Matrix analysis
The twisted cubic and camera calibration
Computer Vision, Graphics, and Image Processing
Three-dimensional computer vision: a geometric viewpoint
Three-dimensional computer vision: a geometric viewpoint
A Theory of Single-Viewpoint Catadioptric Image Formation
International Journal of Computer Vision
Paracatadioptric Camera Calibration
IEEE Transactions on Pattern Analysis and Machine Intelligence
Epipolar Geometry for Central Catadioptric Cameras
International Journal of Computer Vision
Properties of the Catadioptric Fundamental Matrix
ECCV '02 Proceedings of the 7th European Conference on Computer Vision-Part II
A Unifying Theory for Central Panoramic Systems and Practical Applications
ECCV '00 Proceedings of the 6th European Conference on Computer Vision-Part II
A Four-step Camera Calibration Procedure with Implicit Image Correction
CVPR '97 Proceedings of the 1997 Conference on Computer Vision and Pattern Recognition (CVPR '97)
A Complete Panoramic Vision System, Incorporating Imaging, Ranging, and Three Dimensional Navigation
OMNIVIS '00 Proceedings of the IEEE Workshop on Omnidirectional Vision
Approximating a Single Viewpoint in Panoramic Imaging Devices
OMNIVIS '00 Proceedings of the IEEE Workshop on Omnidirectional Vision
Mixing Catadioptric and Perspective Cameras
OMNIVIS '02 Proceedings of the Third Workshop on Omnidirectional Vision
Multiple View Geometry in Computer Vision
Multiple View Geometry in Computer Vision
A Generic Camera Calibration Method for Fish-Eye Lenses
ICPR '04 Proceedings of the Pattern Recognition, 17th International Conference on (ICPR'04) Volume 1 - Volume 01
Geometric Properties of Central Catadioptric Line Images and Their Application in Calibration
IEEE Transactions on Pattern Analysis and Machine Intelligence
Epipolar Geometry of Central Projection Systems Using Veronese Maps
CVPR '06 Proceedings of the 2006 IEEE Computer Society Conference on Computer Vision and Pattern Recognition - Volume 1
A unifying geometric representation for central projection systems
Computer Vision and Image Understanding - Special issue on omnidirectional vision and camera networks
Self-calibration of a general radially symmetric distortion model
ECCV'06 Proceedings of the 9th European conference on Computer Vision - Volume Part IV
Calibration of omnidirectional cameras in practice: A comparison of methods
Computer Vision and Image Understanding
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In this study, we present a calibration technique that is valid for all single-viewpoint catadioptric cameras. We are able to represent the projection of 3D points on a catadioptric image linearly with a 6脳10 projection matrix, which uses lifted coordinates for image and 3D points. This projection matrix can be computed from 3D---2D correspondences (minimum 20 points distributed in three different planes). We show how to decompose it to obtain intrinsic and extrinsic parameters. Moreover, we use this parameter estimation followed by a non-linear optimization to calibrate various types of cameras. Our results are based on the sphere camera model which considers that every central catadioptric system can be modeled using two projections, one from 3D points to a unitary sphere and then a perspective projection from the sphere to the image plane. We test our method both with simulations and real images, and we analyze the results performing a 3D reconstruction from two omnidirectional images.