{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,13]],"date-time":"2026-04-13T01:25:30Z","timestamp":1776043530844,"version":"3.50.1"},"reference-count":56,"publisher":"MDPI AG","issue":"23","license":[{"start":{"date-parts":[[2019,11,21]],"date-time":"2019-11-21T00:00:00Z","timestamp":1574294400000},"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>With extensive application of RGB-D cameras in robotics, computer vision, and many other fields, accurate calibration becomes more and more critical to the sensors. However, most existing models for calibrating depth and the relative pose between a depth camera and an RGB camera are not universally applicable to many different kinds of RGB-D cameras. In this paper, by using the collinear equation and space resection of photogrammetry, we present a new model to correct the depth and calibrate the relative pose between depth and RGB cameras based on a 3D control field. We establish a rigorous relationship model between the two cameras; then, we optimize the relative parameters of two cameras by least-squares iteration. For depth correction, based on the extrinsic parameters related to object space, the reference depths are calculated by using a collinear equation. Then, we calibrate the depth measurements with consideration of the distortion of pixels in depth images. We apply Kinect-2 to verify the calibration parameters by registering depth and color images. We test the effect of depth correction based on 3D reconstruction. Compared to the registration results from a state-of-the-art calibration model, the registration results obtained with our calibration parameters improve dramatically. Likewise, the performances of 3D reconstruction demonstrate obvious improvements after depth correction.<\/jats:p>","DOI":"10.3390\/s19235082","type":"journal-article","created":{"date-parts":[[2019,11,22]],"date-time":"2019-11-22T02:49:27Z","timestamp":1574390967000},"page":"5082","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":20,"title":["A New Model of RGB-D Camera Calibration Based on 3D Control Field"],"prefix":"10.3390","volume":"19","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-2687-000X","authenticated-orcid":false,"given":"Chenyang","family":"Zhang","sequence":"first","affiliation":[{"name":"School of Earth Sciences and Engineering, Hohai University, Nanjing 211100, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Teng","family":"Huang","sequence":"additional","affiliation":[{"name":"School of Earth Sciences and Engineering, Hohai University, Nanjing 211100, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Qiang","family":"Zhao","sequence":"additional","affiliation":[{"name":"Huawei Technologies Co. Ltd., Beijing 100085, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2019,11,21]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"El-Laithy, R.A., Huang, J., and Yeh, M. (2012, January 23\u201326). Study on the use of Microsoft Kinect for robotics applications. Proceedings of the 2012 IEEE\/ION Position, Location and Navigation Symposium, Myrtle Beach, SC, USA.","DOI":"10.1109\/PLANS.2012.6236985"},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Oliver, A., Burkhard, C.W., Kang, S., and MacDonald, B. (2012, January 26\u201328). Using the Kinect as a Navigation Sensor for Mobile Robotics ABSTRACT. Proceedings of the 27th Conference on Image and Vision Computing (IVCNZ \u201912), Dunedin, New Zealand.","DOI":"10.1145\/2425836.2425932"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"647","DOI":"10.1177\/0278364911434148","article-title":"RGB-D mapping: Using Kinect style depth cameras for dense 3D modeling of indoor environments","volume":"31","author":"Henry","year":"2012","journal-title":"Int. J. Robot. Res."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"1318","DOI":"10.1109\/TCYB.2013.2265378","article-title":"Enhanced Computer Vision with Microsoft Kinect Sensor: A Review","volume":"43","author":"Han","year":"2013","journal-title":"IEEE Trans. Cybern."},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Alnowami, M., Tahavori, F., and Wells, K. (2012, January 4\u20139). A quantitative assessment of using the Kinect for Xbox 360 for respiratory surface motion tracking. Proceedings of the SPIE\u2014The International Society for Optical Engineering, San Diego, CA, USA.","DOI":"10.1117\/12.911463"},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Guevara, D.C., Vietri, G., Prabakar, M., and Kim, J. (2013, January 3\u20135). Robotic Exoskeleton System Controlled by Kinect and Haptic Sensors for Physical Therapy. Proceedings of the 2013 29th Southern Biomedical Engineering Conference, Miami, FL, USA.","DOI":"10.1109\/SBEC.2013.44"},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Di, K., Zhao, Q., Wan, W., Wang, Y., and Gao, Y. (2016). RGB-D SLAM Based on Extended Bundle Adjustment with 2D and 3D Information. Sensors, 16.","DOI":"10.3390\/s16081285"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"4","DOI":"10.1109\/MMUL.2012.24","article-title":"Microsoft Kinect Sensor and Its Effect","volume":"19","author":"Zhang","year":"2012","journal-title":"IEEE Multimed."},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Villena-Mart\u00ednez, V., Fuster-Guill\u00f3, A., Azor\u00edn-L\u00f3pez, J., Saval-Calvo, M., Mora-Pascual, J., Garcia-Rodriguez, J., and Garcia-Garcia, A. (2017). A Quantitative Comparison of Calibration Methods for RGB-D Sensors Using Different Technologies. Sensors, 17.","DOI":"10.3390\/s17020243"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.cviu.2015.05.006","article-title":"Kinect range sensing: Structured-light versus Time-of-Flight Kinect","volume":"135","author":"Sarbolandi","year":"2015","journal-title":"Comput. Vis. Image Underst."},{"key":"ref_11","first-page":"3","article-title":"Technical Foundation and Calibration Methods for Time-of-Flight Cameras","volume":"Volume 8200","author":"Grzegorzek","year":"2013","journal-title":"Time-of-Flight and Depth Imaging"},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Haggag, H., Hossny, M., Filippidis, D., Creighton, D., Nahavandi, S., and Puri, V. (2013, January 16\u201318). Measuring depth accuracy in RGBD cameras. Proceedings of the 2013 7th International Conference on Signal Processing and Communication Systems (ICSPCS), Carrara, VIC, Australia.","DOI":"10.1109\/ICSPCS.2013.6723971"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"27569","DOI":"10.3390\/s151127569","article-title":"Calibration of Kinect for Xbox One and Comparison between the Two Generations of Microsoft Sensors","volume":"15","author":"Diana","year":"2015","journal-title":"Sensors"},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Newcombe, R.A., Izadi, S., Hilliges, O., Molyneaux, D., Kim, D., Davison, A.J., Kohli, P., Shotton, J., Hodges, S., and Fitzgibbon, A.W. (2011, January 28). Kinect Fusion: Real-time dense surface mapping and tracking. Proceedings of the 2011 10th IEEE International Symposium on Mixed and Augmented Reality, Basel, Switzerland.","DOI":"10.1109\/ISMAR.2011.6162880"},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Zhang, C., and Zhang, Z. (2011, January 11\u201315). Calibration between depth and color sensors for commodity depth cameras. Proceedings of the 2011 IEEE International Conference on Multimedia and Expo, Barcelona, Spain.","DOI":"10.1109\/ICME.2011.6012191"},{"key":"ref_16","unstructured":"Daniel, H.C., Kannala, J., and Janne, H. (2011, January 29\u201331). Accurate and Practical Calibration of a Depth and Color Camera Pair. Proceedings of the Computer Analysis of Images and Patterns-14th International Conference, Seville, Spain."},{"key":"ref_17","unstructured":"(2019, August 09). Kinect Camera Calibration. Available online: http:\/\/doc-ok.org\/?p=289."},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Jung, J., Jeong, Y., Park, J., Ha, H., Kim, J.D., and Kweon, I.-S. (2011, January 25\u201330). A novel 2.5D pattern for extrinsic calibration of tof and camera fusion system. Proceedings of the 2011 IEEE\/RSJ International Conference on Intelligent Robots and Systems, San Francisco, CA, USA.","DOI":"10.1109\/IROS.2011.6095113"},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Shibo, L., and Qing, Z. (2012, January 26\u201327). A New Approach to Calibrate Range Image and Color Image from Kinect. Proceedings of the 2012 4th International Conference on Intelligent Human-Machine Systems and Cybernetics (IHMSC), Nanchang, China.","DOI":"10.1109\/IHMSC.2012.156"},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Liu, W., Fan, Y., Zhong, Z., and Lei, T. (2012, January 16\u201318). A new method for calibrating depth and color camera pair based on Kinect. Proceedings of the 2012 International Conference on Audio, Language and Image Processing, IEEE, Shanghai, China.","DOI":"10.1109\/ICALIP.2012.6376614"},{"key":"ref_21","first-page":"415","article-title":"Easy-to-Use and Accurate Calibration of RGB-D Cameras from Spheres","volume":"165","author":"Staranowicz","year":"2014","journal-title":"J. Plant Physiol."},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"Chen, C., Yang, B., Song, S., Tian, M., Li, J., Dai, W., and Fang, L. (2018). Calibrate Multiple Consumer RGB-D Cameras for Low-Cost and Efficient 3D Indoor Mapping. Remote Sens., 10.","DOI":"10.3390\/rs10020328"},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Smisek, J., Jancosek, M., and Pajdla, T. (2011, January 6\u201313). 3D with Kinect. Proceedings of the IEEE International Conference on Computer Vision, Barcelona, Spain.","DOI":"10.1109\/ICCVW.2011.6130380"},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Kim, S.Y., Cho, W., Koschan, A., and Abidi, M.A. (2011, January 7\u20138). Depth data calibration and enhancement of time-of-flight video-plus-depth camera. Proceedings of the 2011 Future of Instrumentation International Workshop (FIIW) Proceedings, Oak Ridge, TN, USA.","DOI":"10.1109\/FIIW.2011.6476812"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"227","DOI":"10.1016\/j.jvcir.2013.02.011","article-title":"Calibrated depth and color cameras for accurate 3D interaction in a stereoscopic augmented reality environment","volume":"25","author":"Canessa","year":"2014","journal-title":"J. Vis. Commun. Image Represent."},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Lindner, M., and Kolb, A. (2006). Lateral and Depth Calibration of PMD-Distance Sensors. Advances in Visual Computing, Springer.","DOI":"10.1007\/11919629_53"},{"key":"ref_27","first-page":"67640W","article-title":"Calibration of the Intensity-Related Distance Error of the PMD TOF Camera. In Proceedings of the Intelligent Robots and Computer Vision XXV: Algorithms, Techniques, and Active Vision","volume":"6764","author":"Lindner","year":"2007","journal-title":"Int. Soc. Opt. Photonics"},{"key":"ref_28","doi-asserted-by":"crossref","unstructured":"Fuchs, S., and Hirzinger, G. (2008, January 23\u201328). Extrinsic and depth calibration of ToF cameras. Proceedings of the 2008 IEEE Conference on Computer Vision and Pattern Recognition, Anchorage, AK, USA.","DOI":"10.1109\/CVPR.2008.4587828"},{"key":"ref_29","doi-asserted-by":"crossref","unstructured":"Gui, P., Ye, Q., Chen, H., Zhang, T., and Yang, C. (2014, January 11\u201314). Accurately calibrate kinect sensor using indoor control field. Proceedings of the 2014 Third International Workshop on Earth Observation and Remote Sensing Applications (EORSA), Changsha, China.","DOI":"10.1109\/EORSA.2014.6927839"},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"1501","DOI":"10.1109\/TPAMI.2014.2363827","article-title":"Time-of-Flight Sensor Calibration for a Color and Depth Camera Pair","volume":"37","author":"Jung","year":"2015","journal-title":"IEEE Trans. Pattern Anal. Mach. Intell."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"1437","DOI":"10.3390\/s120201437","article-title":"Accuracy and Resolution of Kinect Depth Data for Indoor Mapping Applications","volume":"12","author":"Khoshelham","year":"2012","journal-title":"Sensors"},{"key":"ref_32","doi-asserted-by":"crossref","unstructured":"Nguyen, C.V., Izadi, S., and Lovell, D. (2012, January 13\u201315). Modeling Kinect Sensor Noise for Improved 3D Reconstruction and Tracking. Proceedings of the 2012 Second International Conference on 3D Imaging, Modeling, Processing, Visualization & Transmission, Zurich, Switzerland.","DOI":"10.1109\/3DIMPVT.2012.84"},{"key":"ref_33","first-page":"1","article-title":"Accurate Intrinsic and Extrinsic Calibration of RGB-D Cameras with GP-based Depth Correction","volume":"99","author":"Chen","year":"2018","journal-title":"IEEE Sens. J."},{"key":"ref_34","doi-asserted-by":"crossref","unstructured":"Ferstl, D., Reinbacher, C., Riegler, G., R\u00fcther, M., and Bischof, H. (2015, January 7\u201310). Learning Depth Calibration of Time-of-Flight Camera. Proceedings of the British Machine Vision Conference, Swansea, UK.","DOI":"10.5244\/C.29.102"},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"309","DOI":"10.1016\/j.robot.2015.08.004","article-title":"Non-Parametric Calibration for Depth Sensors","volume":"74","author":"Cicco","year":"2015","journal-title":"Robot. Auton. Syst."},{"key":"ref_36","doi-asserted-by":"crossref","unstructured":"Teichman, A., Miller, S., and Thrun, S. (2013, January 24\u201328). Unsupervised Intrinsic Calibration of Depth Sensors via SLAM. Proceedings of the Robotics Science and Systems 2013, Berlin, Germany.","DOI":"10.1109\/IROS.2013.6696737"},{"key":"ref_37","doi-asserted-by":"crossref","unstructured":"Quenzel, J., Rosu, R.A., Houben, S., and Behnke, S. (2017, January 24\u201328). Online depth calibration for RGB-D cameras using visual SLAM. Proceedings of the 2017 IEEE\/RSJ International Conference on Intelligent Robots and Systems (IROS), Vancouver, BC, Canada.","DOI":"10.1109\/IROS.2017.8206043"},{"key":"ref_38","doi-asserted-by":"crossref","unstructured":"Miller, S., Teichman, A., and Thrun, S. (2013, January 3\u20137). Unsupervised extrinsic calibration of depth sensors in dynamic scenes. Proceedings of the 2013 IEEE\/RSJ International Conference on Intelligent Robots and Systems, Tokyo, Japan.","DOI":"10.1109\/IROS.2013.6696737"},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"2058","DOI":"10.1109\/TPAMI.2012.125","article-title":"Joint Depth and Color Camera Calibration with Distortion Correction","volume":"34","author":"Herrera","year":"2012","journal-title":"IEEE Trans. Pattern Anal. Mach. Intell."},{"key":"ref_40","first-page":"1584","article-title":"Calibration of Kinect sensor with depth and color camera","volume":"19","author":"Guo","year":"2014","journal-title":"J. Image Graph."},{"key":"ref_41","doi-asserted-by":"crossref","unstructured":"Raposo, C., Barreto, J.P., and Nunes, U. (July, January 29). Fast and accurate calibration of a kinect sensor. Proceedings of the 2013 International Conference on 3DTV-Conference, Seattle, WA, USA.","DOI":"10.1109\/3DV.2013.52"},{"key":"ref_42","doi-asserted-by":"crossref","unstructured":"Jin, B., Lei, H., and Geng, W. (2014). Accurate Intrinsic Calibration of Depth Camera with Cuboids. European Conference on Computer Vision, Springer.","DOI":"10.1007\/978-3-319-10602-1_51"},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"103","DOI":"10.1007\/s41095-017-0103-7","article-title":"Depth error correction for projector-camera based consumer depth cameras","volume":"4","author":"Yamazoe","year":"2018","journal-title":"Comput. Vis. Media"},{"key":"ref_44","doi-asserted-by":"crossref","unstructured":"Darwish, W., Tang, S., Li, W., and Chen, W. (2017). A New Calibration Method for Commercial RGB-D Sensors. Sensors, 17.","DOI":"10.3390\/s17061204"},{"key":"ref_45","unstructured":"Yamazoe, H., Habe, H., Mitsugami, I., and Yagi, Y. (2012, January 11\u201315). Easy depth sensor calibration. Proceedings of the 21st International Conference on Pattern Recognition (ICPR2012), Tsukuba, Japan."},{"key":"ref_46","doi-asserted-by":"crossref","unstructured":"Kim, J.-H., Choi, J.S., and Koo, B.K. (2013, January 24\u201326). Calibration of multi-Kinect and multi-camera setup for full 3D reconstruction. Proceedings of the IEEE ISR 2013, Seoul, South Korea.","DOI":"10.1109\/ISR.2013.6695729"},{"key":"ref_47","doi-asserted-by":"crossref","unstructured":"Chow, J.C.K., Ang, K.D., Lichti, D.D., and Teskey, W.F. (September, January 25). Preformance analysis of a low-cost triangulation-based 3D camera: Microsoft Kinect System. Proceedings of the International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Volume XXXIX-B5, 2012 XXII ISPRS Congress, Melbourne, Australia.","DOI":"10.5194\/isprsarchives-XXXIX-B5-175-2012"},{"key":"ref_48","doi-asserted-by":"crossref","first-page":"465","DOI":"10.1109\/ACCESS.2013.2271860","article-title":"Photogrammetric Bundle Adjustment with Self-Calibration of the PrimeSense 3D Camera Technology: Microsoft Kinect","volume":"1","author":"Chow","year":"2013","journal-title":"IEEE Access"},{"key":"ref_49","doi-asserted-by":"crossref","first-page":"1066","DOI":"10.1109\/34.879788","article-title":"Geometric camera calibration using circular control points","volume":"22","author":"Heikkila","year":"2002","journal-title":"IEEE Trans. Pattern Anal. Mach. Intell."},{"key":"ref_50","first-page":"43","article-title":"Overview of camera calibration for computer vision","volume":"26","author":"Maolin","year":"2000","journal-title":"IEEE\/CAA J. Autom. Sin."},{"key":"ref_51","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_52","first-page":"855","article-title":"Close-Range Camera Calibration","volume":"37","author":"Brown","year":"1987","journal-title":"Photo Eng."},{"key":"ref_53","unstructured":"Feng, W.H. (2002). Close-Range Photogrammetry, Wuhan University Press."},{"key":"ref_54","unstructured":"Zhang, Z.Z.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, Corfu, Greece."},{"key":"ref_55","doi-asserted-by":"crossref","first-page":"13070","DOI":"10.3390\/rs71013070","article-title":"Assessment and Calibration of a RGB-D Camera towards a Potential Use for Close-Range 3D Modeling","volume":"7","author":"Lachat","year":"2015","journal-title":"Remote Sens."},{"key":"ref_56","unstructured":"Bouguet, J.Y. (2019, August 09). Camera Calibration Toolbox. Available online: http:\/\/www.vision.caltech.edu\/bouguetj\/calib_doc\/."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/19\/23\/5082\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T13:36:16Z","timestamp":1760189776000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/19\/23\/5082"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,11,21]]},"references-count":56,"journal-issue":{"issue":"23","published-online":{"date-parts":[[2019,12]]}},"alternative-id":["s19235082"],"URL":"https:\/\/doi.org\/10.3390\/s19235082","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019,11,21]]}}}