15.2 Camera Calibration Techniques

Chapter Contents (Back)
See related papers under General Industrial Applications. One distinction is self-calibration vs. calibrated object. Or: Where is the camera. Camera Calibration.

CVonline: System Models, Calibration and Parameter Estimation,
CV-OnlineJuly 2001.
HTML Version. Survey, Calibration. BibRef 0107

Horn, B.K.P.,
Relative Orientation,
IJCV(4), No. 1, January 1990, pp. 59-78. BibRef 9001
Earlier: DARPA88(826-837). BibRef
And: MIT AI Memo-994, September 1987. Motion, Two Frames. This is also heavily used in the two-frame motion estimation work. Use the standard photogrammetry techniques to find the relative orientation of two cameras. An iterative scheme that requires five matching points (not on a critical surface). See also Closed Form Solutions of Absolute Orientation Using Orthonormal Matrices. BibRef

Horn, B.K.P.,
Relative Orientation Revisited,
JOSA-A(8), No. 10, October 1991, pp. 1630-1638 BibRef 9110

Parrish, Jr., E.A., Goksel, A.K.,
A Camera Model for Natural Scene Processing,
PR(9), No. 3, October 1977, pp. 131-136.
WWW Version. BibRef 7710

Liu, Y., Huang, T.S., and Faugeras, O.D.,
Determination of Camera Location from 2-D to 3-D Line and Point Correspondences,
PAMI(12), No. 1, January 1990, pp. 28-37.
IEEE Abstract. IEEE Top Reference.
WWW Version. BibRef 9001
Earlier: CVPR88(82-88).
IEEE Abstract. IEEE Top Reference. Perspective assumption. 8 line correspondences or 6 point correspondences are required for a linear solution. 3 lines or points are needed for nonlinear. Correspondence is 2-D image to 3-D model. How does this correspond to the photogrammetry approaches? BibRef

Holt, R.J., and Netravali, A.N.,
Camera Calibration Problems: Some New Results,
CVGIP(54), No. 3, November 1991, pp. 368-383.
WWW Version. For 4 non-coplanar points the solution is usually unique, but can have four solutions. BibRef 9111

Kanatani, K.,
Camera Rotation Invariance of Image Characteristics,
CVGIP(39), No. 3, September 1987, pp. 328-354. BibRef 8709
Earlier: CVPR86(266-271). See also Transformation of Optical Flow by Camera Rotation. BibRef

Buchanan, T.,
The Twisted Cubic and Camera Calibration,
CVGIP(42), No. 1, April 1988, pp. 130-132. BibRef 8804

Wei, G.Q., and Ma, S.D.,
Implicit and Explicit Camera Calibration: Theory and Experiments,
PAMI(16), No. 5, May 1994, pp. 469-480.
IEEE Abstract. IEEE Top Reference.
WWW Version. BibRef 9405
Earlier:
A Complete Two-Plane Camera Calibration Method and Experimental Comparisons,
ICCV93(439-446).
WWW Version. BibRef
Earlier:
Two Plane Camera Calibration: A Unified Model,
CVPR91(133-138).
IEEE Abstract. IEEE Top Reference. BibRef

Qiu, M.[MaoLin], Ma, S.D.[Song De],
The Nonparametric Approach for Camera Calibration,
ICCV95(224-229).
WWW Version.
WWW Version. Constrained topological mapping. BibRef 9500

Chen, S.Y., and Tsai, W.H.,
A Systematic Approach to Analytic Determination of Camera Parameters by Line Features,
PR(23), No. 8, 1990, pp. 859-877.
WWW Version. BibRef 9000

Lai, J.Z.C.,
On the Sensitivity of Camera Calibration,
IVC(11), No. 10, December 1993, pp. 656-664.
WWW Version. BibRef 9312

Kumar, R., and Hanson, A.R.,
Robust Methods for Estimating Pose and a Sensitivity Analysis,
CVGIP(60), No. 3, November 1994, pp. 313-342.
WWW Version. BibRef 9411
Earlier:
Application of Pose Determination Techniques to Model Extension and Refinement,
DARPA92(737-744). BibRef
Earlier:
Sensitivity of the Pose Refinement Problem to Accurate Estimation of Camera Parameters,
ICCV90(365-369).
WWW Version. BibRef
And:
Pose Refinement: Application to Model Extension and Sensitivity to Camera Parameters,
DARPA90(660-669). BibRef
And: COINS-TR-90-112, November 1990. Pose Estimation, Evaluation. Analysis of the errors that occur. Eliminate the outliers to improve results. BibRef

Kumar, R., and Hanson, A.R.,
Analysis of Different Robust Methods for Pose Refinement,
Robust90(xx). BibRef 9000
Earlier:
Robust Estimation of Camera Location and Orientation from Noisy Data Having Outliers,
3DWS89(52-60). BibRef
And: COINS-TR-89-120, December 1989. BibRef

Kumar, R.,
Determination of Camera Location and Orientation,
DARPA89(870-881). Given 2-D matching of landmarks in a scene, find the location of the camera by finding the R and T that map the 3-D scene into the 2-D lines. BibRef 8900

Grosky, W.I., and Tamburino, L.A.,
A Unified Approach to the Linear Camera Calibration Problem,
PAMI(12), No. 7, July 1990, pp. 663-671.
IEEE Abstract. IEEE Top Reference.
WWW Version. BibRef 9007
Earlier: ICCV87(511-515). BibRef

Ito, M., Ishii, A.,
A Noniterative Procedure for Rapid and Precise Camera Calibration,
PR(27), No. 2, February 1994, pp. 301-310.
WWW Version. BibRef 9402

Han, M.H., Rhee, S.,
Camera Calibration for Three-Dimensional Measurement,
PR(25), No. 2, February 1992, pp. 155-164.
WWW Version. BibRef 9202

Perrin, S., Redarce, T.,
CCD Camera Modeling and Simulation,
JIRS(17), No. 3, November 1996, pp. 309-325. 9701 BibRef

Cumani, A., Guiducci, A.,
A New Camera Calibration Method for High Accuracy Non-Contact Metrology,
PRL(14), 1993, pp. 415-419. BibRef 9300

Chatterjee, C., Roychowdhury, V.P., Chong, E.K.P.,
A Nonlinear Gauss-Seidel Algorithm for Noncoplanar and Coplanar Camera Calibration with Convergence Analysis,
CVIU(67), No. 1, July 1997, pp. 58-80. 9707
WWW Version. BibRef

Chatterjee, C.[Chanchal], Roychowdhury, V.P.[Vwani P.],
Algorithms for coplanar camera calibration,
MVA(12), No. 2, 2000, pp. 84-97.
HTML Version. 0010 BibRef

Koenderink, J.J., van Doorn, A.J.,
The Generic Bilinear Calibration-Estimation Problem,
IJCV(23), No. 3, June-July 1997, pp. 217-234.
WWW Version. 9708 BibRef

Zhang, Z.Y.[Zheng-You],
On The Optimization Criteria Used in Two-View Motion Analysis,
PAMI(20), No. 7, July 1998, pp. 717-729.
IEEE Abstract. IEEE Top Reference.
WWW Version. 9808 BibRef
Earlier:
Understanding the Relationship Between the Optimization Criteria in Two-View Motion Analysis,
ICCV98(772-777).
WWW Version. Shows the criteria: Gradient weighted epipolar errors and distances between points and their reprojections are equivalent, when epipoles are at infinity. And the first of these and the criterion: distance between points and their epipolar lines are equivalent only when epipole is at infinity and the scales are the same. Thus the first criterion (gradient ...) is sufficient in practice. BibRef

Robert, L.[Luc],
Camera Calibration without Feature Extraction,
CVIU(63), No. 2, March 1996, pp. 314-325.
WWW Version. BibRef 9603
Earlier: ICPR94(A:704-706).
WWW Version. BibRef

Quan, L.[Long], and Lan, Z.[Zhongdan],
Linear N-Point Camera Pose Determination,
PAMI(21), No. 8, August 1999, pp. 774-780.
IEEE Abstract. IEEE Top Reference.
WWW Version. BibRef 9908
Earlier:
Linear N >=4-Point Pose Determination,
ICCV98(778-783).
WWW Version. 4 and 5 points in particular. Camera position and orientation from known correspondences. Linear solutions for 4 and 5 points for generic reference points. BibRef

Quan, L.[Long],
Uncalibrated 1D Camera and 3D Affine Reconstruction of Lines,
CVPR97(60-65).
IEEE Abstract. IEEE Top Reference.
WWW Version. 9704Lines in 3 views; 3D lines into 2D points; tensor rep of 3 views. BibRef

Fiore, P.D.[Paul D.],
Efficient Linear Solution of Exterior Orientation,
PAMI(23), No. 2, February 2001, pp. 140-148.
IEEE Abstract. IEEE Top Reference.
WWW Version. 0102 BibRef
Earlier:
Linear Epipolar Algorithm for Multiframe Orientation,
ICIP00(Vol I: 557-560).
IEEE Abstract. IEEE Top Reference. 0008 Isolate the unknown depths of feature points to get a absolute orientation plus scale problem, then use SVD. BibRef

Ji, Q.[Qiang], Zhang, Y.M.[Yong-Mian],
Camera calibration with genetic algorithms,
SMC-A(31), No. 2, March 2001, pp. 120-130.
IEEE Top Reference. 0104 Genetic Algorithms. BibRef

Hati, S., Sengupta, S.,
Robust camera parameter estimation using genetic algorithm,
PRL(22), No. 3-4, March 2001, pp. 289-298.
HTML Version. 0105 BibRef

Kopparapu, S.K.[Sunil K.], Corke, P.[Peter],
The Effect of Noise on Camera Calibration Parameters,
GM(63), No. 5, September 2001, pp. 277-303.
WWW Version. 0203 BibRef

Salvi, J.[Joaquim], Armangu�, X.[Xavier], Batlle, J.[Joan],
A comparative review of camera calibrating methods with accuracy evaluation,
PR(35), No. 7, July 2002, pp. 1617-1635.
WWW Version. 0204 Evaluation, Camera Calibration. BibRef

Hu, Z.Y., Wu, F.C.,
A Note on the Number of Solutions of the Noncoplanar P4P Problem,
PAMI(24), No. 4, April 2002, pp. 550-555.
IEEE Abstract. IEEE Top Reference.
WWW Version. 0204Perspective Pose estimation. Camera calibration issues. Determine the transformation matrix from the object centered frame to the camera centered frame. BibRef

Livingston, M.A.[Mark A.], Sobel, I.E.[Irwin E.],
Geometric and photometric calibration of cameras,
US_Patent7,038,712, May 2, 2006.
WWW Version. BibRef 0605

Lavest, J.M., Rives, G., La Prest�, J.T.,
Dry camera calibration for underwater applications,
MVA(13), No. 5-6, 2003, pp. 245-253.
HTML Version. 0304 BibRef
Earlier:
Underwater Camera Calibration,
ECCV00(II: 654-668).
WWW Version. 0003 BibRef

Ansar, A.[Adnan], Daniilidis, K.[Kostas],
Linear Pose Estimation from Points or Lines,
PAMI(25), No. 5, May 2003, pp. 578-589.
IEEE Abstract. IEEE Top Reference. 0304 BibRef
Earlier: ECCV02(IV: 282 ff.).
HTML Version. Or:
PDF Version. 0205 BibRef
Earlier:
Linear Augmented Reality Registration,
CAIP01(383 ff.).
HTML Version. 0210For n points or n lines. Compare to: See also Linear N-Point Camera Pose Determination. See also Linear Epipolar Algorithm for Multiframe Orientation. See also Robust Methods for Estimating Pose and a Sensitivity Analysis. BibRef

Leebmann, J.[Johannes],
A stochastic analysis of the calibration problem for Augmented Reality systems with see-through head-mounted displays,
PandRS(57), No. 5-6, April 2003, pp. 400-408.
WWW Version. 0307 BibRef

Izquierdo, E., Guerra, V.,
Estimating the essential matrix by efficient linear techniques,
CirSysVideo(13), No. 9, September 2003, pp. 925-935.
IEEE Abstract. IEEE Top Reference. 0310 BibRef

Chen, C.S.[Chu-Song], Chang, W.Y.[Wen-Yan],
On Pose Recovery for Generalized Visual Sensors,
PAMI(26), No. 7, July 2004, pp. 848-861.
IEEE Abstract. IEEE Top Reference. 0406I.e. camera pose from a non-perspective camera. BibRef

Smith, L.N.[Lyndon N.], Smith, M.L.[Melvyn L.],
Automatic machine vision calibration using statistical and neural network methods,
IVC(23), No. 10, 20 September 2005, pp. 887-899.
WWW Version. 0509 BibRef

Sun, W.[Wei], Cooperstock, J.R.[Jeremy R.],
An empirical evaluation of factors influencing camera calibration accuracy using three publicly available techniques,
MVA(17), No. 1, April 2006, pp. 51-67.
WWW Version. 0604 BibRef
Earlier:
Requirements for Camera Calibration: Must Accuracy Come with a High Price?,
WACV05(I: 356-361).
WWW Version. 0502 BibRef

Wu, Y.H.[Yi-Hong], Hu, Z.Y.[Zhan-Yi],
A robust method to recognize critical configuration for camera calibration,
IVC(24), No. 12, 1 December 2006, pp. 1313-1318.
WWW Version. 0610 BibRef
Earlier:
Detecting Critical Configuration of Six Points,
ACCV06(II:447-456).
WWW Version. 0601Camera calibration; Invariant; Critical configuration How to detect when you are in the critical configuration (i.e. cannot do the calibration). BibRef

Unal, G.[Gozde], Yezzi, A.J.[Anthony J.], Soatto, S.[Stefano], Slabaugh, G.G.[Gregory G.],
A Variational Approach to Problems in Calibration of Multiple Cameras,
PAMI(29), No. 8, August 2007, pp. 1322-1338.
WWW Version. 0707 BibRef
Earlier: A1, A2, Only: CVPR04(I: 172-178).
IEEE Abstract. IEEE Top Reference. 0408 BibRef

Su, J.B.[Jian-Bo],
Camera calibration based on receptive fields,
PR(40), No. 10, October 2007, pp. 2837-2845.
WWW Version. 0707Camera calibration; Receptive field; Sensor fusion; Uncertainty; Weighted regression BibRef

Habib, A.[Ayman], Kim, K.[Kyungok], Shin, S.W.[Sung-Woong], Kim, C.[Changjae], Bang, K.I.[Ki-In], Kim, E.M.[Eui-Myoung], Lee, D.C.[Dong-Cheon],
Comprehensive Analysis of Sensor Modeling Alternatives for High-Resolution Imaging Satellites,
PhEngRS(73), No. 11, November 2007, pp. 1241-1252.
WWW Version. 0709A detailed analysis of sensor modeling alternatives for highresolution commercial imaging satellites. BibRef

Dell'Acqua, A.[Andrea], Sarti, A.[Augusto], Tubaro, S.[Stefano],
3D Motion from structures of points, lines and planes,
IVC(26), No. 3, March 2008, pp. 529-549.
WWW Version. 0711 BibRef
Earlier:
Three-view camera calibration using geometric algebra,
ICIP03(I: 305-308).
IEEE Abstract. IEEE Top Reference. 0312Camera tracking; Geometric Algebra; Extended Kalman Filter Camera Motion using lines and planes. BibRef

Defferara, C., Negroni, F., Sarti, A., Tubaro, S.,
New perspectives on camera calibration using geometric algebra,
ICIP02(II: 573-576).
IEEE Abstract. IEEE Top Reference. 0210 BibRef

Stewenius, H.[Henrik], Nister, D.[David], Kahl, F.[Fredrik], Schaffalitzky, F.[Frederik],
A Minimal Solution for Relative Pose with Unknown Focal Length,
IVC(26), No. 7, 2 July 2008, pp. 871-877.
WWW Version. 0804 BibRef
Earlier: CVPR05(II: 789-794).
WWW Version. 0507Relative pose; Relative orientation; Camera calibration BibRef

Grossmann, E.[Etienne], Lee, E.J.[Eun-Joo], Hislop, P.[Peter], Nist�r, D.[David], Stew�nius, H.[Henrik],
Are two rotational flows sufficient to calibrate a smooth non-parametric sensor?,
CVPR06(I: 1222-1229).
WWW Version. 0606 BibRef

Fergus, R.[Rob], Torralba, A.[Antonio], Freeman, W.T.[William T.],
Random Lens Imaging,
CSAIL-2006-058, September 2006.
WWW Version. BibRef 0609

Moreno-Noguer, F.[Francesc], Lepetit, V.[Vincent], Fua, P.[Pascal],
Accurate Non-Iterative O(n) Solution to the PnP Problem,
ICCV07(1-8).
WWW Version. 0710Pose of a calibrated camera from n 3D-to-2D point correspondences. BibRef

Caulier, Y.[Yannick], Spinnler, K.[Klaus],
Calibration of lD cameras: Determination of 3D reconstruction accuracy,
VMV04(55-62). 0411 BibRef

Handel, H.[Holger],
Analyzing the Influences of Camera Warm-Up Effects on Image Acquisition,
ACCV07(II: 258-268).
WWW Version. 0711Image shifts .1 pixel in warmup. BibRef

Yuan, D.[Ding], Chung, R.[Ronald],
Camera-to-Camera Geometry Estimation Requiring no Overlap in their Visual Fields,
ICIP07(I: 229-232).
WWW Version. 0709 BibRef

Uematsu, Y.[Yuko], Teshima, T.[Tomoaki], Saito, H.[Hideo], Cao, H.H.[Hong-Hua],
D-Calib: Calibration Software for Multiple Cameras System,
CIAP07(285-290).
WWW Version. 0709 BibRef

Dupont, R., Keriven, R., Fuchs, P.,
An improved calibration technique for coupled single-row telemeter and CCD camera,
3DIM05(89-94).
WWW Version. 0508 BibRef

Sundareswara, R.[Rashmi], Schrater, P.R.,
Bayesian modelling of camera calibration and reconstruction,
3DIM05(394-401).
WWW Version. 0508 BibRef

Parian, J.A., Gruen, A.,
Panoramic Camera Calibration Using 3D Straight Lines,
PanoPhot05(xx-yy).
PDF Version. 0502 BibRef

Bakstein, H.,
Calibration Procedure for a 360x360 Mosaic Camera,
PanoPhot05(xx-yy).
PDF Version. 0502 BibRef

Sheikh, Y.[Yaser], Gritai, A.[Alexei], Shah, M.[Mubarak],
On the Spacetime Geometry of Galilean Cameras,
CVPR07(1-8).
WWW Version. 0706Camera moving at constant velocity. Perspective and pushbroom. BibRef

Segvic, S.[Sinisa], Schweighofer, G.[Gerald], Pinz, A.[Axel],
Influence of numerical conditioning on the accuracy of relative orientation,
BenCOS07(1-8).
WWW Version. 0706 BibRef

Hermans, C.[Chris], Dumont, M.[Maarten], Bekaert, P.[Philippe],
Extrinsic Recalibration in Camera Networks,
CRV07(3-10).
WWW Version. 0705 BibRef

Francken, Y.[Yannick], Hermans, C.[Chris], Bekaert, P.[Philippe],
Screen-Camera Calibration using a Spherical Mirror,
CRV07(11-20).
WWW Version. 0705 BibRef

Mohamed, R., Ahmed, A., Eid, A., Farag, A.,
Support Vector Machines for Camera Calibration Problem,
ICIP06(1029-1032). 0610
WWW Version. BibRef

Fuhrland, M.,
Development of a CCD camera based reflex goniometer,
IEVM06(xx-yy).
PDF Version. 0609Bi Axial angle measurements for mirror. Calibrating 3D. BibRef

Remondino, F.[Fabio], Fraser, C.S.,
Digital camera calibration methods: considerations and comparisons,
IEVM06(xx-yy).
PDF Version. 0609 BibRef

Michaelsen, E.[Eckart], von Hansen, W.[Wolfgang], Kirchhof, M.[Michael], Meidow, J.[Jochen], Stilla, U.[Uwe],
Estimating the Essential Matrix: GOODSAC versus RANSAC,
PCV06(xx-yy).
PDF Version. 0609 BibRef

Baba, M.[Masashi], Mukunoki, M.[Masayuki], Asada, N.[Naoki],
A Unified Camera Calibration Using Geometry and Blur of Feature Points,
ICPR06(I: 816-819).
WWW Version. 0609 BibRef

Mikulastik, P.A.[Patrick A.], Broszio, H.[Hellward], Thorm�hlen, T.[Thorsten], Urfalioglu, O.[Onay],
Error Analysis of Feature Based Disparity Estimation,
PSIVT06(1-12).
WWW Version. 0612 BibRef
And:
Error Analysis of Camera Parameter Estimation based on Collinear Features,
CRV06(32-32).
WWW Version. 0607 BibRef

Chen, I.H.[I-Hsien], Wang, S.J.[Sheng-Jyh],
Efficient Vision-Based Calibration for Visual Surveillance Systems with Multiple PTZ Cameras,
CVS06(24).
WWW Version. 0602Pan-Tilt-Zoom. Estimate tilt angle, then altitude. BibRef

Szlavik, Z., Sziranyi, T.,
Bayesian Estimation of Common Areas in Multi-Camera Systems,
ICIP06(1045-1048). 0610
WWW Version. BibRef

Szl�vik, Z.[Zolt�n], Havasi, L.[L�szl�], Szir�nyi, T.[Tam�s],
Geometrical Scene Analysis Using Co-motion Statistics,
ACIVS07(968-979).
WWW Version. 0708 BibRef
Earlier:
Estimation of Common Groundplane Based on Co-motion Statistics,
ICIAR04(II: 347-354).
WWW Version. 0409 BibRef

Szlavik, Z., Sziranyi, T., Havasi, L., Benedek, C.,
Optimizing of Searching Co-Motion Point-Pairs for Statistical Camera Calibration,
ICIP05(II: 1178-1181).
WWW Version. 0512 BibRef

Martins, N.[Nuno], Ara�jo, H.[H�lder],
A Calibration Algorithm for POX-Slits Camera,
IbPRIA05(I:168).
WWW Version. 0509 BibRef

Ramalingam, S.[Srikumar], Sturm, P.F.[Peter F.], Lodha, S.K.[Suresh K.],
Theory and Calibration for Axial Cameras,
ACCV06(I:704-713).
WWW Version. 0601 BibRef
Earlier:
Generic Calibration of Axial Cameras,
INRIARR-5827, 2006.
HTML Version. BibRef
Earlier:
Towards Complete Generic Camera Calibration,
CVPR05(I: 1093-1098).
WWW Version. 0507 See also generic structure-from-motion framework, A. BibRef

Ramalingam, S.[Srikumar], Sturm, P.F.[Peter F.], Boyer, E.[Edmond],
A Factorization Based Self-Calibration for Radially Symmetric Cameras,
3DPVT06(480-487).
WWW Version. 0606 BibRef

Sturm, P.F., Ramalingam, S., Lodha, S.K.,
On Calibration, Structure-From-Motion and Multi-View Geometry for General Camera Models,
PanoPhot05(xx-yy).
PDF Version. 0502 BibRef

Sturm, P.F.[Peter F.],
Multi-View Geometry for General Camera Models,
CVPR05(I: 206-212).
WWW Version. 0507 BibRef

Chang, W.Y.[Wen-Yan], Chen, C.S.[Chu-Song],
Pose estimation for multiple camera systems,
ICPR04(III: 262-265).
WWW Version. 0409Use all information. Treat the camera system as a single generalized camera. See also Using many cameras as one. BibRef

Vigueras, J.F., Berger, M.O., Simon, G.,
On the influence of fixing the principal point in frame-by-frame multiplanar calibration,
ICPR04(IV: 120-123).
WWW Version. 0409 BibRef

Ouellet, J.N., Hebert, P.,
Developing Assistant Tools for Geometric Camera Calibration: Assessing the Quality of Input Images,
ICPR04(IV: 80-83).
WWW Version. 0409 BibRef

Yu, J.Y.[Jing-Yi], McMillan, L.[Leonard],
General Linear Cameras,
ECCV04(Vol II: 14-27).
WWW Version. 0405unifies many previous camera models into a single representation. capable of describing all perspective (pinhole), orthographic, and many multiperspective (including pushbroom and two-slit) cameras, as well as epipolar plane images. BibRef

Sturm, P.F.[Peter F.], Ramalingam, S.[Srikumar],
A Generic Concept for Camera Calibration,
ECCV04(Vol II: 1-13).
WWW Version. 0405 BibRef

Im, J.H.[Jang-Hwan], Min, J.H.[Ji-Hong], Ohk, H.S.[Hyung-Soo], Choi, J.S.[Jong-Soo],
Two Linear Methods for Camera Calibration and Their Applications to Augmented Reality and 3D Reconstruction,
SCIA03(625-631).
WWW Version. 0310 BibRef