{
  "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.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.39214",
  "author_total": 4,
  "authors": [
    {
      "name": "Oscar Mickelin"
    },
    {
      "name": "Yunpeng Shi"
    },
    {
      "name": "Amit Singer"
    },
    {
      "name": "Eric J. Verbeke"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/60k2asqy5cab9.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.39214",
  "fulltext_url": null,
  "id": "60k2asqy5cab9",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.39214",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.CV"
    ],
    [
      "arxiv",
      "cs.NA"
    ],
    [
      "arxiv",
      "math.NA"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2610.39214",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/60k2asqy5cab9.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:36:32Z",
      "native_id": "2610.39214",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.39214"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NA",
      "subfield": "numerical-analysis"
    }
  ],
  "title": "Fast rigid rotational alignment of voxelized 3-D density maps in sliced Wasserstein distance",
  "title_text": "Fast rigid rotational alignment of voxelized 3-D density maps in sliced Wasserstein distance",
  "type": "preprint",
  "updated_at": "2026-11-01T12:20:50Z",
  "url": "https://research.draconitic.com/paper/60k2asqy5cab9",
  "venue": "arXiv",
  "versions": []
}