{
  "abstract": "Registration maps propagate labels, measure local volume change, and map results back through their inverses; requiring invertibility. Voxelwise checks can miss folds between grid points. We study the canonical continuous extension of a nodal displacement field by trilinear interpolation and give a test that proves its Jacobian determinant positive in every grid cell or rejects the map. The test is rigorous under IEEE 754 binary64 arithmetic (correct rounding, no contraction). With a fixed boundary, certification implies a bi-Lipschitz homeomorphism of the image domain. We introduce SeqVP, built around this certificate. A proximal Jacobian-determinant-curl formulation yields inner problems whose penalties on changes in the map, Jacobian determinant, and curl vanish to first order at the current iterate. The method decreases a fixed outer energy up to a floating-point resolution guard and certifies every committed iterate. After certified initialization, stopping at any time returns a folding-free map. A Poisson-preconditioned gradient method with Jacobian-aware step prediction and affine-scaling damping, initialized by certified handoff from an uncertified binary32 pre-optimizer, handles a 1 mm brain MRI with about 2e7 unknowns in 90 s on one GPU. On 49 held-out OASIS pairs, SeqVP achieves mean Dice 0.821 over 35 structures and 0.889 over 4 tissue classes, with certified zero folding. Gains are 0.022 and 0.025 over ANTs SyN, and 0.022 and 0.023 over uniGradICON with instance optimization at equal time (paired, Holm-adjusted p < 0.001), but maps are rougher. SeqVP is level with ANTs on LPBA40, behind it on IBSR18, and ahead of all label-free baselines on 20 large-deformation pairs. On fields from nine methods, the certificate finds non-positive-Jacobian cells in every ANTs SyN map (median 10, missed by voxelwise checks) and in maps from NiftyReg, ConvexAdam, uniGradICON, and TransMorph.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.06954",
  "author_total": 3,
  "authors": [
    {
      "name": "Baihan Zhao"
    },
    {
      "name": "Zicong Zhou"
    },
    {
      "name": "Guojun Liao"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/0n9gzczcr2d25.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.06954",
  "fulltext_url": null,
  "id": "0n9gzczcr2d25",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.06954",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.GR"
    ],
    [
      "arxiv",
      "math.AP"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.06954",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-03",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/0n9gzczcr2d25.ris",
  "sources": [
    {
      "first_seen": "2026-11-06T18:21:34Z",
      "native_id": "2611.06954",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.06954"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Certified folding-free deformable image registration: A whole-cell Jacobian certificate and a sequential variational solver",
  "title_text": "Certified folding-free deformable image registration: A whole-cell Jacobian certificate and a sequential variational solver",
  "type": "preprint",
  "updated_at": "2026-11-09T00:20:47Z",
  "url": "https://research.draconitic.com/paper/0n9gzczcr2d25",
  "venue": "arXiv",
  "versions": []
}