Calibration of 3D kinematic systems using orthogonality constraints

Processing images acquired by multi-camera systems is nowadays an effective and convenient way of performing 3D reconstruction. The basic output, i.e. the 3D location of points, can easily be further processed to also acquire information about additional kinematic data: velocity and acceleration. Hence, many such reconstruction systems are referred to as 3D kinematic systems and are very broadly used, among other tasks, for human motion analysis. A prerequisite for the actual reconstruction of the unknown points is the calibration of the multi-camera system. At present, many popular 3D kinematic systems offer so-called wand calibration, using a rigid bar with attached markers, which is from the end user’s point of view preferred over many traditional methods. During this work a brief criticism on different calibration strategies is given and typical calibration approaches for 3D kinematic systems are explained. In addition, alternative ways of calibration are proposed, especially for the initialization stage. More specifically, the proposed methods rely not only on the enforcement of known distances between markers, but also on the orthogonality of two or three rigidly linked wands. Besides, the proposed ideas utilize common present calibration tools and shorten the typical calibration procedure. The obtained reconstruction accuracy is quite comparable with that obtained by commercial 3D kinematic systems.

[1]  Pietro Cerveri,et al.  Calibrating a video camera pair with a rigid bar , 2000, Pattern Recognit..

[2]  Rajiv Gupta,et al.  Stereo from uncalibrated cameras , 1992, Proceedings 1992 IEEE Computer Society Conference on Computer Vision and Pattern Recognition.

[3]  Soren W. Henriksen,et al.  Manual of photogrammetry , 1980 .

[4]  Bill Triggs,et al.  Autocalibration and the absolute quadric , 1997, Proceedings of IEEE Computer Society Conference on Computer Vision and Pattern Recognition.

[5]  Mario Cifrek,et al.  3D Shape Recovery with no Explicit Video Projector Calibration , 2004, WSCG.

[6]  Hans-Gerd Maas.  Image sequence based automatic multi-camera system calibration techniques 1 Revised version of a pap , 1999 .

[7]  K. Atkinson.  Close Range Photogrammetry and Machine Vision , 1996 .

[8]  Andrew Zisserman,et al.  Metric rectification for perspective images of planes , 1998, Proceedings. 1998 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (Cat. No.98CB36231).

[9]  S. Finsterwalder.  Die geometrischen Grundlagen der Photogrammetrie. , 1897 .

[10]  Bernhard P. Wrobel,et al.  Multiple View Geometry in Computer Vision , 2001 .

[11]  Berthold K. P. Horn,et al.  Closed-form solution of absolute orientation using orthonormal matrices , 1988 .

[12]  T. B. Putsyata,et al.  Analytical dynamics , 1973 .

[13]  J. G. Semple,et al.  Algebraic Projective Geometry , 1953 .

[14]  J. Chris McGlone.  Bundle adjustment with object space geometric constraints for site modeling , 1995, Defense, Security, and Sensing.

[15]  Andrew W. Fitzgibbon,et al.  Simultaneous linear estimation of multiple view geometry and lens distortion , 2001, Proceedings of the 2001 IEEE Computer Society Conference on Computer Vision and Pattern Recognition. CVPR 2001.

[16]  William H. Press,et al.  Numerical recipes in C , 2002 .

[17]  Ray A. Jarvis,et al.  A Perspective on Range Finding Techniques for Computer Vision , 1983, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[18]  Songde Ma,et al.  Implicit and Explicit Camera Calibration: Theory and Experiments , 1994, IEEE Trans. Pattern Anal. Mach. Intell..

[19]  Didier Henrion,et al.  Globally Optimal Estimates for Geometric Reconstruction Problems , 2005, Tenth IEEE International Conference on Computer Vision (ICCV'05) Volume 1.

[20]  Andrew W. Fitzgibbon,et al.  Bundle Adjustment - A Modern Synthesis , 1999, Workshop on Vision Algorithms.

[21]  R. Poppele,et al.  A single-camera method for three-dimensional video imaging , 2002, Journal of Neuroscience Methods.

[22]  Olivier D. Faugeras,et al.  What can be seen in three dimensions with an uncalibrated stereo rig , 1992, ECCV.

[23]  Olivier D. Faugeras,et al.  A theory of self-calibration of a moving camera , 1992, International Journal of Computer Vision.

[24]  Tomás Svoboda,et al.  A Convenient Multicamera Self-Calibration for Virtual Environments , 2005, Presence: Teleoperators & Virtual Environments.

[25]  B. Caprile,et al.  Using vanishing points for camera calibration , 1990, International Journal of Computer Vision.

[26]  Duane C. Brown,et al.  Close-Range Camera Calibration , 1971 .

[27]  Zhengyou Zhang,et al.  A Flexible New Technique for Camera Calibration , 2000, IEEE Trans. Pattern Anal. Mach. Intell..

[28]  H. Hatze,et al.  High-precision three-dimensional photogrammetric calibration and object space reconstruction using a modified DLT-approach. , 1988, Journal of biomechanics.

[29]  Olivier D. Faugeras,et al.  Automatic calibration and removal of distortion from scenes of structured environments , 1995, Optics & Photonics.

[30]  T. Kanade,et al.  A Method of Time-Coded Parallel Planes of Light for Depth Measurement , 1981 .

[31]  Patricia A. Duffy,et al.  Kay, Ronald D., and William M. Edwards. Farm Management, 4th ed. New York: WCB/McGraw-Hill, 1999, price unknown , 1999 .

[32]  Peter F. Sturm,et al.  Critical motion sequences for the self-calibration of cameras and stereo systems with variable focal length , 1999, Image Vis. Comput..

[33]  Zhengyou Zhang,et al.  On the epipolar geometry between two images with lens distortion , 1996, Proceedings of 13th International Conference on Pattern Recognition.

[34]  D. C. Douglas Hung,et al.  3D scene modelling by sinusoid encoded illumination , 1993, Image Vis. Comput..

[35]  Takeo Kanade,et al.  Quasiconvex Optimization for Robust Geometric Reconstruction , 2005, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[36]  Joaquim Salvi,et al.  Overview of coded light projection techniques for automatic 3D profiling , 2003, 2003 IEEE International Conference on Robotics and Automation (Cat. No.03CH37422).

[37]  Paul Allard,et al.  Three-dimensional analysis of human movement , 1995 .

[38]  Richard I. Hartley,et al.  Kruppa's Equations Derived from the Fundamental Matrix , 1997, IEEE Trans. Pattern Anal. Mach. Intell..

[39]  Vwani P. Roychowdhury,et al.  Camera Calibration For Image Processing , 1999 .

[40]  W. Hargrove,et al.  Photogrammetric Engineering & Remote Sensing , 2022 .

[41]  G. Sansoni,et al.  Three-dimensional imaging based on Gray-code light projection: characterization of the measuring algorithm and development of a measuring system for industrial applications. , 1997, Applied optics.

[42]  Stephen J. Maybank,et al.  On plane-based camera calibration: A general algorithm, singularities, applications , 1999, Proceedings. 1999 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (Cat. No PR00149).

[43]  O. Faugeras,et al.  Straight Lines Have to Be Straight Automatic Calibration and Removal of Distortion from Scenes of Structured Environments , 2001 .

[44]  Olivier Faugeras,et al.  Three-Dimensional Computer Vision , 1993 .

[45]  Robert A. Hummel,et al.  Experiments with the intensity ratio depth sensor , 1985, Comput. Vis. Graph. Image Process..

[46]  Enrico Gobbetti,et al.  Encyclopedia of Electrical and Electronics Engineering , 1999 .