Abstract
Geometric algebra is a universal mathematical language which provides very comprehensive techniques for analyzing the complex geometric situations occurring in robotics and computer vision. The application of the 4D motor algebra for the linearization of the the hand-eye calibration problem is presented. Geometric algebra and its associated linear algebra framework is a very elegant language to express all the ideas of projective geometry. Using purely geometric derivations, the constraints for point and line correspondences in n-views and projective invariants are computed.
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References
Daniilidis K. and Bayro-Corrochano E. The dual quaternion approach to hand-eye calibration. IEEE Proceedings of ICPR’96 Viena, Austria, Vol. I, pages 318–322, August, 1996.
Lasenby, J., Bayro-Corrochano, E., Lasenby, A. and Sommer. G. 1996. A New Methodology for the Computation of Invariants in Computer Vision. Cambridge University, CUED/F-INENG/TR. 244.
Chen H. A screw motion approach to uniqueness analysis of head-eye geometry. In IEEE Conf. Computer Vision and Pattern Recognition, pages 145–151, Maui, Hawaii, June 3–6, 1991.
Hestenes, D. 1986. A unified language for mathematics and physics. Clifford algebras and their applications in mathematical physics. Eds. J.S.R. Chisolm and A.K. Common, D.Reidel, Dordrecht, pl.
Shiu Y.C. and Ahmad S. Calibration of wrist-mounted robotic sensors by solving homogeneous transform equations of the form AX = B. IEEE Trans. Robotics and Automation, 5: 16–27, 1989.
Sommer G., Bayro-Corrochano E. and Bülow T. 1997. Geometric algebra as a framework for the perception—action cycle. Workshop on Theoretical Foundation of Computer Vision, Dagstuhl, March 13–19, 1996, Springer Wien.
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© 1997 Springer-Verlag Berlin Heidelberg
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Bayro-Corrochano, E., Lasenby, J., Sommer, G. (1997). What Can Grassmann, Hamilton and Clifford Tell Us about Computer Vision and Robotics. In: Paulus, E., Wahl, F.M. (eds) Mustererkennung 1997. Informatik aktuell. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-60893-3_16
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DOI: https://doi.org/10.1007/978-3-642-60893-3_16
Publisher Name: Springer, Berlin, Heidelberg
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