{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,23]],"date-time":"2026-06-23T03:54:55Z","timestamp":1782186895450,"version":"3.54.5"},"reference-count":28,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2023,2,26]],"date-time":"2023-02-26T00:00:00Z","timestamp":1677369600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Natural Science Foundation of China","award":["12072184"],"award-info":[{"award-number":["12072184"]}]},{"name":"National Natural Science Foundation of China","award":["12002197"],"award-info":[{"award-number":["12002197"]}]},{"name":"National Natural Science Foundation of China","award":["11727804"],"award-info":[{"award-number":["11727804"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Remote Sensing"],"abstract":"<jats:p>Calibration of the stereo vision systems is a crucial step for precise 3D measurements. Restricted by the outdoors\u2019 large field of view (FOV), the conventional method based on precise calibration boards is not suitable since the calibration process is time consuming and the calibration accuracy is not guaranteed. In this paper, we propose a calibration method for estimating the extrinsic parameters of the stereo vision system aided by an inclinometer and a range sensor. Through the parameters given by the sensors, the initial rotation angle of the extrinsic parameters and the translation vector are pre-established by solving a set of linear equations. The metric scale of the translation vector is determined by the baseline length provided by the range sensor or GNSS signals. Finally, the optimal extrinsic parameters of the stereo vision systems are obtained by nonlinear optimization of inverse depth parameterization. The most significant advantage of this method is that it enhances the capability of the stereo vision measurement in the outdoor environment, and can achieve fast and accurate calibration results. Both simulation and outdoor experiments have verified the feasibility and correctness of this method, and the relative error in the outdoor large FOV was less than 0.3%. It shows that this calibration method is a feasible solution for outdoor measurements with a large FOV and long working distance.<\/jats:p>","DOI":"10.3390\/rs15051300","type":"journal-article","created":{"date-parts":[[2023,2,27]],"date-time":"2023-02-27T02:04:11Z","timestamp":1677463451000},"page":"1300","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":11,"title":["Sensor-Aided Calibration of Relative Extrinsic Parameters for Outdoor Stereo Vision Systems"],"prefix":"10.3390","volume":"15","author":[{"given":"Jing","family":"Wang","sequence":"first","affiliation":[{"name":"Shanghai Key Laboratory of Mechanics in Energy Engineering, School of Mechanics and Engineering Science, Shanghai University, Shanghai 200444, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Banglei","family":"Guan","sequence":"additional","affiliation":[{"name":"College of Aerospace Science and Engineering, National University of Defense Technology, Changsha 410073, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yongsheng","family":"Han","sequence":"additional","affiliation":[{"name":"Shandong Water Conservancy Vocational College, Rizhao 276826, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Zhilong","family":"Su","sequence":"additional","affiliation":[{"name":"Shanghai Key Laboratory of Mechanics in Energy Engineering, School of Mechanics and Engineering Science, Shanghai University, Shanghai 200444, China"},{"name":"Shaoxing Institute of Technology, Shanghai University, Shaoxing 312074, China"},{"name":"Shanghai Institute of Aircraft Mechanics and Control, Zhangwu Road, Shanghai 200092, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Qifeng","family":"Yu","sequence":"additional","affiliation":[{"name":"College of Aerospace Science and Engineering, National University of Defense Technology, Changsha 410073, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6432-3579","authenticated-orcid":false,"given":"Dongsheng","family":"Zhang","sequence":"additional","affiliation":[{"name":"Shanghai Key Laboratory of Mechanics in Energy Engineering, School of Mechanics and Engineering Science, Shanghai University, Shanghai 200444, China"},{"name":"Shaoxing Institute of Technology, Shanghai University, Shaoxing 312074, China"},{"name":"Shanghai Institute of Aircraft Mechanics and Control, Zhangwu Road, Shanghai 200092, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2023,2,26]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"44","DOI":"10.1016\/j.optlaseng.2014.03.011","article-title":"Characterization of the strain-life fatigue properties of thin sheet metal using an optical extensometer","volume":"60","author":"Zhang","year":"2014","journal-title":"Opt. Lasers Eng."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"108072","DOI":"10.1016\/j.ymssp.2021.108072","article-title":"Characterizing dynamic deformation of marine propeller blades with stroboscopic stereo digital image correlation","volume":"162","author":"Su","year":"2022","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_3","first-page":"855","article-title":"Close-Range Camera Calibration","volume":"37","author":"Brown","year":"2002","journal-title":"Photogramm. Eng."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"37","DOI":"10.1016\/j.isprsjprs.2015.10.006","article-title":"Sensor modelling and camera calibration for close-range photogrammetry","volume":"115","author":"Luhmann","year":"2016","journal-title":"ISPRS J. Photogramm. Remote Sens."},{"key":"ref_5","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_6","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. Mach. Intell."},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Faugeras, O.D., Luong, Q.T., and Maybank, S.J. (1992, January 19\u201322). Camera self-calibration: Theory and experiments. Proceedings of the Computer Vision\u2014ECCV\u201992, Berlin\/Heidelberg, Germany.","DOI":"10.1007\/3-540-55426-2_37"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"389","DOI":"10.1007\/s00138-013-0541-x","article-title":"Intrinsic and extrinsic active self-calibration of multi-camera systems","volume":"25","author":"Bajramovic","year":"2014","journal-title":"Mach. Vis. Appl."},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Yamazaki, S., Mochimaru, M., and Kanade, T. (2011, January 20\u201325). Simultaneous self-calibration of a projector and a camera using structured light. Proceedings of the CVPR 2011 WORKSHOPS, Colorado Springs, CO, USA.","DOI":"10.1109\/CVPRW.2011.5981781"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"1281","DOI":"10.4304\/jsw.9.5.1281-1287","article-title":"A Novel Stratified Self-calibration Method of Camera Based on Rotation Movement","volume":"9","author":"Li","year":"2014","journal-title":"J. Softw."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"2210","DOI":"10.1109\/TCSVT.2017.2731792","article-title":"Extrinsic Camera Calibration Without Visible Corresponding Points Using Omnidirectional Cameras","volume":"28","author":"Miyata","year":"2018","journal-title":"IEEE Trans. Circuits Syst. Video Technol."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"109999","DOI":"10.1016\/j.measurement.2021.109999","article-title":"Stereo camera calibration for large field of view digital image correlation using zoom lens","volume":"185","author":"Gao","year":"2021","journal-title":"Measurement"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"1245","DOI":"10.1016\/j.optlaseng.2011.06.011","article-title":"A calibration method for stereo vision sensor with large FOV based on 1D targets","volume":"49","author":"Sun","year":"2011","journal-title":"Opt. Lasers Eng."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"1106","DOI":"10.1080\/09500340.2019.1601783","article-title":"An improved two-point calibration method for stereo vision with rotating cameras in large FOV","volume":"66","author":"Wang","year":"2019","journal-title":"J. Mod. Opt."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.measurement.2014.11.027","article-title":"A novel and accurate calibration method for cameras with large field of view using combined small targets","volume":"64","author":"Liu","year":"2015","journal-title":"Measurement"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"2956","DOI":"10.1364\/OE.379099","article-title":"Improved separated-parameter calibration method for binocular vision measurements with a large field of view","volume":"28","author":"Zhang","year":"2020","journal-title":"Opt. Express"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"106287","DOI":"10.1016\/j.ymssp.2019.106287","article-title":"Frequency domain triangulation for full-field 3D operating-deflection-shape identification","volume":"133","author":"Gorjup","year":"2019","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"1619","DOI":"10.1002\/we.2505","article-title":"Multicamera measurement system to evaluate the dynamic response of utility-scale wind turbine blades","volume":"23","author":"Poozesh","year":"2020","journal-title":"Wind Energy"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"107991","DOI":"10.1016\/j.measurement.2020.107991","article-title":"A calibration strategy for vision-guided robot assembly system of large cabin","volume":"163","author":"Jiang","year":"2020","journal-title":"Measurement"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"756","DOI":"10.1109\/TPAMI.2004.17","article-title":"An efficient solution to the five-point relative pose problem","volume":"26","author":"Nister","year":"2004","journal-title":"IEEE Trans. Pattern Anal. Mach. Intell."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"580","DOI":"10.1109\/34.601246","article-title":"In defense of the eight-point algorithm","volume":"19","author":"Hartley","year":"1997","journal-title":"IEEE Trans. Pattern Anal. Mach. Intell."},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"Fathian, K., and Gans, N.R. (2014, January 4\u20136). A new approach for solving the Five-Point Relative Pose Problem for vision-based estimation and control. Proceedings of the 2014 American Control Conference, Portland, OR, USA, 2014.","DOI":"10.1109\/ACC.2014.6859364"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"106252","DOI":"10.1016\/j.optlaseng.2020.106252","article-title":"Inertial measurement unit aided extrinsic parameters calibration for stereo vision systems","volume":"134","author":"Feng","year":"2020","journal-title":"Opt. Lasers Eng."},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"D\u2019Alfonso, L., Garone, E., Muraca, P., and Pugliese, P. (2013, January 17\u201319). On the use of the inclinometers in the PnP problem. Proceedings of the 2013 European Control Conference (ECC), Zurich, Switzerland.","DOI":"10.23919\/ECC.2013.6669852"},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Zhang, D., Yu, Z., Xu, Y., Ding, L., Ding, H., Yu, Q., and Su, Z. (2022). GNSS Aided Long-Range 3D Displacement Sensing for High-Rise Structures with Two Non-Overlapping Cameras. Remote Sens., 14.","DOI":"10.3390\/rs14020379"},{"key":"ref_26","unstructured":"Shi, J., and Tomasi, C. (1994, January 21\u201323). Good features to track. Proceedings of the 1994 IEEE Conference on Computer Vision and Pattern Recognition, Seattle, WA, USA."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"014110","DOI":"10.1117\/1.OE.59.1.014110","article-title":"Unmanned aerial vehicle-aided stereo camera calibration for outdoor applications","volume":"59","author":"Feng","year":"2020","journal-title":"Opt. Eng."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"6648","DOI":"10.1364\/AO.397655","article-title":"Real-time Matching Strategy for RotaryObjects using Digital Image Correlation","volume":"59","author":"Yang","year":"2020","journal-title":"Appl. Opt."}],"container-title":["Remote Sensing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2072-4292\/15\/5\/1300\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T18:43:12Z","timestamp":1760121792000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2072-4292\/15\/5\/1300"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,2,26]]},"references-count":28,"journal-issue":{"issue":"5","published-online":{"date-parts":[[2023,3]]}},"alternative-id":["rs15051300"],"URL":"https:\/\/doi.org\/10.3390\/rs15051300","relation":{},"ISSN":["2072-4292"],"issn-type":[{"value":"2072-4292","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,2,26]]}}}