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From Pixel Generation to Topological Inference: Structural Dual Super-Resolution for Trustworthy Cross-Physical-Domain Trabecular Morphology Learning

Fan Zhang, Yi Zhang, Ling Wang

arXiv:2609.34716v2cs.CV

TL;DR

Clinical CT and UHRCT cannot resolve individual trabeculae, and their physical differences and coarse pairing challenge pixel-based super-resolution. SDN couples forward physical degradation with inverse structural inference to estimate shared morphology; its estimates largely match SRµCT across seven morphological metrics, with reported generalization across sources.

  • Problem

    Clinical CT and UHRCT at 100 µm cannot resolve individual trabeculae, while 3.2 µm SRµCT provides high-resolution references but is not applicable for in vivo imaging.

    Source: §1 · p. 2

  • Method

    SDN couples forward physical degradation with inverse structural inference through structural duality constraints, targeting invariant morphology rather than freely generated details.

    Source: §1 · pp. 2–3

  • Results

    SDN's morphological parameters largely match SRµCT across seven metrics, with SSIM reaching 0.8, and the model generalizes from 3.2 µm SSRF to independent 3.25 µm isotropic BSRF data.

    Source: §4.3 · p. 8, §5 · p. 10

  • Takeaways & Limitations

    The reported cross-source results support structural inference of trabecular morphology rather than pixel generation.

    Source: §5 · p. 10

    Under 32× downsampling, slight Tb.Th and Tb.Sp deviations remain because of intrinsic information loss that no method can fully recover.

    Source: §4.3 · p. 8

Abstract

from arXiv · show

Clinical CT and UHRCT cannot resolve individual trabeculae, whereas synchrotron radiation microCT (SRuCT) provides high-resolution references but is not applicable for in vivo imaging. The two domains differ by a 32x resolution gap, are only coarsely paired, and exhibit severe physical differences including partial volume effects, noise, and artifacts. Existing super-resolution networks and pretrained-prior methods (GLEAN/StyleGAN2, Stable SR/LDM) underperform because they target pixel generation---diverse details and SSIM/PSNR---and do not model these physical differences. Pixel generation for a 32x resolution gap is intrinsically ill-posed. We propose a paradigm shift from pixel generation to topological inference: deterministically predicting invariant microstructures from macro-scale low-resolution inputs, evaluated by morphological parameters. The core of our 2D morphology learning lies in training on 2D slices while evaluating on 3D morphological parameters, ensuring that the learned representations capture true three-dimensional trabecular topology rather than 2D pixel statistics. We realize this paradigm via structural dual super-resolution, coupling forward physical degradation (micro-to-macro) with inverse structural inference (macro-to-micro) through structural duality constraints. The method is an end-to-end, few-shot, compact structural dual network (SDN), comprising a bidirectional modeling network, a multi-scale structural consistency discriminator, and four structural duality constraints. On the test set, SDN achieves morphological parameters largely consistent with SRuCT across six metrics, with SSIM reaching 0.8. Trained on 3.2 um SSRF data, the model generalizes well to 3.25 um isotropic BSRF data from an independent source, validating cross-source generalization and confirming trustworthy structural inference rather than pixel generation.

1 Introduction

Clinical UHRCT cannot resolve individual trabeculae, and its physical differences from SRµCT make pixel-level super-resolution unreliable. The paper reframes the task as deterministic topological inference and introduces structural dual super-resolution for cross-domain morphology learning.

1 Introduction

  • At 100 µm, clinical CT and UHRCT cannot resolve individual trabeculae, while 3.2 µm SRµCT provides references but is not applicable for in vivo imaging.The domains differ by 31.25× in resolution and are coarsely paired, with severe physical differences including partial-volume effects, noise, and artifacts.Source: §1 · p. 2
  • The authors argue that deterministic inference of invariant microstructures, evaluated by morphological parameters, is needed instead of pixel-based generation of diverse details.They frame this shift as topological inference with minimal tolerance for hallucination.Source: §1 · p. 2
  • BV/TV was 0.1163 for SDN versus 0.1156 for SRµCT, and Tb.Th was 10.3 µm versus 7.3 µm; SDN's SSIM reached 0.8.Clinical UHRCT alone yielded BV/TV 0.3793 (228% error) and Tb.Th 357.2 µm (4793% error).Source: §1 · pp. 2–3
  • SDN couples forward physical degradation from microCT to UHRCT with inverse structural inference, using duality constraints and a structural consistency discriminator to target shared morphology.The design includes four structural duality constraints and avoids freely generating details.Source: §1 · pp. 2–3
  • The proposed evaluation prioritizes seven morphological parameters and reports generalization from 3.2 µm SSRF data to independent 3.25 µm isotropic BSRF data.The contribution passage also reports outperforming GAN- and diffusion-based methods that rely on large-scale pretraining.Source: §1 · p. 3

2 Related Work

Related work covers medical super-resolution, hallucination in generative reconstruction, and trabecular morphology assessment. The paper positions cross-physical-domain morphology learning from clinical UHRCT as a distinct task evaluated primarily through morphological parameters.

Medical Image Super-Resolution

  • Medical CT super-resolution methods often use synthetic degradation and pixel-wise losses, while typical same-device resolution gaps are no more than 8×, unlike this 31.25× cross-device setting.The authors note that large-scale SRµCT imaging remains impractical given limited human specimens and scarce synchrotron facilities.Source: §2 · pp. 3–4

Hallucination in Super-Resolution

  • Generative models can fabricate plausible but nonexistent structures, a concern the authors connect to medical imaging's low tolerance for hallucination.They describe hallucination in medical super-resolution as largely unexplored.Source: §2 · p. 4

Trabecular Morphology Assessment

  • The paper formulates cross-physical-domain trabecular morphology learning from clinical UHRCT, with morphological parameters as the primary evaluation.The cited clinical practice uses HR-pQCT or microCT to compute these parameters.Source: §2 · p. 4

3 Method

The method reframes cross-domain trabecular super-resolution as deterministic inference of shared morphology from coarsely paired, physically different CT domains. Its structural dual network couples modeled micro-to-macro degradation with macro-to-micro inference, using structural consistency and morphology-centered evaluation.

3.1 Problem Setting

  • Clinical UHRCT and SRµCT are coarsely paired across a 31.25× resolution gap and differ in physical imaging effects; the goal is to infer their shared trabecular morphology.The setup models the gap as 32× microstructure super-resolution.Source: §3.1 · p. 4

3.2 Paradigm: From Pixel Generation to Topological Inference

  • Topological inference deterministically predicts invariant topology and morphology without free-form texture, shifting the objective and evaluation from pixel similarity to morphological parameters.The proposed constraints are multi-scale structural duality, with minimal tolerance for hallucination.Source: §3.2 · p. 4

3.3 Realization: Structural Dual Network

  • The structural dual network couples forward physical degradation F from microCT to UHRCT with inverse structural inference I, enforcing shared topology through structural duality constraints.The constraints act on both I(F(x)) and F(I(y)); training does not require an explicit morphological parameter extractor.Source: §3.3 · p. 5

3.4 Forward Physical Degradation: Micro-to-Macro / 3.5 Inverse Structural Inference: Macro-to-Micro

  • Forward degradation models resolution loss, partial-volume mixing, noise and detector response, and artifacts; inverse inference addresses those effects while recovering shared morphology rather than exact pixels.The forward model uses learnable blur and 32× downsampling; the inverse process is a structural-level, not strict mathematical, inverse because degradation is irreversible.Source: §3.4 · p. 5, §3.5 · p. 6

3.6 Pyramid Structural Consistency Discriminator

  • The pyramid structural consistency discriminator compares structural maps rather than raw images, assessing macro layout, structural transitions, and local morphology at low, middle, and high scales.Its patch-level score map enforces topological consistency rather than pixel-level realism.Source: §3.6 · p. 6

3.7 Loss Functions / 3.7.2 Structural Duality Loss / 3.7.3 Regularization

  • The loss combines adversarial, low-frequency, gradient, SSIM, frequency, identity, and total-variation terms; four structural duality constraints jointly enforce topology without an explicit parameter extractor.The structural distance is implicitly defined by the combination of the four constraints; identity and total variation are regularizers.Source: §3.7 · p. 6, §3.7.2 · p. 7, §3.7.3 · p. 7

3.8 Training Strategy

  • F, I, and the pyramid discriminator are trained jointly end-to-end without pretraining or stage-wise decoupling, converging with 1,787 coarsely paired samples through alternating updates.Training alternates discriminator updates with updates to F and I.Source: §3.8 · p. 7

3.9 Evaluation

  • Evaluation prioritizes Tb.Th, Tb.Sp, Tb.N, Conn.D, BV/TV, SMI, and DA as morphology measures, while SSIM, PSNR, and Dice are auxiliary image-level references.These parameters characterize trabecular morphology and are described as clinically meaningful for osteoporosis diagnosis and fracture-risk assessment.Source: §3.9 · p. 7

4 Experiments

On SSRF, SDN produces morphological measurements largely consistent with SRµCT; it also generalizes to independent BSRF data and demonstrates whole-femoral-head reconstruction. The experiments assess morphometry as the primary outcome and include ablations and comparisons with pretrained methods.

4.1 Datasets

  • The dataset comprises 1,787 coarsely paired slices from six patients, with five patients used for training and one for testing.The generalization test uses the same test patient imaged at BSRF.Source: §4.1 · p. 7

4.2 Evaluation Metrics

  • Morphological parameters are the primary evaluation metrics, while SSIM, PSNR, and Dice/F1 are auxiliary image-level metrics.The seven morphological parameters include Tb.Th, Tb.Sp, Tb.N, connectivity, BV/TV, DA, and SMI.Source: §4.2 · p. 8

4.3 Results

  • SSIM reaches 0.8, while SDN's morphological parameters are largely consistent with SRµCT across seven metrics.The improvement is particularly pronounced for Tb.Th and Tb.Sp, which are most affected by partial volume effects in clinical UHRCT.Source: Table 1 · p. 8, §4.3 · p. 8
  • SSIM is 0.8 vs. 0.3 for SDN versus GLEAN, despite SDN's lower PSNR, reflecting structural rather than pixel-value fidelity.The authors interpret this contrast as SDN prioritizing trabecular topology over exact pixel-value recovery.Source: §4.3 · p. 8
  • Compared with GLEAN and Stable SR trained on large-scale synthetic interpolated pairs, SDN outperforms these pretrained methods using 1,787 coarsely paired real samples and no synthetic data.The reported comparison includes a generative prior pretrained on 309,482 high-resolution images.Source: §4.3 · p. 8

4.4 Cross-Physical-Domain Generalization

  • SDN trained on 3.2 µm SSRF data generalizes well to independent 3.25 µm isotropic BSRF data.The BSRF test set evaluates cross-physical-domain generalization.Source: §4.4 · p. 8, Table 2 · p. 8

4.5 Ablation Studies

  • The full SDN achieves the best performance across all metrics; duality constraints reduce partial-volume errors, while regularization suppresses noise.The ablation attributes these effects to low-frequency and edge consistency across domains and to prevention of trivial mappings.Source: Figure 3 · p. 9, §4.5 · p. 9

4.6 Clinical Application: Whole Femoral Head Super-Resolution

  • The reconstructed whole-femoral-head heatmap resolves individual trabeculae, whereas the input UHRCT heatmap classifies most regions as high-density.The reported application demonstrates trabecular density quantification from clinical UHRCT as an anatomical reference for precise screw placement.Source: §4.6 · p. 9

5 Conclusion

The conclusion presents structural dual super-resolution as a few-shot approach to cross-physical-domain trabecular morphology inference and reports cross-source generalization and close 3D morphological agreement. The included disclosures cover AI use, ethics, and reproducibility resources.

5 Conclusion

  • The authors report that 2D-slice training achieves 3D morphological parameters closely matching SRµCT, with generalization from 3.2 µm SSRF to 3.25 µm isotropic BSRF data.They identify 3D training as future work that may further improve morphological metrics.Source: §5 · pp. 9–10

AI use statement

  • The authors used generative AI tools for writing polish and state that they reviewed the AI-assisted work and take responsibility for the final content.They report no use of generative AI for other tasks requiring disclosure.Source: AI use statement · p. 10

Ethics statement

  • The study reports institutional ethics approval, informed consent, anonymization, and compliance with applicable human-participant research requirements.The statement also cites the Declaration of Helsinki and ICLR Code of Ethics.Source: Ethics statement · p. 10

Reproducibility statement

  • The reproducibility statement directs readers to Appendix A.1 for data processing, A.2 for metric definitions, and A.3 for pretraining experiments.The statement presents these appendices as resources for reproducibility.Source: Reproducibility statement · pp. 10–11

A.1 Data Description

The dataset pairs synchrotron microCT and clinical CT images from human osteoporotic bone samples.

A.1 Data Description

  • The dataset contains discarded bone samples, high-resolution SRµCT images, clinical CT images, and registered cross-modal paired data.Source: §A.1 · p. 12

A.1.1 Sample Collection and Ethical Approval

The study collected discarded femoral-head samples from patients undergoing replacement surgery, with sample eligibility and preparation specified.

A.1.1 Sample Collection and Ethical Approval

  • Discarded femoral-head samples after replacement surgery were collected with hospital ethics committee approval; consent was waived for de-identified discarded samples.Source: §A.1.1 · p. 12
  • Eligible participants were over 65 with primary osteoporosis and osteoporotic femoral-neck fragility fracture requiring hip-joint resection.Exclusions included severe degenerative destruction, improper preservation, and bone tumors, infection, secondary osteoporosis, or other metabolic bone diseases affecting microstructure.Source: §A.1.1 · pp. 12–13
  • Samples were fixed in 4% paraformaldehyde for 24–48 hours, stored in 70% ethanol at 4 °C, and kept moist during scanning.Bone strips were cut to approximately 4 mm × 4 mm cross-section, with intact trabecular regions retained for imaging.Source: §A.1.1 · p. 13

Shanghai Synchrotron Radiation Facility BL13HB Beamline

SSRF BL13HB supports micron-scale three-dimensional trabecular imaging, with adjustable energy and a field of view that accommodates the bone strips. The described protocol uses 3.2 µm voxels and scans each sample in approximately 1–2 hours.

Shanghai Synchrotron Radiation Facility BL13HB Beamline

  • The BL13HB beamline is dedicated to X-ray imaging and biomedical applications, with a maximum spatial resolution of 0.8 µm and adjustable 8–40 keV energy.The bone strips, approximately 4 mm × 4 mm in cross-section, fit within its field of view.Source: Shanghai Synchrotron Radiation… · p. 13
  • The approximately 4 mm × 4 mm bone strips fit fully within the beamline’s field of view.Source: Shanghai Synchrotron Radiation… · p. 13
  • Scans used 3.2 µm reconstructed voxels, 1200–1800 projections over 360°, and approximately 1–2 hours per sample.Exposure was 0.5–2 seconds per projection; energy was 25–35 keV, adjusted for sample thickness.Source: Shanghai Synchrotron Radiation… · p. 13

Beijing Synchrotron Radiation Facility 4W1A X-ray Imaging Beamline

This appendix describes BSRF imaging, clinical CT acquisition, dataset construction, and definitions of the three-dimensional morphology measures. Supplementary results include an image-metric comparison and tables scoped to BSRF and synthetic UHRCT testsets.

Beijing Synchrotron Radiation Facility 4W1A X-ray Imaging Beamline

  • BSRF imaging used a 3.25 µm voxel size, with approximately 10 µm effective spatial resolution; its 63 paired samples were reserved for generalization testing.The beamline uses absorption/phase contrast imaging, with an approximately 6–26 keV energy range.Source: Beijing Synchrotron Radiation Facility… · p. 13, §A.1.5 · p. 14

A.1.3 Clinical CT Imaging

  • Clinical CT used two protocols with 0.15 mm or 0.1 mm slice spacing, followed by cross-modal registration and cropping to the modalities’ common field of view.Registration combines coarse markers or anatomical landmarks with rigid registration using mutual information or normalized mutual information.Source: §A.1.3 · pp. 13–14, §A.1.4 · p. 14

A.1.5 Dataset Composition

  • The dataset contains 1787 SSRF pairs and 63 BSRF pairs, alongside registered and cropped images, imaging metadata, and registration records.Figure 5 shows same-site pairs that are coarsely paired, not strictly aligned, with a 31.25× resolution gap; Figure 6 contrasts 100 µm UHRCT with 3.2 µm SRµCT.Source: §A.1.5 · p. 14, Figure 5 · p. 14, Figure 6 · p. 15

A.2 Morphological Parameters

  • Morphological parameters are computed on binarized 3D trabecular images using ImageJ/BoneJ, Otsu thresholding, and a trabecular-only region of interest.Source: §A.2 · p. 15, §A.2.8 · p. 18

A.2.1 Degree of Anisotropy (DA)

  • DA is derived from directional mean-intercept lengths and the fabric-tensor eigenvalues; it is described as an independent predictor of bone stiffness and fracture risk.Parallel test lines are traced in multiple directions; DA ranges from 0 for fully isotropic to 1 for fully anisotropic.Source: §A.2.1 · p. 16

A.2.2 Bone Volume Fraction (BV/TV)

  • BV/TV is mineralized bone volume as a percentage of total volume, while Tb.Th averages local trabecular thickness estimated by maximal-sphere fitting.For BV/TV, bone and total volume are counted as bone voxels and all voxels within the region of interest, respectively.Source: §A.2.2 · p. 16, §A.2.3 · p. 16

A.2.4–A.2.7

  • Tb.Sp measures marrow-cavity width, Tb.N trabeculae per unit length, Conn.D redundant connections per unit volume, and SMI plate-like versus rod-like geometry.The appendix describes sphere fitting in marrow for Tb.Sp, Euler-characteristic-based connectivity for Conn.D, and differential bone-surface analysis for SMI.Source: §A.2.4 · p. 17, §A.2.5 · p. 17, §A.2.6 · p. 17

A.3 Supplementary Results

  • SDN has lower PSNR but significantly higher SSIM than GLEAN; Tables 5 and 6 compare morphometric parameters on BSRF and interpolated synthetic UHRCT testsets.The table captions specify testset scope but do not provide cell values.Source: Table 5 · p. 18, Table 6 · p. 18, Figure 7 · p. 19

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