{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T22:12:58Z","timestamp":1760220778012,"version":"build-2065373602"},"reference-count":24,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2012,5,30]],"date-time":"2012-05-30T00:00:00Z","timestamp":1338336000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>A novel and practical self-calibration method for misaligned non-central catadioptric cameras is proposed in this paper. Without the aid of any special calibration patterns in the scene, the developed method is able to automatically estimate the pose parameters of the mirror with respect to the perspective camera. First it uses the ellipse corresponding to the mirror boundary in the image to compute the possible solutions for mirror postures. With two pose candidates, thereafter we propose a novel selection method to find the correct solution by using the image of the lens boundary. The whole calibration process is automatic and convenient to carry out since nothing more than a single image acquired from the catadioptric camera is needed. Experimental results both on synthesized and real images prove our success.<\/jats:p>","DOI":"10.3390\/s120607299","type":"journal-article","created":{"date-parts":[[2012,5,30]],"date-time":"2012-05-30T11:08:12Z","timestamp":1338376092000},"page":"7299-7317","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":10,"title":["The Camera Itself as a Calibration Pattern: A Novel Self-Calibration Method for Non-Central Catadioptric Cameras"],"prefix":"10.3390","volume":"12","author":[{"given":"Zhiyu","family":"Xiang","sequence":"first","affiliation":[{"name":"Zhejiang Provincial Key Laboratory of Information Network Technology, Zhejiang University, No. 38, Zheda Road, Hangzhou 310027, China"},{"name":"Department of Information Science and Electronic Engineering, Zhejiang University, No. 38, Zheda Road, Hangzhou 310027, China"}]},{"given":"Bo","family":"Sun","sequence":"additional","affiliation":[{"name":"Department of Information Science and Electronic Engineering, Zhejiang University, No. 38, Zheda Road, Hangzhou 310027, China"}]},{"given":"Xing","family":"Dai","sequence":"additional","affiliation":[{"name":"Department of Information Science and Electronic Engineering, Zhejiang University, No. 38, Zheda Road, Hangzhou 310027, China"}]}],"member":"1968","published-online":{"date-parts":[[2012,5,30]]},"reference":[{"key":"ref_1","unstructured":"Nayar, S.K. (1997, January 17\u201319). Catadioptric Omnidirectional Camera. San Juan, Puerto Rico."},{"key":"ref_2","unstructured":"Fernando, C.G., Munasinghe, R., and Chittooru, J. (2005, January 20\u201322). Catadioptric Vision Systems: Survey. Tuskegee, AL, USA."},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Agrawal, A., Taguchi, Y., and Ramalingam, S. (2011, January 21\u201323). Beyond Alhazen's Problem: Analytical Projection Model for Non-Central Catadioptric Cameras with Quadric Mirrors. Colorado Springs, CO, USA.","DOI":"10.1109\/CVPR.2011.5995596"},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Srinivasan, M.V. (2003, January 16\u201322). A New Class of Mirrors for Wide-Angle Imaging. Madison, WI, USA. 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Calibration of Catadioptric Sensors by Polarization Imaging. Roma, Italy.","DOI":"10.1109\/ROBOT.2007.364083"},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Ainouz-Zemouche, S., Morel, O., Mosaddegh, S., and Fofi, D. (2009, January 7\u201311). Adapted Processing of Catadioptric Images Using Polarization Imaging. Cairo, Egypt.","DOI":"10.1109\/ICIP.2009.5414488"},{"key":"ref_10","unstructured":"Fabrizio, J., Tarel, J., and Benosman, R. (2002, January 2). Calibration of Panoramic Catadioptric Sensors Made Easier. Washington DC, USA."},{"key":"ref_11","unstructured":"Goncalves, N., and Araujo, H. (2004, January 6\u20139). Projection Model, 3D Reconstruction and Rigid Motion Estimation from Non-Central Catadioptric Cameras. Thessaloniki, Greece."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"1984","DOI":"10.1093\/ietisy\/e89-d.7.1984","article-title":"Calibration Method for Misaligned Catadioptric Camera","volume":"E89 (D)","author":"Mashita","year":"2006","journal-title":"IEICE Trans. Inform. Syst."},{"key":"ref_13","unstructured":"Kang, S.B. (2000, January 13\u201315). Catadioptric Self-Calibration. Hilton Head, SC, USA. Volume 1."},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Stelow, D., Mishler, J., Koes, D., and Singh, S. (2001, January 8\u201314). Precise Omnidirectional Camera Calibration. Kauai, HI, USA. Volume 1.","DOI":"10.1109\/CVPR.2001.990542"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.cviu.2008.06.004","article-title":"Estimating Parameters of Noncentral Catadioptric Systems Using Bundle Adjustment","volume":"113","author":"Goncalves","year":"2009","journal-title":"Comput. Vision Image Understand."},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Caglioti, V., Taddei, P., Boracchi, G., Gasparini, S., and Giusti, A. (2007, January 14\u201320). Single-Image Calibration of Off-Axis Catadioptric Cameras Using Lines. Rio de Janeiro, Brazil.","DOI":"10.1109\/ICCV.2007.4409192"},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Agrawal, A., Taguchi, Y., and Ramalingam, S. (2010, January 5\u201311). Analytical Projection for Axial Non-Central Dioptric and Catadioptric Cameras. Crete, Greece. Volume 6313.","DOI":"10.1007\/978-3-642-15558-1_10"},{"key":"ref_18","unstructured":"Chen, Q., Wu, H., and Wada, T. (July, January 27). Camera Calibration with Two Arbitrary Coplanar Circles. Washington DC, USA. Volume 3."},{"key":"ref_19","unstructured":"Bouguet, J.Y. Camera Calibration Toolbox for Matlab. Available online: http:\/\/www.vision.caltech.edu\/bouguetj\/calib_doc\/ (accessed on 7 January 2012)."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"476","DOI":"10.1109\/34.765658","article-title":"Direct Least Square Fitting of Ellipses","volume":"21","author":"Fitzgibbon","year":"1999","journal-title":"IEEE Trans. Patt. Anal. Mach. Intell."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"381","DOI":"10.1145\/358669.358692","article-title":"Random Sample Consensus: A Paradigm for Model Fitting with Applications to Image Analysis and Automated Cartography","volume":"24","author":"Fischler","year":"1981","journal-title":"Commun. ACM"},{"key":"ref_22","unstructured":"Xiang, Z., and Sun, B. (2011, January 24\u201326). A Novel Self-Calibration Method for Non-Central Catadioptric Camera System. Guangzhou, China. Volume 1."},{"key":"ref_23","unstructured":"Press, W.H., Vetterling, W.T., Teukolsky, S.A., and Flannery, B.P. (1997). Numerical Recipes in C: The Art of Scientific Computing, Cambridge University Press. [2nd ed.]."},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Mei, C., and Rives, P. (2007, January 10\u201314). Single View Point Omnidirectional Camera Calibration from Planar Grids. 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