Abstract
The “AX=XB” sensor calibration problem is ubiquitous in the fields of robotics and computer vision. In this problem A, X, and B are each homogeneous transformations (i.e., rigid-body motions) with A and B given from sensor measurements, and X is the unknown that is sought. For decades this problem is known to be solvable for X when a set of exactly measured compatible A’s and B’s with known correspondence is given. However, in practical problems, it is often the case that the data streams containing the A’s and B’s will present at different sample rates, they will be asynchronous, and each stream may contain gaps in information. Practical scenarios in which this can happen include hand-eye calibration and ultrasound image registration. We therefore present a method for calculating the calibration transformation, X, that works for data without any a priori knowledge of the correspondence between the As and Bs.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Chen, H.H.: A Screw Motion Approach to Uniqueness Analysis of Head-Eye Geometry. In: IEEE Conference on CVPR, pp. 145–151 (1991)
Arun, K.S., Huang, T.S., Blostein, S.D.: Least-Squares Fitting of Two 3-D Point Sets. IEEE Trans. on Pattern Analysis and Machine Intel. 9(5), 698–700 (1987)
Park, F.C., Martin, B.J.: Robot Sensor Calibration: Solving AX = XB on the Euclidean Group. IEEE Trans. Robotics and Automation 10(5), 717–721 (1994)
Shiu, Y.C., Ahmad, S.: Calibration of Wrist-Mounted Robotic Sensors by Solving Homogeneous Transform Equations of the Form AX = XB. IEEE Trans. Robotics and Automation 5(1), 16–29 (1989)
Dong, W., Rostoucher, D., Gauthier, M.: Kinematics Parameters Estimation for an AFM/Robot Integrated Micro-Force Measurement System. In: IEEE/RSJ International Conference on Intelligent Robots and Systems, October 18-22, pp. 6143–6148 (2010)
Kim, S.-J., Jeong, M.-H., Lee, J.-J., Lee, J.-Y., Kim, K.-G., You, B.-J., Oh, S.-R.: Robot Head-Eye Calibration Using the Minimum Variance Method. In: IEEE International Conference on Robotics and Biomimetics, December 14-18, pp. 1446–1451 (2010)
Dai, Y., Trumpf, J., Li, H., Barnes, N., Hartley, R.: Rotation Averaging with Application to Camera-Rig Calibration. In: Zha, H., Taniguchi, R.-I., Maybank, S. (eds.) ACCV 2009, Part II. LNCS, vol. 5995, pp. 335–346. Springer, Heidelberg (2010)
Chirikjian, G.S.: Stochastic Models, Information Theory, and Lie Groups, vol. 2. Birkhäuser, Basel (2011)
Mills, D.L.: Internet Time Synchronization: Network Time Protocol. IEEE Transactions on Communications 39(10), 1482–1493 (1991)
Mair, E., Fleps, M., Suppa, M., Burschka, D.: Spatio-temporal initialization for IMU to camera registration. In: 2011 IEEE ROBIO, pp. 557–564 (December 2011)
Pennec, X.: Intrinsic Statistics on Riemannian Manifolds: Basic Tools for Geometric Measurements. Jour. of Mathematical Imaging and Vision 25(1), 127–154 (2006)
Tron, R., Vidal, R., Terzis, A.: Distributed pose averaging in camera networks via consensus on SE(3). In: Second ACM/IEEE ICDSC, pp. 1–10 (September 7, 2008)
Fletcher, P.T., Joshi, S., Lu, C., Pizer, S.M.: Gaussian Distributions on Lie Groups and Their Application to Statistical Shape Analysis. In: Taylor, C.J., Noble, J.A. (eds.) IPMI 2003. LNCS, vol. 2732, pp. 450–462. Springer, Heidelberg (2003)
Glover, J., Rus, D., Roy, N.: Probabilistic models of object geometry for grasp planning. In: Brock, O., Trinkle, J.C., Ramos, F. (eds.) Robotics Science and Systems IV. MIT Press (June 2009)
Wang, Y., Chirikjian, G.S.: Nonparametric Second-Order Theory of Error Propagation on the Euclidean Group. International Journal of Robotics Research 27(11-12), 1258–1273 (2008)
Boctor, E.M.: Enabling Technologies for Ultrasound Imagin. In: Computer-Assisted Intervention, CS Department, Johns Hopkins University. Thesis (2006)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Ackerman, M.K., Chirikjian, G.S. (2013). A Probabilistic Solution to the AX=XB Problem: Sensor Calibration without Correspondence. In: Nielsen, F., Barbaresco, F. (eds) Geometric Science of Information. GSI 2013. Lecture Notes in Computer Science, vol 8085. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-40020-9_77
Download citation
DOI: https://doi.org/10.1007/978-3-642-40020-9_77
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-40019-3
Online ISBN: 978-3-642-40020-9
eBook Packages: Computer ScienceComputer Science (R0)