{
  "abstract": "For configurations of landmarks reconstructed from camera images, classical projective shape analysis identifies antipodal spherical representatives of projective coordinates, while oriented projective shape (OPS) retains their distinction. In 3D, a fixed oriented-projective coordinate representation of a OPS is point on product of 3D spheres. We develop nonparametric multisample inference for equality of population extrinsic means on this product. Quaternion multiplication helps create a global orthonormal tangent frame field, in which we obtain explicit extrinsic covariance blocks that preserve dependence between registered landmarks. A covariance-weighted MANOVA statistic has a chi-square null limit under nonfocality of distributions and positive-definite extrinsic covariance assumptions. An inverse-free discrepancy has a weighted chi-square limit when covariance matrices may be singular, and centered, groupwise nonparametric bootstrap procedures are justified asymptotically. We apply a fixed-observed-covariance nonparametric bootstrap version of the weighted statistic to 31 seven-landmark facial reconstructions from five subjects. Separate tests at the right inner brow and chin reject equality of the five OPS mean directions after Bonferroni adjustment. The analysis concerns a common mixed-sign frame domain and marginal landmarks; it does not establish pairwise subject differences or a joint six-dimensional facial test.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.24021",
  "author_total": 3,
  "authors": [
    {
      "name": "Musab Alamoudi"
    },
    {
      "name": "Robert L. Paige"
    },
    {
      "name": "Victor Patrangenaru"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/c2g3w4zp2a0ag.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.24021",
  "fulltext_url": null,
  "id": "c2g3w4zp2a0ag",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.24021",
  "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",
      "stat.ME"
    ],
    [
      "arxiv",
      "stat.OT"
    ],
    [
      "openalex",
      "2608|Morphological variations and asymmetry"
    ]
  ],
  "openalex": "W7223005078",
  "pdf_url": "https://arxiv.org/pdf/2610.24021",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-16",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/c2g3w4zp2a0ag.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:33:54Z",
      "native_id": "2610.24021",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.24021"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:stat.ME",
      "subfield": "statistics"
    }
  ],
  "title": "Extrinsic MANOVA for Oriented Projective Shapes",
  "title_text": "Extrinsic MANOVA for Oriented Projective Shapes",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:54Z",
  "url": "https://research.draconitic.com/paper/c2g3w4zp2a0ag",
  "venue": "arXiv",
  "versions": []
}