{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,20]],"date-time":"2026-02-20T19:24:04Z","timestamp":1771615444708,"version":"3.50.1"},"reference-count":31,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2018,10,29]],"date-time":"2018-10-29T00:00:00Z","timestamp":1540771200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Nowadays, binocular stereo vision (BSV) is extensively used in real-time 3D reconstruction, which requires cameras to quickly implement self-calibration. At present, the camera parameters are typically estimated through iterative optimization. The calibration accuracy is high, but the process is time consuming. Hence, a system of BSV with rotating and non-zooming cameras is established in this study, in which the cameras can rotate horizontally and vertically. The cameras\u2019 intrinsic parameters and initial position are estimated in advance by using Zhang\u2019s calibration method. Only the yaw rotation angle in the horizontal direction and pitch in the vertical direction for each camera should be obtained during rotation. Therefore, we present a novel self-calibration method by using a single feature point and transform the imaging model of the pitch and yaw into a quadratic equation of the tangent value of the pitch. The closed-form solutions of the pitch and yaw can be obtained with known approximate values, which avoid the iterative convergence problem. Computer simulation and physical experiments prove the feasibility of the proposed method. Additionally, we compare the proposed method with Zhang\u2019s method. Our experimental data indicate that the averages of the absolute errors of the Euler angles and translation vectors relative to the reference values are less than 0.21\u00b0 and 6.6 mm, respectively, and the averages of the relative errors of 3D reconstruction coordinates do not exceed 4.2%.<\/jats:p>","DOI":"10.3390\/s18113666","type":"journal-article","created":{"date-parts":[[2018,10,29]],"date-time":"2018-10-29T11:10:41Z","timestamp":1540811441000},"page":"3666","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":19,"title":["A Method for Extrinsic Parameter Calibration of Rotating Binocular Stereo Vision Using a Single Feature Point"],"prefix":"10.3390","volume":"18","author":[{"given":"Yue","family":"Wang","sequence":"first","affiliation":[{"name":"State Key Laboratory of Precision Measuring Technology and Instruments, Tianjin University, Tianjin 300072, China"},{"name":"Key Laboratory of MOEMS of the Ministry of Education, Tianjin University, Tianjin 300072, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6199-1632","authenticated-orcid":false,"given":"Xiangjun","family":"Wang","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Precision Measuring Technology and Instruments, Tianjin University, Tianjin 300072, China"},{"name":"Key Laboratory of MOEMS of the Ministry of Education, Tianjin University, Tianjin 300072, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3158-8746","authenticated-orcid":false,"given":"Zijing","family":"Wan","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Precision Measuring Technology and Instruments, Tianjin University, Tianjin 300072, China"},{"name":"Key Laboratory of MOEMS of the Ministry of Education, Tianjin University, Tianjin 300072, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jiahao","family":"Zhang","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Precision Measuring Technology and Instruments, Tianjin University, Tianjin 300072, China"},{"name":"Key Laboratory of MOEMS of the Ministry of Education, Tianjin University, Tianjin 300072, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2018,10,29]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"345","DOI":"10.1109\/70.34770","article-title":"A technique for fully autonomous and efficient 3D robotics hand\/eye calibration","volume":"5","author":"Tsai","year":"1989","journal-title":"IEEE Trans. Robot. Autom."},{"key":"ref_2","unstructured":"Tsai, R.Y. (1986, January 22\u201326). An efficient and accurate camera calibration technique for 3D machine vision. Proceedings of the CVPR\u201986: IEEE Computer Society Conference on Computer Vision and Pattern Recognition, Miami Beach, FL, USA."},{"key":"ref_3","unstructured":"Tian, S.-X., Lu, S., and Liu, Z.-M. (2015, January 28\u201330). Levenberg-Marquardt algorithm based nonlinear optimization of camera calibration for relative measurement. Proceedings of the 34th Chinese Control Conference, Hangzhou, China."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"2484","DOI":"10.1016\/j.patcog.2007.12.010","article-title":"Camera self-calibration from bivariate polynomials derived from Kruppa\u2019s equations","volume":"41","author":"Habed","year":"2008","journal-title":"Pattern Recognit."},{"key":"ref_5","unstructured":"Wang, L., Kang, S.-B., Shum, H.-Y., and Xu, G.-Y. (2001, January 7\u201314). Error analysis of pure rotation based self-calibration. Proceedings of the Eighth IEEE International Conference on Computer Vision, Vancouver, BC, Canada."},{"key":"ref_6","unstructured":"Hemayed, E.E. (2003, January 21\u201322). A survey of camera calibration. Proceedings of the IEEE Conference on Advanced Video and Signal Based Surveillance, Miami, FL, USA."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"103","DOI":"10.14358\/PERS.81.2.103","article-title":"Direct linear transformation into object space coordinates in close-range photogrammetry","volume":"81","author":"Karara","year":"2015","journal-title":"Photogramm. Eng. Remote Sens."},{"key":"ref_8","first-page":"308","article-title":"Automatic calibration of computer vision based on RAC calibration algorithm","volume":"7","author":"Zhang","year":"2015","journal-title":"Metall. Min. Ind."},{"key":"ref_9","unstructured":"Zhang, Z. (1999, January 20\u201327). Flexible camera calibration by viewing a plane from unknown orientations. Proceedings of the Seventh IEEE International Conference on Computer Vision, Kerkyra, Greece."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"173","DOI":"10.1016\/0146-664X(81)90024-1","article-title":"Camera models based on data from two calibration planes","volume":"17","author":"Martins","year":"1981","journal-title":"Comput. Graph. Image Process."},{"key":"ref_11","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 2nd European Conference on Computer Vision, Santa Margherita Ligure, Italy.","DOI":"10.1007\/3-540-55426-2_37"},{"key":"ref_12","first-page":"820","article-title":"Camera linear self-calibration method based on the Kruppa equation","volume":"37","author":"Li","year":"2003","journal-title":"J. Xi'an Jiaotong Univ."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"1036","DOI":"10.1109\/34.329005","article-title":"Euclidean reconstruction and invariants from multiple images","volume":"16","author":"Hartley","year":"1994","journal-title":"IEEE Trans. Pattern Anal. Mach. Intell."},{"key":"ref_14","unstructured":"Triggs, B. (1997, January 17\u201319). Auto-calibration and the absolute quadric. Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition, San Juan, PR, USA."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"114","DOI":"10.1109\/70.481755","article-title":"A self-calibration technique for active vision system","volume":"12","year":"1996","journal-title":"IEEE Trans. Robot. Autom."},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Zhang, Z., and Tang, Q. (2016, January 6\u20138). Camera self-calibration based on multiple view images. Proceedings of the Nicograph International (NicoInt), Hanzhou, China.","DOI":"10.1109\/NicoInt.2016.16"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"1994","DOI":"10.1109\/TPAMI.2012.250","article-title":"Keeping a pan-tilt-zoom camera calibrated","volume":"35","author":"Wu","year":"2013","journal-title":"IEEE Trans. Pattern Anal. Mach. Intell."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"375","DOI":"10.1007\/s00138-011-0326-z","article-title":"Optimizing PTZ camera calibration from two images","volume":"23","author":"Junejo","year":"2012","journal-title":"Mach. Vis. Appl."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"159","DOI":"10.1007\/BF01214428","article-title":"A camera calibration technique using three sets of parallel lines","volume":"3","author":"Echigo","year":"1990","journal-title":"Mach. Vis. Appl."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"1091","DOI":"10.1109\/TSMCB.2006.872271","article-title":"Dynamic calibration of Pan-Tilt-Zoom cameras for traffic monitoring","volume":"36","author":"Song","year":"2006","journal-title":"IEEE Trans. Syst. Man Cybern. Part B"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"90","DOI":"10.1109\/TITS.2003.821213","article-title":"Dynamic camera calibration of roadside traffic management cameras for vehicle speed estimation","volume":"4","author":"Schoepflin","year":"2003","journal-title":"IEEE Trans. Intell. Transp. Syst."},{"key":"ref_22","unstructured":"Kim, H., and Hong, K.S. (2000, January 3\u20137). A practical self-calibration method of rotating and zooming cameras. Proceedings of the 15th International Conference on Pattern Recognition, Barcelona, Spain."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"5601","DOI":"10.1016\/j.optcom.2011.08.045","article-title":"Online self-camera orientation based on laser metrology and computer algorithms","volume":"284","year":"2011","journal-title":"Opt. Commun."},{"key":"ref_24","first-page":"1219","article-title":"Binocular self-calibration performed via adaptive genetic algorithm based on laser line imaging","volume":"63","year":"2016","journal-title":"J. Mod. Opt."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1109\/TRA.2003.820921","article-title":"Self-calibration of a rotating camera with a translational offset","volume":"20","author":"Ji","year":"2004","journal-title":"IEEE Trans. Robot. Autom."},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Cai, H., Zhu, W., Li, K., and Liu, M. (2011, January 28\u201330). A linear camera self-calibration approach from four points. Proceedings of the 4th International Symposium on Computational Intelligence and Design, Hangzhou, China.","DOI":"10.1109\/ISCID.2011.59"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"432","DOI":"10.1007\/s10851-012-0336-0","article-title":"A Self-calibration algorithm based on a unified framework for constraints on multiple views","volume":"44","author":"Tang","year":"2012","journal-title":"J. Math. Imaging Vis."},{"key":"ref_28","unstructured":"Yu, H., and Wang, Y. (2006, January 21\u201323). An improved self-calibration method for active stereo camera. Proceedings of the Sixth World Congress on Intelligent Control and Automation, Dalian, China."},{"key":"ref_29","unstructured":"De Agapito, L., Hartley, R.I., and Hayman, E. (1999, January 23\u201325). Linear self-calibration of a rotating and zooming camera. Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition, Fort Collins, CO, USA."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"370","DOI":"10.1109\/JAS.2017.7510556","article-title":"Effective self-calibration for camera parameters and hand-eye geometry based on two feature points motions","volume":"4","author":"Sun","year":"2017","journal-title":"IEEE\/CAA J. Autom. Sin."},{"key":"ref_31","doi-asserted-by":"crossref","unstructured":"Chen, J., Zhu, F., and Little, J.J. (2018, January 12\u201315). A two-point method for PTZ camera calibration in sports. Proceedings of the IEEE Winter Conference on Applications of Computer Vision (WACV), Lake Tahoe, NV, USA.","DOI":"10.1109\/WACV.2018.00038"}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/18\/11\/3666\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T15:26:45Z","timestamp":1760196405000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/18\/11\/3666"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,10,29]]},"references-count":31,"journal-issue":{"issue":"11","published-online":{"date-parts":[[2018,11]]}},"alternative-id":["s18113666"],"URL":"https:\/\/doi.org\/10.3390\/s18113666","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,10,29]]}}}