PreprintarXiv licencearXiv
Fast rigid rotational alignment of voxelized 3-D density maps in sliced Wasserstein distance
Abstract
We develop a fast method for the rigid alignment of voxelized three-dimensional density functions over SO(3) using sliced optimal transport. Our approach efficiently transforms each density map into a tensor of one-dimensional quantile functions, taken from central slices over the unit sphere, such that the Euclidean distance of the transformed volumes approximates the sliced 2-Wasserstein distance. Our formulation is therefore compatible with existing, fast, voxel-based Euclidean alignment algorithms. We provide theoretical analysis and numerical experiments demonstrating that the sliced 2-Wasserstein distance is a robust metric for comparing three-dimensional shapes and for computing their rigid alignment.
Related
- The p-Bures-Wasserstein distance via 3×3 block matrices (with application to p-Bures-Wasserstein barycenters)
- Relations between different definitions of the quantum Wasserstein distance
- λ-geodesic convexity of the squared sliced-Wasserstein distance
- Martingale central limit theorems in p-Wasserstein distance
- Degenerate McKean--Vlasov SDE with Yamada--Osgood Coefficients and Arbitrary Modulus of Continuity in Wasserstein Distance
BibTeX
@misc{mickelin2026fast,
title = {{Fast rigid rotational alignment of voxelized 3-D density maps in sliced Wasserstein distance}},
author = {Oscar Mickelin and Yunpeng Shi and Amit Singer and Eric J. Verbeke},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.39214},
eprint = {2610.39214},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.39214},
}
RIS
TY - UNPB
TI - Fast rigid rotational alignment of voxelized 3-D density maps in sliced Wasserstein distance
AU - Oscar Mickelin
AU - Yunpeng Shi
AU - Amit Singer
AU - Eric J. Verbeke
PY - 2026
DA - 2026/10/29
PB - arXiv
DO - 10.48550/arxiv.2610.39214
UR - https://arxiv.org/abs/2610.39214
AB - We develop a fast method for the rigid alignment of voxelized three-dimensional density functions over SO(3) using sliced optimal transport. Our approach efficiently transforms each density map into a tensor of one-dimensional quantile functions, taken from central slices over the unit sphere, such that the Euclidean distance of the transformed volumes approximates the sliced 2-Wasserstein distance. Our formulation is therefore compatible with existing, fast, voxel-based Euclidean alignment algorithms. We provide theoretical analysis and numerical experiments demonstrating that the sliced 2-Wasserstein distance is a robust metric for comparing three-dimensional shapes and for computing their rigid alignment.
ER -