{
  "abstract": "Regressing the 3D orientation of a symmetric object with a signed rotation representation is ill posed: the rotations that render an indistinguishable image form an equivalence class, so physically identical poses receive inconsistent labels. This is a common case in robotic manipulation, bin picking, and part feeding, where machined parts are routinely symmetric about an axis or a mirror plane. We extend the YOLO26 segmentation architecture with a rotation-regression branch whose target, building on Saxena et al., gives each sign-ambiguous axis its own outer product rather than a signed vector, and each directed axis a signed vector, so physically equivalent poses map to the same target of 6, 9, or 12 values instead of 9 to 39. The training data comes from a MuJoCo-based synthetic rendering pipeline with an on-the-fly composition loader that combines randomly posed, rotated part instances into each training image. We evaluate the outer-product representation against direct, signed regression on four part categories spanning axial and mirror-plane symmetry, testing both on held-out synthetic images and on 21 real, annotated MVTec ITODD instances, and additionally compare this grayscale-only system with the published SARR networks, including their depth-input variant, on the same real parts using the BOP ARB metric.",
  "abstract_shown": true,
  "affiliations": [
    "Faculty of Electrical Engineering and Computer Science, University of Maribor, Koroška cesta 46, SI-2000 Maribor, Slovenia"
  ],
  "article_type": null,
  "arxiv": null,
  "author_total": 2,
  "authors": [
    {
      "affs": [
        0
      ],
      "name": "Rok Pahič",
      "orcid": "0000-0003-0985-9439"
    },
    {
      "affs": [
        0
      ],
      "name": "Aleš Hace",
      "orcid": "0000-0003-4802-168X"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/ebymy9pn3qbth.bib",
  "cited_by": 0,
  "doi": "10.3390/math14214014",
  "fulltext_url": null,
  "id": "ebymy9pn3qbth",
  "issns": [
    "2227-7390"
  ],
  "landing_url": "https://www.mdpi.com/2227-7390/14/21/4014",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": null,
  "native_subjects": [],
  "openalex": null,
  "pdf_url": null,
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-03",
  "publisher": "MDPI AG",
  "ris": "https://research.draconitic.com/paper/ebymy9pn3qbth.ris",
  "sources": [
    {
      "first_seen": "2026-11-04T00:23:28Z",
      "native_id": "10.3390/math14214014",
      "source": "crossref",
      "url": "https://www.mdpi.com/2227-7390/14/21/4014"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "issn:2227-7390",
      "subfield": "general"
    }
  ],
  "title": "Symmetry-Aware Orientation Estimation via Outer-Product Rotation Targets in YOLO26",
  "title_text": "Symmetry-Aware Orientation Estimation via Outer-Product Rotation Targets in YOLO26",
  "type": "peer-reviewed",
  "updated_at": "2026-11-05T00:20:49Z",
  "url": "https://research.draconitic.com/paper/ebymy9pn3qbth",
  "venue": "Mathematics",
  "versions": []
}