Conformal Geometric Algebra for Endoscope-Traking System Calibration in Neurosurgery

  • Silena Herold-García
  • Jorge Rivera-Rovelo
  • Eduardo Bayro-Corrochano
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4756)


One necessary task in the operating room is to establish a common reference frame, in order to relate the information obtained from different sensors, and to combine both the preoperative with the intraoperative information. To estimate the transformations between different data, fiducial markers are typically used. In this paper we present a formulation of the known hand-eye calibration problem, to estimate the transformation between an endoscopic camera and the set of spherical markers placed on it, using the conformal geometric algebra framework. Such markers are tracked by an optical stereo tracking system, which help to relate the real world with the virtual model created before surgery. Experimental results shows that our method is reliable and useful for medical applications in real time like neurosurgery.


Hand-Eye Calibration Geometric Algebra Neurosurgery Endoscope Calibration 


  1. 1.
    Bayro-Corrochano, E.: Robot perception and action using conformal geometry. In: Handbook of Geometric Computing. Applications in Pattern Recognition, Computer Vision, Neurocomputing and Robotics. ch. 13, Springer Verlag, Heidelberg (2005)Google Scholar
  2. 2.
    Rosenhahn, B., Sommer, G.: Pose Estimation in Conformal Geometric Algebra. Christian-Albrechts-University of Kiel, Technical Report No. 0206, pp. 13–36 (2002)Google Scholar
  3. 3.
    Tsai, R.Y., Lenz, R.K.: A New Technique for Fully Autonomous and Efficient 3D Robotics Hand/Eye Calibration. IEEE Transactions on Robotics and Automation 5(3), 345–358 (1989)CrossRefGoogle Scholar
  4. 4.
    Horaud, R., Dornaika, F.: Hand-Eye Calibration. International Journal on Robotics Research 14(3), 195–210 (1995)CrossRefGoogle Scholar
  5. 5.
    Daniilidis, K.: Hand-Eye Calibration Using Dual Quaternions. The International Journal of Robotics Research 18(3), 286–298 (1999)CrossRefMathSciNetGoogle Scholar
  6. 6.
    Bayro-Corrochano, E., Sommer, G., Dannilidis, K.: Motor Algebra for 3D Kinematics: The Case of the Hand-Eye Calibration. Journal of Mathematical Imaging and Vision 13, 79–100 (2000)zbMATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    Zhang, Z.: A Flexible New Technique for Camera Calibration. Microsoft Research 1–21 (1999)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Silena Herold-García
    • 1
  • Jorge Rivera-Rovelo
    • 2
  • Eduardo Bayro-Corrochano
    • 2
  1. 1.Universidad de Oriente, Santiago de Cuba 
  2. 2.CINVESTAV del IPN, Unidad Guadalajara, Department of Electric Engineering and Computer Sciences, Av. Científica 1145, El Bajío, Zapopan, JaliscoMéxico

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