{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,16]],"date-time":"2026-05-16T00:05:56Z","timestamp":1778889956462,"version":"3.51.4"},"reference-count":36,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2024,4,9]],"date-time":"2024-04-09T00:00:00Z","timestamp":1712620800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Major Research Plan of the National Natural Science Foundation of China","award":["92048301"],"award-info":[{"award-number":["92048301"]}]},{"name":"Major Research Plan of the National Natural Science Foundation of China","award":["52025054"],"award-info":[{"award-number":["52025054"]}]},{"name":"National Outstanding Youth Science Fund Project of National Natural Science Foundation of China","award":["92048301"],"award-info":[{"award-number":["92048301"]}]},{"name":"National Outstanding Youth Science Fund Project of National Natural Science Foundation of China","award":["52025054"],"award-info":[{"award-number":["52025054"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>In the human\u2013robot collaboration system, the high-precision distortion correction of the camera as an important sensor is a crucial prerequisite for accomplishing the task. The traditional correction process is to calculate the lens distortion with the camera model parameters or separately from the camera model. However, in the optimization process calculate with the camera model parameters, the mutual compensation between the parameters may lead to numerical instability, and the existing distortion correction methods separated from the camera model are difficult to ensure the accuracy of the correction. To address this problem, this study proposes a model-independent lens distortion correction method based on the image center area from the perspective of the actual camera lens distortion principle. The proposed method is based on the idea that the structured image preserves its ratios through perspective transformation, and uses the local image information in the central area of the image to correct the overall image. The experiments are verified from two cases of low distortion and high distortion under simulation and actual experiments. The experimental results show that the accuracy and stability of this method are better than other methods in training and testing results.<\/jats:p>","DOI":"10.3390\/s24082406","type":"journal-article","created":{"date-parts":[[2024,4,10]],"date-time":"2024-04-10T03:07:48Z","timestamp":1712718468000},"page":"2406","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":20,"title":["A Distortion Correction Method Based on Actual Camera Imaging Principles"],"prefix":"10.3390","volume":"24","author":[{"given":"Wenxin","family":"Yin","sequence":"first","affiliation":[{"name":"State Key Laboratory of Robotics and System, Harbin Institute of Technology, Harbin 150001, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xizhe","family":"Zang","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Robotics and System, Harbin Institute of Technology, Harbin 150001, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0009-0006-0663-9560","authenticated-orcid":false,"given":"Lei","family":"Wu","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Robotics and System, Harbin Institute of Technology, Harbin 150001, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8138-2802","authenticated-orcid":false,"given":"Xuehe","family":"Zhang","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Robotics and System, Harbin Institute of Technology, Harbin 150001, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jie","family":"Zhao","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Robotics and System, Harbin Institute of Technology, Harbin 150001, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2024,4,9]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"970","DOI":"10.1080\/0951192X.2016.1268269","article-title":"Active collision avoidance for human-robot collaboration driven by vision sensors","volume":"30","author":"Mohammed","year":"2017","journal-title":"Int. J. Comput. Integr. Manuf."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"3349","DOI":"10.1109\/TPAMI.2020.2983686","article-title":"Deep High-Resolution Representation Learning for Visual Recognition","volume":"43","author":"Wang","year":"2021","journal-title":"IEEE Trans. Pattern Anal. Mach. Intell."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"17","DOI":"10.1016\/j.cirp.2018.04.066","article-title":"Deep learning-based human motion recognition for predictive context-aware human-robot collaboration","volume":"67","author":"Wang","year":"2018","journal-title":"CIRP Ann. Manuf. Technol."},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Sun, J., Wang, P., Qin, Z.K., and Qiao, H. (July, January 29). Overview of Camera Calibration for Computer Vision. Proceedings of the 2014 11th World Congress on Intelligent Control and Automation, Shenyang, China.","DOI":"10.1109\/WCICA.2014.7052692"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"321","DOI":"10.1007\/3-540-55426-2_37","article-title":"Camera Self-Calibration\u2014Theory and Experiments","volume":"588","author":"Faugeras","year":"1992","journal-title":"Lect. Notes Comput. Sci."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"123","DOI":"10.1007\/BF00127171","article-title":"A Theory of Self-Calibration of a Moving Camera","volume":"8","author":"Maybank","year":"1992","journal-title":"Int. J. Comput. Vis."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"45","DOI":"10.1016\/j.jocs.2018.12.002","article-title":"Self-calibration of projective camera based on trajectory basis","volume":"31","author":"Liu","year":"2019","journal-title":"J. Comput. Sci."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"114","DOI":"10.1109\/70.481755","article-title":"A self-calibration technique for active vision systems","volume":"12","year":"1996","journal-title":"IEEE Trans. Robot. Autom."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"5","DOI":"10.1023\/A:1007957826135","article-title":"Self-calibration of stationary cameras","volume":"22","author":"Hartley","year":"1997","journal-title":"Int. J. Comput. Vis."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"323","DOI":"10.1109\/JRA.1987.1087109","article-title":"A Versatile Camera Calibration Technique for High-Accuracy 3d Machine Vision Metrology Using Off-the-Shelf Tv Cameras and Lenses","volume":"3","author":"Tsai","year":"1987","journal-title":"IEEE J. Robot. Autom."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"965","DOI":"10.1109\/34.159901","article-title":"Camera Calibration with Distortion Models and Accuracy Evaluation","volume":"14","author":"Weng","year":"1992","journal-title":"IEEE Trans. Pattern Anal."},{"key":"ref_12","unstructured":"Gao, H.W., Wu, C.D., Gao, L.F., and Li, B. (2006, January 21\u201323). An improved two-stage camera calibration method. Proceedings of the 2006 6th World Congress on Intelligent Control and Automation, Dalian, China."},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Zhou, G.Q., Li, H.X., Song, R.H., Wang, Q.Y., Xu, J.S., and Song, B. (2022). Orthorectification of Fisheye Image under Equidistant Projection Model. Remote Sens, 14.","DOI":"10.3390\/rs14174175"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"1330","DOI":"10.1109\/34.888718","article-title":"A flexible new technique for camera calibration","volume":"22","author":"Zhang","year":"2000","journal-title":"IEEE Trans. Pattern Anal."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"1066","DOI":"10.1109\/34.879788","article-title":"Geometric camera calibration using circular control points","volume":"22","year":"2000","journal-title":"IEEE Trans. Pattern Anal."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"339","DOI":"10.1109\/TMM.2012.2229264","article-title":"Real-Time, Full 3-D Reconstruction of Moving Foreground Objects from Multiple Consumer Depth Cameras","volume":"15","author":"Alexiadis","year":"2013","journal-title":"IEEE Trans. Multimed."},{"key":"ref_17","unstructured":"Bouguet, J. (2023, October 07). Camera Calibration Toolbox for Matlab. Available online: http:\/\/www.vision.caltech.edu\/bouguetj\/calib_doc\/download\/index.html."},{"key":"ref_18","first-page":"120","article-title":"The OpenCV library","volume":"25","author":"Bradski","year":"2000","journal-title":"Dr. Dobb\u2019s J. Softw. Tools Prof. Program."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"2233562","DOI":"10.1080\/21642583.2023.2233562","article-title":"Camera calibration method based on circular array calibration board","volume":"11","author":"Chen","year":"2023","journal-title":"Syst. Sci. Control Eng."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"14","DOI":"10.1007\/PL00013269","article-title":"Straight lines have to be straight\u2014Automatic calibration and removal of distortion from scenes of structured environments","volume":"13","author":"Devernay","year":"2001","journal-title":"Mach. Vis. Appl."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"892157","DOI":"10.3389\/fphy.2022.892157","article-title":"A New Calibration Method of Stereo Line-Scan Cameras for 2D Coordinate Measurement","volume":"10","author":"Wang","year":"2022","journal-title":"Front. Phys."},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"Xue, Z.C., Xue, N., Xia, G.S., and Shen, W.M. (2019, January 15\u201320). Learning to Calibrate Straight Lines for Fisheye Image Rectification. Proceedings of the 2019 IEEE\/CVF Conference on Computer Vision and Pattern Recognition (CVPR), Long Beach, CA, USA.","DOI":"10.1109\/CVPR.2019.00174"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"1215","DOI":"10.1109\/TIP.2005.846025","article-title":"Nonmetric calibration of camera lens distortion: Differential methods and robust estimation","volume":"14","author":"Ahmed","year":"2005","journal-title":"IEEE Trans. Image Process."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"325","DOI":"10.14358\/PERS.82.5.325","article-title":"Camera Self-Calibration with Lens Distortion from a Single Image","volume":"82","author":"Liu","year":"2016","journal-title":"Photogramm. Eng. Remote Sens."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"1688","DOI":"10.1016\/j.patcog.2009.10.003","article-title":"Robust metric calibration of non-linear camera lens distortion","volume":"43","year":"2010","journal-title":"Pattern Recogn."},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Xiong, P.B., Wang, S.K., Wang, W.B., Ye, Q.X., and Ye, S.J. (2021). Model-Independent Lens Distortion Correction Based on Sub-Pixel Phase Encoding. Sensors, 21.","DOI":"10.3390\/s21227465"},{"key":"ref_27","doi-asserted-by":"crossref","unstructured":"Weng, J.W., Zhou, W.S., Ma, S.M., Qi, P., and Zhong, J.G. (2021). Model-Free Lens Distortion Correction Based on Phase Analysis of Fringe-Patterns. Sensors, 21.","DOI":"10.3390\/s21010209"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"143","DOI":"10.1016\/j.optlaseng.2017.06.008","article-title":"Accuracy evaluation of optical distortion calibration by digital image correlation","volume":"98","author":"Gao","year":"2017","journal-title":"Opt. Laser Eng."},{"key":"ref_29","doi-asserted-by":"crossref","unstructured":"Jin, Z.Y., Li, Z.X., Gan, T.Y., Fu, Z.M., Zhang, C.A., He, Z.Y., Zhang, H., Wang, P., Liu, J.Q., and Ye, X.S. (2022). A Novel Central Camera Calibration Method Recording Point-to-Point Distortion for Vision-Based Human Activity Recognition. Sensors, 22.","DOI":"10.3390\/s22093524"},{"key":"ref_30","doi-asserted-by":"crossref","unstructured":"Rai, L., Gibbs, J.D., and Wibowo, H. (2012, January 5\u20137). A C-Arm Calibration Method with Application to Fluoroscopic Image-guided Procedures. Proceedings of the Conference on Medical Imaging\u2014Image-Guided Procedures, Robotic Interventions and Modeling, San Diego, CA, USA.","DOI":"10.1117\/12.911565"},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"457","DOI":"10.1016\/S0030-3992(03)00053-7","article-title":"Calibrating camera radial distortion with cross-ratio invariability","volume":"35","author":"Zhang","year":"2003","journal-title":"Opt. Laser Technol."},{"key":"ref_32","doi-asserted-by":"crossref","unstructured":"Hartley, R., and Zisserman, A. (2004). Multiple View Geometry in Computer Vision: Camera Models, Cambridge University Press.","DOI":"10.1017\/CBO9780511811685"},{"key":"ref_33","doi-asserted-by":"crossref","unstructured":"Liebold, F., Mader, D., Sardemann, H., Eltner, A., and Maas, H.-G. (2023). A Bi-Radial Model for Lens Distortion Correction of Low-Cost UAV Cameras. Remote Sens., 15.","DOI":"10.3390\/rs15225283"},{"key":"ref_34","first-page":"444","article-title":"Decentering distortion of lenses","volume":"32","author":"Brown","year":"1966","journal-title":"Photogramm. Eng."},{"key":"ref_35","first-page":"855","article-title":"Close-range camera calibration","volume":"37","author":"Brown","year":"1971","journal-title":"Photogramm. Eng."},{"key":"ref_36","unstructured":"Harris, C., and Stephens, M. (September, January 31). A combined corner and edge detector. Proceedings of the Alvey Vision Conference, Manchester, UK."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/24\/8\/2406\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T14:25:22Z","timestamp":1760106322000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/24\/8\/2406"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,4,9]]},"references-count":36,"journal-issue":{"issue":"8","published-online":{"date-parts":[[2024,4]]}},"alternative-id":["s24082406"],"URL":"https:\/\/doi.org\/10.3390\/s24082406","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024,4,9]]}}}