Phantom-Free Geometric Refinement for Industrial CBCT Using Physical Constraints and a Normalized Low-Rank Projection Prior

Geometric misalignment degrades industrial cone-beam computed tomography (CBCT), particularly when a dedicated calibration phantom cannot be deployed during object acquisition. This study presents a three-stage, scan-specific geometric refinement framework that searches a bounded five-coordinate correction space around a nominal geometry. Coarse candidates are screened using the normalized residual between a geometry-corrected center-of-mass trajectory and its best-fitting low-order periodic model. Translation- and rotation-dominant coordinates are then refined within system-specific physical bounds, and an energy-normalized nuclear-norm score of corrected row-wise sinograms is used for local correlation refinement. The periodic and low-rank terms are treated as object-dependent surrogate objectives rather than as standalone guarantees of physical parameter identifiability. An exact-ASTRA implementation check using a Shepp–Logan volume verified the detector-plane reindexing convention: applying the injected correction reduced valid-mask projection discrepancy to 35.2%, 13.7%, and 8.66% of the uncorrected values for small, medium, and large perturbations, respectively, with round-trip resampling NRMSE of 0.022–0.023 and a mean valid fraction of 98.4%. Three industrial datasets acquired with horizontal gantry CT, temperature-stage in situ CT, and vertical micro-CT provided comparative reconstruction evidence. In addition, a controlled reduced-resolution industrial object reprojection benchmark was used for direct comparison with MI-PSO, PR, and a stability-regularized implementation of the public epipolar-consistency formulation (Open-ECC-R). Over 20 fixed-ROI axial slices, Open-ECC-R increased the mean SSIM from 0.6852 ± 0.0454 for the uncalibrated reconstruction to 0.8450 ± 0.0155 and reduced the NRMSE from 0.5180 ± 0.0526 to 0.1671 ± 0.0125. The proposed method achieved the highest mean SSIM of 0.9933 ± 0.0002 and the lowest NRMSE of 0.0321 ± 0.0009. For the Bluetooth earphone dataset, local sagittal and axial MTF50 estimates increased from 0.84 to 0.94 lp/mm and from 0.45 to 1.05 lp/mm, respectively. These results support scan-specific image-quality refinement around a nominal geometry while avoiding unsupported claims of absolute parameter recovery.