IEEE Transactions on Pattern Analysis and Machine Intelligence
A buyer's guide to conic fitting
BMVC '95 Proceedings of the 6th British conference on Machine vision (Vol. 2)
Direct Least Square Fitting of Ellipses
IEEE Transactions on Pattern Analysis and Machine Intelligence
Multiple view geometry in computer visiond
Multiple view geometry in computer visiond
Numerical Recipes in C++: the art of scientific computing
Numerical Recipes in C++: the art of scientific computing
Paracatadioptric Camera Calibration
IEEE Transactions on Pattern Analysis and Machine Intelligence
Catadioptric Projective Geometry
International Journal of Computer Vision
Statistical Bias of Conic Fitting and Renormalization
IEEE Transactions on Pattern Analysis and Machine Intelligence
Epipolar Geometry of Panoramic Cameras
ECCV '98 Proceedings of the 5th European Conference on Computer Vision-Volume I - Volume I
A Method for 3D Reconstruction of Piecewise Planar Objects from Single Panoramic Images
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
A Theory of Catadioptric Image Formation
ICCV '98 Proceedings of the Sixth International Conference on Computer Vision
International Journal of Computer Vision
Geometric Properties of Central Catadioptric Line Images and Their Application in Calibration
IEEE Transactions on Pattern Analysis and Machine Intelligence
International Journal of Computer Vision
A new linear algorithm for calibrating central catadioptric cameras
Pattern Recognition
Processing Sparse Panoramic Images via Space Variant Operators
Journal of Mathematical Imaging and Vision
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The paracatadioptric camera is one of the most popular panoramic systems currently available in the market. It provides a wide field of view by combining a parabolic shaped mirror with a camera inducing an orthographic projection. Previous work proved that the para-catadioptric projection of a line is a conic curve, and that the sensor can be fully calibrated from the image of three or more lines. Howover, the estimation of the conic curves where the lines are projected is hard to accomplish because of the partial occlusion. In general only a small arc of the conic is visible in the image, and conventional conic fitting techniques are unable to accurately estimate the curve. The present work provides methods to overcome this problem. We show that in uncalibrated paracatadioptric views a set of conic curves is a set of line projections if and only if certain properties are verified. These properties are used to constrain the search space and correctly estimate the curves. The conic fitting is solved naturally by an eigensystem whenever the camera is skewless and the aspect ratio is known. For the general situation the line projections are estimated using non-linear optimization. The set of paracatadioptric lines is used in a geometric construction to determine the camera parameters and calibrate the system. We also propose an algorithm to estimate the conic locus corresponding to a line projection in a calibrated paracatadioptric image. It is proved that the set of all line projections is a hyperplane in the space of conic curves. Since the position of the hyperplane depends only on the sensor parameters, the accuracy of the estimation can be improved by constraining the search to conics lying in this subspace. We show that the fitting problem can be solved by an eigensystem, which leads to a robust and computationally efficient method for paracatadioptric line estimation.