{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,16]],"date-time":"2026-08-16T04:26:35Z","timestamp":1786854395335,"version":"build-2736575974"},"reference-count":31,"publisher":"MDPI AG","issue":"16","license":[{"start":{"date-parts":[[2026,8,14]],"date-time":"2026-08-14T00:00:00Z","timestamp":1786665600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100018537","name":"National Science and Technology Major Project","doi-asserted-by":"crossref","award":["2025ZD1606500"],"award-info":[{"award-number":["2025ZD1606500"]}],"id":[{"id":"10.13039\/501100018537","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"crossref","award":["52305572"],"award-info":[{"award-number":["52305572"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"crossref"}]},{"award":["52305572"],"award-info":[{"award-number":["52305572"]}],"id":[{"id":"https:\/\/ror.org\/01h0zpd94","id-type":"ROR","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>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\u2013Logan 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\u20130.023 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 \u00b1 0.0454 for the uncalibrated reconstruction to 0.8450 \u00b1 0.0155 and reduced the NRMSE from 0.5180 \u00b1 0.0526 to 0.1671 \u00b1 0.0125. The proposed method achieved the highest mean SSIM of 0.9933 \u00b1 0.0002 and the lowest NRMSE of 0.0321 \u00b1 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.<\/jats:p>","DOI":"10.3390\/s26165161","type":"journal-article","created":{"date-parts":[[2026,8,14]],"date-time":"2026-08-14T15:48:36Z","timestamp":1786722516000},"page":"5161","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Phantom-Free Geometric Refinement for Industrial CBCT Using Physical Constraints and a Normalized Low-Rank Projection Prior"],"prefix":"10.3390","volume":"26","author":[{"ORCID":"https:\/\/orcid.org\/0009-0004-7626-1562","authenticated-orcid":false,"given":"Yanxu","family":"Sun","sequence":"first","affiliation":[{"name":"Center of Ultra-Precision Optoelectronic Instrument Engineering, Harbin Institute of Technology, Harbin 150080, China"},{"name":"Key Laboratory of Ultra-Precision Instruments and Intelligence of the Ministry of Industry and Information Technology, Harbin Institute of Technology, Harbin 150080, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Xingyuan","family":"Bian","sequence":"additional","affiliation":[{"name":"Center of Ultra-Precision Optoelectronic Instrument Engineering, Harbin Institute of Technology, Harbin 150080, China"},{"name":"Key Laboratory of Ultra-Precision Instruments and Intelligence of the Ministry of Industry and Information Technology, Harbin Institute of Technology, Harbin 150080, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Igor A.","family":"Konyakhin","sequence":"additional","affiliation":[{"name":"Higher School of Engineering and Technology, ITMO University, Kronverksky Pr. 49, Bldg. A, St. Petersburg 197101, Russia"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4418-8936","authenticated-orcid":false,"given":"Junning","family":"Cui","sequence":"additional","affiliation":[{"name":"Center of Ultra-Precision Optoelectronic Instrument Engineering, Harbin Institute of Technology, Harbin 150080, China"},{"name":"Key Laboratory of Ultra-Precision Instruments and Intelligence of the Ministry of Industry and Information Technology, Harbin Institute of Technology, Harbin 150080, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2026,8,14]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"693","DOI":"10.1016\/j.cirp.2022.05.001","article-title":"Advances in the metrological traceability and performance of X-ray computed tomography","volume":"71","author":"Dewulf","year":"2022","journal-title":"CIRP Ann."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"544","DOI":"10.1016\/j.precisioneng.2019.06.007","article-title":"X-ray computed tomography: From medical imaging to dimensional metrology","volume":"60","author":"Herazo","year":"2019","journal-title":"Precis. 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