Matrix computations (3rd ed.)
A Theory of Single-Viewpoint Catadioptric Image Formation
International Journal of Computer Vision
A Mathematical Introduction to Robotic Manipulation
A Mathematical Introduction to Robotic Manipulation
Catadioptric Stereo Using Planar Mirrors
International Journal of Computer Vision
Multiple View Geometry in Computer Vision
Multiple View Geometry in Computer Vision
Mirror-Based Trinocular Systems in Robot-Vision
ICPR '00 Proceedings of the International Conference on Pattern Recognition - Volume 4
An Invitation to 3-D Vision: From Images to Geometric Models
An Invitation to 3-D Vision: From Images to Geometric Models
Planar catadioptric stereo: single and multi-view geometry for calibration and localization
ICRA'09 Proceedings of the 2009 IEEE international conference on Robotics and Automation
How to compute the pose of an object without a direct view?
ACCV'06 Proceedings of the 7th Asian conference on Computer Vision - Volume Part II
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The image of a planar mirror reflection (IPMR) can be interpreted as a virtual view of the scene, acquired by a camera with a pose symmetric to the pose of the real camera with respect to the mirror plane. The epipolar geometry of virtual views associated with different IPMRs is well understood, and it is possible to recover the camera motion and perform 3D scene reconstruction by applying standard structure-from-motion methods that use image correspondences as input. In this article we address the problem of estimating the pose of the real camera, as well as the positions of the mirror plane, by assuming that the rigid motion between N virtual views induced by planar mirror reflections is known. The solution of this problem enables the registration of objects lying outside the camera field-of-view, which can have important applications in domains like non-overlapping camera network calibration and robot vision. We show that the positions of the mirror planes can be uniquely determined by solving a system of linear equations. This enables to estimate the pose of the real camera in a straightforward closed-form manner using a minimum of N = 3 virtual views. Both synthetic tests and real experiments show the superiority of our approach with respect to current state-of-the-art methods.