A Robust Least Squares Solution to the Calibrated Two-View Geometry with Two Known Orientation Angles

Conference paper

DOI: 10.1007/978-3-662-44911-0_9

Part of the Communications in Computer and Information Science book series (CCIS, volume 458)
Cite this paper as:
Nakano G., Takada J. (2014) A Robust Least Squares Solution to the Calibrated Two-View Geometry with Two Known Orientation Angles. In: Battiato S., Coquillart S., Laramee R., Kerren A., Braz J. (eds) Computer Vision, Imaging and Computer Graphics -- Theory and Applications. VISIGRAPP 2013. Communications in Computer and Information Science, vol 458. Springer, Berlin, Heidelberg


This paper proposes a robust least squares solution to the calibrated two-view geometry with two known orientation angles. Using the knowledge reduces the degrees of freedom (DoF) from five to three: one from a remaining angle and two from a translation vector. This paper determines that the three parameters are obtained by solving a minimization problem of the smallest eigenvalue containing the unknown angle. The proposed solution minimizes a new simple cost function based on the matrix determinant in order to avoid the complicated eigenvalue computation. The estimated parameters are optimal since the cost function is minimized under three DoFs. Experimental results of synthetic data show that the robustness of the proposed solution is up to 1.5\(^\circ \) angle noise, which is approximately three times that of a conventional solution. Moreover, 60 point correspondences, fewer than half those in conventional solutions, are sufficient to reach the performance boundary.


Two-view geometry Relative pose problem Essential matrix Structure from motion Two known orientation angles 

Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  1. 1.Information and Media Processing LaboratoriesNEC CorporationNakahara-ku, KawasakiJapan

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