OSCR

Hyperelastic Regularization for Near-Diffeomorphic Transformer-Based Brain MRI Registration.

Code ↔ Paper

20 matches between paragraphs of the paper and lines of its authors' code, computed by the harvester (lexical-v1). Click a colored paragraph or line to see its counterpart.

The 20 matches
  1. [1] § 2. Materials and Methods › 2.1. Dataset and Preprocessing › 2.1.1. OASIS Cross-Cohort Protocols (Zero-Shot and In-Cohort Retraining) ↔ draft/build_drafts.py, lines 20–114 · score 0.85 · Benjamini Hochberg FDR, Learn2Reg, structural brain MRI, OASIS train, paired Wilcoxon, positive Jacobian ratio
  2. [2] § 3. Results › 3.4. IXI→OASIS Zero-Shot Cross-Cohort Generalization ↔ scripts/oasis_roi_analysis.py, lines 1–50 · score 0.84 · cortical ribbon, lateral ventricles, ROI Jacobian, paired Wilcoxon, zero shot, ROIs
  3. [3] § 2. Materials and Methods › 2.2. Baseline Models ↔ IXI/analysis_comprehensive/generate_submission_figures.py, lines 174–215 · score 0.79 · nnFormer, CycleMorph, CoTr, VoxelMorph, TransMorphBayes, PVT
  4. [4] § 2. Materials and Methods › 2.8. Statistical Analysis ↔ draft/build_drafts.py, lines 20–114 · score 0.78 · Benjamini Hochberg FDR, confidence intervals, paired Wilcoxon signed, positive Jacobian ratio, SDlogJ, rank
  5. [5] § 2. Materials and Methods › 2.8. Statistical Analysis ↔ scripts/bootstrap_ci.py, lines 1–43 · score 0.70 · confidence intervals, core models, bootstrap, TransMorphBayes, MIDIR, HypEReg
  6. [6] § 2. Materials and Methods › 2.3. Proposed HypEReg-TransMorph Framework ↔ draft/build_arxiv_tex.py, lines 1–70 · score 0.70 · implausible local, local volume change, hyperelastic regularization, suppression, TransMorph, HypEReg
  7. [7] § 2. Materials and Methods › 2.4. Loss Function › 2.4.1. Relation to the Burger–Modersitzki–Ruthotto (BMR) Hyperelastic Energy ↔ IXI/TransMorph/losses_her.py, lines 74–144 · score 0.69 · BMR length, surrogate, filled, Jacobian determinant, smoothness, components
  8. [8] § 3. Results › 3.5. Inference Efficiency › Cross-Model Training Cost ↔ IXI/analysis_comprehensive/generate_submission_figures.py, lines 174–215 · score 0.63 · CycleMorph, CoTr, VoxelMorph, TransMorphBayes, MIDIR, HypEReg
  9. [9] § 3. Results › 3.7. Downstream Multi-Atlas Segmentation on OASIS ↔ scripts/oasis_downstream.py, lines 1–47 · score 0.62 · majority voting, multi atlas, IDs, fusion, Downstream, OASIS
  10. [10] § 2. Materials and Methods › 2.1. Dataset and Preprocessing › 2.1.2. OASIS-2 Longitudinal Morphometry Protocol ↔ scripts/oasis_roi_analysis.py, lines 1–50 · score 0.60 · FreeSurfer, OASIS zero shot, anatomical, ROI, TransMorph, HypEReg
  11. [11] § 2. Materials and Methods › 2.1. Dataset and Preprocessing › 2.1.1. OASIS Cross-Cohort Protocols (Zero-Shot and In-Cohort Retraining) ↔ draft/build_arxiv_tex.py, lines 1–70 · score 0.60 · brain MRI, April, positive Jacobian, SDlogJ, protocol, style
  12. [12] § 3. Results › 3.7. Downstream Multi-Atlas Segmentation on OASIS ↔ figures/visualize_downstream_segmentation_bars.py, lines 48–110 · score 0.58 · fusion gain, fused Dice, thalamus, hippocampus, Downstream, ROI
  13. [13] § 3. Results › 3.8. Jacobian Morphometry Validation (OASIS-2 Longitudinal and ROI) › 3.8.3. Validation of the FastSurfer ROI Reference Trajectories ↔ IXI/analysis.py, lines 16–72 · score 0.56 · cerebral cortex, lateral ventricles, hippocampus
  14. [14] § 3. Results › 3.3. Design Rationale, Ablation Study, and Hyperparameter Sensitivity ↔ IXI/TransMorph/losses_her.py, lines 74–144 · score 0.53 · smoothness penalty, ablation, component, hyperelastic, Rationale, loss
  15. [15] § 3. Results › 3.5. Inference Efficiency ↔ IXI/profile_forward_runtime_memory.py, lines 32–67 · score 0.53 · peak memory, forward runtime, GB, profiling, CUDA, model
  16. [16] § 2. Materials and Methods › 2.5. Training Details ↔ IXI/Baseline_Transformers/train_CoTr.py, lines 27–166 · score 0.52 · weight decay, AMSGrad, Adam, pin, backward, batch
  17. [17] § 2. Materials and Methods › 2.5. Training Details ↔ IXI/Baseline_Transformers/train_PVT.py, lines 28–167 · score 0.52 · weight decay, AMSGrad, Adam, pin, backward, batch
  18. [18] § 2. Materials and Methods › 2.6. Evaluation Metrics ↔ IXI/analysis_comprehensive/run_inference.py, lines 271–317 · score 0.51 · bending energy, divergence, Jacobian determinant, VOI, space, ASSD
  19. [19] § 3. Results › 3.2. Deformation Regularity and Folding Suppression ↔ IXI/analysis_comprehensive/interim_completed_report.py, lines 166–279 · score 0.50 · ASSD mm, HD95 mm, sdlogJ, accuracy, metrics, Dice
  20. [20] § 2. Materials and Methods › 2.4. Loss Function › 2.4.1. Relation to the Burger–Modersitzki–Ruthotto (BMR) Hyperelastic Energy ↔ OASIS/surface_distance/metrics.py, lines 200–243 · score 0.50 · surface area, distance, bounded, correlated, voxels, volume

Paper

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The authors' code

Python · 126 lines · 8.3 KB · MIT · 2 matches

  1. from __future__ import annotations
  3. import re
  4. from pathlib import Path
  7. ROOT = Path(__file__).resolve().parents[1]
  8. DRAFT = ROOT / "draft"
  9. SRC = DRAFT / "template.tex"
  10. OUT_WITH_OASIS = DRAFT / "template_with_oasis.tex"
  11. OUT_IXI_ONLY = DRAFT / "template_ixi_only.tex"
  14. def _replace_once(text: str, old: str, new: str) -> str:
  15. if old not in text:
  16. raise ValueError(f"Expected snippet not found:\n{old[:120]}...")
  17. return text.replace(old, new, 1)
  20. def make_ixi_only(tex: str) -> str:
  21. # Abstract: keep IXI-focused summary only.
  22. abstract_ixi = (
  23. r"\abstract{Background: Deformable brain MRI registration requires preserving deformation topology in addition to overlap accuracy. "
  24. r"Methods: HypEReg-TransMorph augments a TransMorph backbone with hyperelastic regularization terms targeting volume-change moderation and anti-folding control. "
  25. r"We evaluate the method on the IXI atlas-to-subject protocol against learning-based and classical baselines, and report paired Wilcoxon signed-rank tests with Benjamini--Hochberg FDR correction where available. "
  26. r"Results: HypEReg-TransMorph maintains competitive overlap (Dice: 0.7537 \(\pm\) 0.0275) while reducing topology violations (non-positive Jacobian ratio: 0.0000 vs.\ 0.0153 for TransMorph) and improving Jacobian regularity (SDlogJ: 0.3280 vs.\ 0.4920). "
  27. r"Conclusions: HypEReg-TransMorph yields topology-preserving deformations on IXI, supporting downstream Jacobian-based morphometric analysis.}"
  28. )
  29. tex = re.sub(
  30. r"\\abstract\{Background:.*?analysis\.\}",
  31. lambda _m: abstract_ixi,
  32. tex,
  33. count=1,
  34. flags=re.S,
  35. )
  37. # Contribution bullet: remove OASIS statement.
  38. tex = _replace_once(
  39. tex,
  40. r"\item Subject-level paired statistical validation (Wilcoxon + BH-FDR), with dual-protocol evaluation across IXI and OASIS (\PH{OASIS stats pending Stage B}), to test robustness of topology-preserving behavior.",
  41. r"\item Subject-level paired statistical validation (Wilcoxon + BH-FDR) on the unified IXI protocol to test robustness of topology-preserving behavior.",
  42. )
  44. # Remove OASIS dataset paragraph in Methods.
  45. tex = re.sub(
  46. r"\nTo assess generalization beyond IXI atlas-to-subject, we additionally evaluate on OASIS.*?atlas-to-subject evaluation\.\n",
  47. "\n",
  48. tex,
  49. count=1,
  50. flags=re.S,
  51. )
  53. # Results text: remove OASIS table reference.
  54. tex = _replace_once(
  55. tex,
  56. r"Table~\ref{tab2} reports the compact IXI model comparison, now expanded to include overlap and regularity metrics in one place. HypEReg-TransMorph maintains competitive overlap while improving deformation regularity relative to unconstrained Transformer baselines. Table~\ref{tab_oasis} mirrors the same panel for OASIS and is currently presented with explicit placeholders pending Stage-B OASIS training/inference completion.",
  57. r"Table~\ref{tab2} reports the compact IXI model comparison, expanded to include overlap and regularity metrics in one place. HypEReg-TransMorph maintains competitive overlap while improving deformation regularity relative to unconstrained Transformer baselines.",
  58. )
  60. # Remove full OASIS table block.
  61. tex = re.sub(
  62. r"\n\\begin\{table\}\[H\]\n\\caption\{OASIS.*?\\end\{table\}\n",
  63. "\n",
  64. tex,
  65. count=1,
  66. flags=re.S,
  67. )
  69. # Figure captions / TODOs mentioning OASIS.
  70. tex = _replace_once(
  71. tex,
  72. r"\caption{Qualitative registration comparisons on representative IXI and OASIS subjects. \PH{figure regenerated in Stage B from saved deformation fields}.\label{fig2}}",
  73. r"\caption{Qualitative registration comparisons on representative IXI subjects. \PH{figure regenerated in Stage B from saved deformation fields}.\label{fig2}}",
  74. )
  75. tex = _replace_once(
  76. tex,
  77. r"% TODO Stage B: regenerate with IXI+OASIS dual panel metrics.",
  78. r"% TODO Stage B: regenerate with IXI panel metrics.",
  79. )
  80. tex = _replace_once(
  81. tex,
  82. r"\caption{Consolidated metric overview across selected methods (Dice, non\_jac, SDlogJ, bending energy, and runtime). \PH{figure regenerated in Stage B from IXI+OASIS panel data}.\label{fig5}}",
  83. r"\caption{Consolidated metric overview across selected methods (Dice, non\_jac, SDlogJ, bending energy, and runtime). \PH{figure regenerated in Stage B from IXI panel data}.\label{fig5}}",
  84. )
  86. # Discussion / limitations: remove OASIS-specific paragraphs and wording.
  87. tex = _replace_once(
  88. tex,
  89. r"The CNN/B-spline baseline MIDIR also achieves zero non-positive Jacobian ratio on IXI, with SDlogJ (0.3148) marginally lower than HypEReg-TransMorph (0.3280). The two methods reach comparable regularity through different routes: MIDIR enforces smoothness implicitly via B-spline parameterization, while HypEReg-TransMorph enforces regularity explicitly through differentiable hyperelastic penalties on dense flow. HypEReg is plug-in to dense-flow backbones without changing parameterization, and preserves overlap expressivity (Dice 0.7537 vs.\ 0.7423 for MIDIR on IXI). Cross-dataset evidence on OASIS is summarized as \PH{OASIS MIDIR-vs-HypEReg discussion pending Stage B}.",
  90. r"The CNN/B-spline baseline MIDIR also achieves zero non-positive Jacobian ratio on IXI, with SDlogJ (0.3148) marginally lower than HypEReg-TransMorph (0.3280). The two methods reach comparable regularity through different routes: MIDIR enforces smoothness implicitly via B-spline parameterization, while HypEReg-TransMorph enforces regularity explicitly through differentiable hyperelastic penalties on dense flow. HypEReg is plug-in to dense-flow backbones without changing parameterization, and preserves overlap expressivity (Dice 0.7537 vs.\ 0.7423 for MIDIR on IXI).",
  91. )
  92. tex = re.sub(
  93. r"\nThe OASIS inter-subject regime produces larger anatomical displacements.*?hyperelastic-regularization mechanism\.\n",
  94. "\n",
  95. tex,
  96. count=1,
  97. flags=re.S,
  98. )
  99. tex = _replace_once(
  100. tex,
  101. r"Several limitations should be acknowledged. First, this manuscript retains a single training seed; multi-seed confidence intervals are future work. Second, a per-term ablation isolating \(\mathcal{L}_{\mathrm{length}}\), \(\mathcal{L}_{\mathrm{volume}}\), and \(\mathcal{L}_{\mathrm{fold}}\) was not rerun under the final operating-point pipeline; instead, cross-dataset OASIS validation is used as the main generalization check. Third, although IXI and OASIS cover two protocols, the study is still limited to structural brain MRI and does not yet include pathology-rich or multi-modal settings. Fourth, sensitivity sweeps for \(\beta\) and \(\gamma\) were not performed, and \(\alpha=0\) is a deliberate operating-point choice. Fifth, software-stack reproducibility against a stable PyTorch release is tracked as \PH{stable-PyTorch verification pending Stage B}.",
  102. r"Several limitations should be acknowledged. First, this manuscript retains a single training seed; multi-seed confidence intervals are future work. Second, a per-term ablation isolating \(\mathcal{L}_{\mathrm{length}}\), \(\mathcal{L}_{\mathrm{volume}}\), and \(\mathcal{L}_{\mathrm{fold}}\) was not rerun under the final operating-point pipeline. Third, the study is currently limited to structural brain MRI and does not yet include pathology-rich or multi-modal settings. Fourth, sensitivity sweeps for \(\beta\) and \(\gamma\) were not performed, and \(\alpha=0\) is a deliberate operating-point choice. Fifth, software-stack reproducibility against a stable PyTorch release is tracked as \PH{stable-PyTorch verification pending Stage B}.",
  103. )
  105. # Guardrail: no OASIS/Learn2Reg/table ref remains.
  106. forbidden = [r"\bOASIS\b", r"\boasis\b", r"Learn2Reg", r"tab_oasis"]
  107. for pat in forbidden:
  108. m = re.search(pat, tex)
  109. if m:
  110. ctx = tex[max(0, m.start() - 120) : min(len(tex), m.end() + 120)]
  111. raise ValueError(
  112. f"Found forbidden pattern in IXI-only draft: {pat}\nContext:\n{ctx}"
  113. )
  114. return tex
  117. def main() -> None:
  118. source = SRC.read_text(encoding="utf-8")
  119. OUT_WITH_OASIS.write_text(source, encoding="utf-8")
  120. OUT_IXI_ONLY.write_text(make_ixi_only(source), encoding="utf-8")
  121. print(f"Wrote: {OUT_WITH_OASIS}")
  122. print(f"Wrote: {OUT_IXI_ONLY}")
  125. if __name__ == "__main__":
  126. main()

build_drafts.py at commit c63392e, under MIT · at the source

Overview

Authors: Shiyi Xu1, Mohan Xu2, Erjin Zhou3
ORCID iDs: Shiyi Xu, Mohan Xu, Erjin Zhou
  1. Capital Medical University Second Clinical School, Capital Medical University, Beijing 100050, China
  2. School of Physics, Peking University, Beijing 100871, China
  3. Dexmal, Beijing 100096, China
Institutions: Capital Medical University (China); Peking University (China)
Journal: Journal of imaging, volume 12, issue 7, article 276
Dates: received 10 May 2026; accepted 16 June 2026; published online 24 June 2026
Type: Research article · Language: English
License: CC BY
Identifiers: DOI 10.3390/jimaging12070276 · PMID 42506122 · PMCID PMC13413009 · OpenAlex W7165811961
Open access: gold, a free copy (OpenAlex)
Status: code verified
Categories: structural MRI / diffusion (modality), methods / tools (subfield)
Methods: Connectivity, Statistics, Machine learning, fMRI & imaging
Keywords: deformable image registration, brain MRI, TransMorph, Jacobian determinant, Jacobian-aware regularization, hyperelastic regularization, folding suppression, diffeomorphic registration
Topic: Medical Image Segmentation Techniques (Computer Vision and Pattern Recognition, Computer Science), according to OpenAlex
Funding: NIMH NIH HHS (P50 MH071616); NIA NIH HHS (P01 AG003991, P50 AG005681, R01 AG021910); NCRR NIH HHS (U24 RR021382)
Citations: cited by 1 paper (Europe PMC); 43 references in the paper

Abstract

Transformer-based deformable brain MRI registration achieves high overlap accuracy, but predicted displacement fields can contain voxels with a non-positive Jacobian determinant—local foldings that violate the diffeomorphism assumption required by tensor-based morphometry and atlas-fusion segmentation workflows. We introduce HypEReg, a non-linear hyperelastic regularizer that acts directly on the Jacobian determinant of the predicted displacement field. HypEReg couples a clamped-rational volume-distortion penalty (detJϕ−1)2/max(detJϕ,ϵ) with an explicit per-voxel anti-folding hinge [max(0,ϵ−detJϕ)]2, integrated as a purely loss-side module into a TransMorph backbone with no inference-graph modifications. On the IXI atlas-to-subject benchmark (115 test subjects), HypEReg-TransMorph maintains grouped Dice (0.7537) while reducing the det(Jϕ)≤0 voxel ratio from 1.502×10−2 (TransMorph) to 1.5×10−5, with identical per-case runtime and parameter count to the unregularized baseline. In strict zero-shot transfer to OASIS Learn2Reg test pairs (no fine-tuning), HypEReg-TransMorph achieves Dice 0.7756 with a det(Jϕ)≤0 ratio of 7.6×10−5, roughly two orders of magnitude below plain TransMorph zero-shot (Dice 0.7691; ratio 9.6×10−3); downstream multi-atlas label fusion further confirms the practical benefit of fold suppression (fused Dice 0.8271 vs. 0.8201 for TransMorph). OASIS-2 longitudinal and ROI analyses support deformation plausibility (lower folding/SDlogJ and stronger ventricular ROI agreement), while clinical-covariate associations remain exploratory rather than biomarker-validating. Determinant-level, non-linear hyperelastic regularization substantially suppresses folding in Transformer dense-flow brain MRI registration while preserving alignment accuracy and adding zero inference cost, providing a practical drop-in regularization strategy that improves the reliability of deformation fields for morphometry-oriented deformable registration.

Reproduced under the paper's license (CC BY), from the paper cited above.

Repositories

Its files are read in the Code ↔ Paper reader above, with 20 matches between paragraphs and lines of code.

Zzxmh/HypEReg-TransMorph

License: MIT
State: the link answers, verified on 27 September 2026
Evidence: files inventoried
Commit: c63392e925fc533429e811d86b2c5c22f3d85e21, 11 May 2026
Languages: Python (277), Shell (8)
Size: 502 files, 285 scripts
Software Heritage: not archived
Found in: “Data Availability Statement”
Holds: README, license file, environment (requirements-stable.txt, requirements.txt, IXI/requirements-ixi-eval.txt, Docker/TransMorph_build_Docker/Dockerfile, Docker/TransMorph_build_Docker/requirements.txt), documentation
Not found: CITATION.cff, tests, continuous integration
Tools: PyTorch (173 files), NumPy (157 files), Matplotlib (60 files), SciPy (47 files), pandas (12 files), scikit-image (12 files), NiBabel (11 files), nnU-Net (7 files), ANTs (5 files), scikit-learn (2 files), Pillow (1 file), SimpleITK (1 file)
Availability: 1 check, the latest on 27 September 2026: the link answers
  • 27 September 2026: the link answers
287 files
At the source: github.com/Zzxmh/HypEReg-TransMorph

Zenodo 19888526

License: MIT
State: the link answers, verified on 27 September 2026
Evidence: files inventoried
Size: 1 file
Software Heritage: not checked
Found in: “Data Availability Statement”
Not found: README, license file, CITATION.cff, environment file, tests, continuous integration, documentation
Availability: 1 check, the latest on 27 September 2026: the link answers (HTTP 200)
  • 27 September 2026: the link answers (HTTP 200)
At the source: doi.org/10.5281/zenodo.19888526

Zenodo 20113717

License: MIT
State: the link answers, verified on 27 September 2026
Evidence: files inventoried
Size: 1 file
Software Heritage: not checked
Found in: the references
Not found: README, license file, CITATION.cff, environment file, tests, continuous integration, documentation
Availability: 1 check, the latest on 27 September 2026: the link answers (HTTP 200)
  • 27 September 2026: the link answers (HTTP 200)
At the source: zenodo.org/records/20113717

The paper's code and data availability statement is in the Data section.

Tracing map

Proposed by the machine: these links were found in the paper and verified at the source, without human review. The map will receive a Zenodo DOI once one of the paper's authors has validated it with their ORCID.

What the map holds:

  • 3 repositories of the authors' code, each at its verified commit, with its license and how the link was found in the paper;
  • 285 scripts, each with its path and the digest of its content;
  • 20 matches between paragraphs of the paper and lines of the code (method lexical-v1);
  • neither the text of the paper nor the code itself.

Its JSON (tracing-map.json) is deposited on Zenodo with its DOI once the map is validated.

Data

No dataset and no data link were found in the paper.

Data Availability Statement

The data presented in this study are available in IXI at https://brain-development.org/ixi-dataset/(CC BY-SA 3.0) (accessed on 6 April 2026) and the preprocessed split follows the public TransMorph-style IXI preprocessing release. OASIS/OASIS-2 imaging data are available through the Open Access Series of Imaging Studies portal (https://www.oasis-brains.org/) (accessed on 11 April 2026) under the corresponding OASIS data-use terms; the OASIS cross-subject benchmark definitions and splits follow the Learn2Reg challenge materials [22]. Source code, configuration files, per-case metric tables, and figure/statistics scripts are openly available at https://github.com/Zzxmh/HypEReg-TransMorph (accessed on 16 April 2026) and archived at Zenodo: https://doi.org/10.5281/zenodo.19888526 [43]. Trained model weights are available from the corresponding author upon reasonable request.

Reproduced under the paper's license (CC BY), from the paper cited above.

Versions

The history of this record: each version stored by the harvester or made by a correction of its authors or of the maintainers of its code, and what changed in its facts. The texts of the paper (its abstract, its availability statements) are not part of it; versions that changed only those are not listed.

Version 1, 27 September 2026: the first record

Recorded: type, language, journal, volume, issue, pages, dates, 3 authors, 8 keywords, 3 funders, 34 references.

Cite

This paper

Xu, S., Xu, M., & Zhou, E. (2026). Hyperelastic Regularization for Near-Diffeomorphic Transformer-Based Brain MRI Registration. Journal of imaging, 12(7), 276. https://doi.org/10.3390/jimaging12070276

BibTeX

@article{xu2026hyperelastic,
author = {Xu, Shiyi and Xu, Mohan and Zhou, Erjin},
title = {{Hyperelastic Regularization for Near-Diffeomorphic Transformer-Based Brain MRI Registration}},
journal = {Journal of imaging},
year = {2026},
month = jun,
volume = {12},
number = {7},
pages = {276},
publisher = {Multidisciplinary Digital Publishing Institute (MDPI)},
issn = {2313-433X},
doi = {10.3390/jimaging12070276},
url = {https://doi.org/10.3390/jimaging12070276},
pmid = {42506122},
pmcid = {PMC13413009}
}

RIS

TY - JOUR
AU - Xu, Shiyi
AU - Xu, Mohan
AU - Zhou, Erjin
TI - Hyperelastic Regularization for Near-Diffeomorphic Transformer-Based Brain MRI Registration
T2 - Journal of imaging
J2 - J Imaging
PY - 2026
DA - 2026/06/24
VL - 12
IS - 7
SP - 276
SN - 2313-433X
PB - Multidisciplinary Digital Publishing Institute (MDPI)
DO - 10.3390/jimaging12070276
UR - https://doi.org/10.3390/jimaging12070276
LA - en
ER -

CSL-JSON

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"type": "article-journal",
"title": "Hyperelastic Regularization for Near-Diffeomorphic Transformer-Based Brain MRI Registration",
"container-title": "Journal of imaging",
"author": [
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"container-title-short": "J Imaging",
"volume": "12",
"issue": "7",
"page": "276",
"DOI": "10.3390/jimaging12070276",
"PMID": "42506122",
"PMCID": "PMC13413009",
"ISSN": "2313-433X",
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"language": "en",
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"date-parts": [
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]
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The tracing map gets a citation of its own once an author has validated it and it has a DOI.

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