Work

Fast rigid rotational alignment of voxelized 3-D density maps in sliced Wasserstein distance

Year: 2026

Type: preprint

Abstract: We develop a fast method for the rigid alignment of voxelized three-dimensional density functions over $\mathsf{SO}(3)$ 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.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2610.39214

Authors: Mickelin, Oscar, Shi, Yunpeng, Singer, Amit, Verbeke, Eric J.

Institutions: Tsinghua University, University of California, Davis, Princeton University, The University of Osaka Premium Research Institute for Human Metaverse Medicine, The University of Osaka

Language: English

Topic: Geometric Analysis and Curvature Flows

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: National Science Foundation, Defense Advanced Research Projects Agency, Air Force Office of Scientific Research

Awards: Fast and Robust Algorithms in Cryo-Electron Microscopy Imaging, NSF-BSF: Theory, algorithms, and applications of estimation over groups, G4688056592

OpenAlex ID: W7224854127

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