول مفتوح أخضر
اقتبس هذه المقالة
APA 7
Bhattacharjee, S. S., Campbell, D., & Shome, R. (2026). Rubix: Global Correspondence-Free Point Set Alignment through Assignment Geometry. https://omanscience.com/ar/articles/rubix-global-correspondence-free-point-set-alignment-through-assignment-geometry
MLA 9
Bhattacharjee, Subhransu S., et al. "Rubix: Global Correspondence-Free Point Set Alignment through Assignment Geometry." https://omanscience.com/ar/articles/rubix-global-correspondence-free-point-set-alignment-through-assignment-geometry.
شيكاغو (المؤلف–التاريخ)
Bhattacharjee, Subhransu S., Dylan Campbell, and Rahul Shome. 2026. "Rubix: Global Correspondence-Free Point Set Alignment through Assignment Geometry." https://omanscience.com/ar/articles/rubix-global-correspondence-free-point-set-alignment-through-assignment-geometry.
هارفارد
Bhattacharjee, S. S., Campbell, D. and Shome, R. (2026) 'Rubix: Global Correspondence-Free Point Set Alignment through Assignment Geometry', Available at: https://omanscience.com/ar/articles/rubix-global-correspondence-free-point-set-alignment-through-assignment-geometry.
فانكوفر
Bhattacharjee SS, Campbell D, Shome R. Rubix: Global Correspondence-Free Point Set Alignment through Assignment Geometry. https://omanscience.com/ar/articles/rubix-global-correspondence-free-point-set-alignment-through-assignment-geometry
IEEE
S. S. Bhattacharjee, D. Campbell, and R. Shome, "Rubix: Global Correspondence-Free Point Set Alignment through Assignment Geometry," https://omanscience.com/ar/articles/rubix-global-correspondence-free-point-set-alignment-through-assignment-geometry.