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

Fan Zhang; Yi Zhang; Ling Wang

cs.CVSep 28, 2026

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

Authors: Fan Zhang, Yi Zhang, Ling Wang

Organizations: Institute of High Energy Physics, Chinese Academy of Sciences Beijing 100049, China · Department of Radiology Beijing Jishuitan Hospital Beijing, China

Abstract

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.

Figures & tables

Figure 1: GLEAN fails to remove partial volume effects in clinical UHRCT as (a)-(e). Stable SR (using synthetic UHRCT data) leaves residual noise at inference as (f)-(h). For GLEAN, first, we performed large-scale pre-training of the generator using 309,482 high-resolution SR $\mu$ CT images in StyleGAN2, and then used the generator as the prior for the super-resolution network. (d) and (e) show the PSNR and SSIM results for the 37 CT images in the test set of GLEAN, respectively.

Figure 2: The framework of Structural Dual Network.

Method	BV/TV	Tb.Th mean (mm)	Tb.Sp mean (mm)	Tb.N (1/mm)	SMI	DA	Conn.D (1/mm 3 )
UHRCT	0.3793	0.3572	0.3327	1.0619	-0.7616	3.0564	1000.98
SR $\mu$ CT (GT)	0.1156	0.0073	0.0321	15.86	-0.3444	334.49	$3.05\times 10^{7}$
SDN	0.1163	0.0103	0.0552	11.26	-0.5053	446.54	$3.05\times 10^{7}$
SDN (no tv)	0.1126	0.0100	0.0522	11.29	-0.1594	382.83	$3.05\times 10^{7}$
SDN (no reg)	0.1472	0.0112	0.0473	13.16	-0.4203	424.3	$3.052\times 10^{7}$
F, I only	0.1784	0.0123	0.0407	14.52	-0.6024	377.3	$3.052\times 10^{7}$

Table 1: Comparison of morphometric parameters on SSRF testset.

Figure 3: The results of ablation studies of Structural Dual Network.

Method	BV/TV	Tb.Th mean	Tb.Th std	Tb.Sp mean	Tb.Sp std	Tb.N (1/mm)	SMI	DA	Conn.D (1/mm 3 )
UHRCT	0.2971	0.3235	0.0997	0.3832	0.2041	0.918	0.158	3.83	1000.9
SR $\mu$ CT	0.1425	0.0087	0.0052	0.0335	0.0255	16.41	-0.270	285.4	$2.91\times 10^{7}$
SDN	0.1166	0.0105	0.0066	0.0535	0.0445	11.11	-0.277	302.9	$2.91\times 10^{7}$
SDN (no tv)	0.0945	0.0091	0.0050	0.0539	0.0454	10.33	-0.028	285.4	$2.91\times 10^{7}$

Table 2: Comparison of morphometric parameters on BSRF testset for Cross-Physical-Domain Generalization.

Figure 4: Clinical application: whole femoral head super-resolution. (a) Input clinical UHRCT slice. (b) Heatmap on UHRCT, where most regions are incorrectly classified as high-density. (c) SDN SR reconstruction. (d) Heatmap on the reconstructed microCT, resolving individual trabeculae.

Appendix figures & tables7 assets

Supplementary material from the paper’s appendix.

Appendix

Figure 5: Examples of four coarsely paired SR $\mu$ CT–UHRCT images in our dataset. Each pair consists of a SR $\mu$ CT slice (left) and the corresponding clinical UHRCT slice (right) at the same anatomical site. The resolution gap is 31.25 $\times$ , and the two domains are not strictly aligned. Both images are displayed at the same physical size to highlight the 31.25 $\times$ resolution gap.

Figure 6: Real-size comparison between clinical UHRCT and SR $\mu$ CT. The left panel shows UHRCT at 100 $\mu$ m resolution, where individual trabeculae are indistinguishable due to severe partial volume effects. The right panel shows SR $\mu$ CT at 3.2 $\mu$ m resolution, resolving individual trabecular structures.

Dimension	Synchrotron radiation microCT ( $X$ )	Clinical UHRCT ( $Y$ )
Resolution	$3.2~\mu$ m	$100~\mu$ m
X-ray	Monochromatic	Polychromatic
Detector	Photon-counting	Energy-integrating
Partial volume effect	Negligible	Severe, bone/marrow mixing
Noise	Very low quantum noise	Quantum + electronic noise
Detector blur	Minimal	Significant

Appendix

Table 3: Physical differences between synchrotron radiation microCT and clinical UHRCT.

Parameter	Unit	Definition	Osteoporotic Change
DA	—	Degree of anisotropy (0 = isotropic, 1 = anisotropic)	Decreases
BV/TV	%	Bone volume fraction	Decreases
Tb.Th	$\mu$ m	Trabecular thickness	Decreases
Tb.Sp	$\mu$ m	Trabecular separation	Increases
Tb.N	mm -1	Trabecular number	Decreases
Conn.D	mm -3	Connectivity density	Decreases

Appendix

Table 4: Summary of morphological parameters.

Figure 7: Image-level metric comparison. SDN achieves lower PSNR but significantly higher SSIM than GLEAN, indicating that SDN focuses on structural inference rather than pixel-level restoration.

Method	BV/TV	Tb.Th mean (mm)	Tb.Th std (mm)	Tb.Sp mean (mm)	Tb.Sp std (mm)	Tb.N (1/mm)	SMI	DA	Conn.D (1/mm 3 )
UHRCT	0.3793	0.3572	0.1128	0.3327	0.1815	1.0619	-0.7616	3.0564	1000.98
SR $\mu$ CT	0.1156	0.0073	0.0027	0.0321	0.0250	15.86	-0.3444	334.49	$3.05\times 10^{7}$
SDN	0.1163	0.0103	0.0062	0.0552	0.0464	11.26	-0.5053	446.54	$3.05\times 10^{7}$
SDN (no tv)	0.1126	0.0100	0.0057	0.0522	0.0417	11.29	-0.1594	382.83	$3.05\times 10^{7}$
SDN (no reg)	0.1472	0.0112	0.0070	0.0473	0.0381	13.16	-0.4203	424.3	$3.052\times 10^{7}$
F, I only	0.1784	0.0123	0.0082	0.0407	0.0332	14.52	-0.6024	377.3	$3.052\times 10^{7}$

Appendix

Table 5: Comparison of morphometric parameters on BSRF testset (without synthetic data). Dataset: 1787 paired UHRCT-SR

\mu

CT.

Parameter	HR (SR $\mu$ CT)	LR (UHRCT)	GLEAN ( Chan et al., 2023 )	Stable SR ( Wang et al., 2024 )
BV/TV	0.1284	0.37	0.1437 (MAPE 12.22%)	0.2406 (MAPE 86.72%)
Tb.Th (mm)	0.0747	0.35	0.1152 (MAPE 57.82%)	0.0193 (MAPE 73.70%)
Tb.Sp (mm)	0.5185	0.33	0.7128 (MAPE 40.77%)	0.0649 (MAPE 87.31%)
Tb.N (mm -1 )	1.7967	1.06	1.2647 (MAPE 27.76%)	13.2656 (MAPE 661.89%)

Appendix

Table 6: Comparison of morphometric parameters on interploated synthetic UHRCT testset: HR (SR

\mu

CT), LR (UHRCT), GLEAN and Stable SR. MAPE values are given in parentheses relative to HR. Dataset: 52874 paired UHRCT(contained interploated synthetic data)-SR

\mu

CT, pretrained on 309482 SR

\mu

CT.

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