A theory of self-calibration of a moving camera
International Journal of Computer Vision
Self-calibration from multiple views with a rotating camera
ECCV '94 Proceedings of the third European conference on Computer vision (vol. 1)
Kruppa's Equations Derived from the Fundamental Matrix
IEEE Transactions on Pattern Analysis and Machine Intelligence
Self-Calibration of a Moving Camera from PointCorrespondences and Fundamental Matrices
International Journal of Computer Vision
Stratified Self-Calibration with the Modulus Constraint
IEEE Transactions on Pattern Analysis and Machine Intelligence
A Case Against Kruppa's Equations for Camera Self-Calibration
IEEE Transactions on Pattern Analysis and Machine Intelligence
Multiple view geometry in computer visiond
Multiple view geometry in computer visiond
The Geometry of Multiple Images: The Laws That Govern The Formation of Images of A Scene and Some of Their Applications
Camera Self-Calibration: Theory and Experiments
ECCV '92 Proceedings of the Second European Conference on Computer Vision
Kruppa Equation Revisited: Its Renormalization and Degeneracy
ECCV '00 Proceedings of the 6th European Conference on Computer Vision-Part II
Autocalibration and the absolute quadric
CVPR '97 Proceedings of the 1997 Conference on Computer Vision and Pattern Recognition (CVPR '97)
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Given the fundamental matrix between a pair of images taken by a nonstationary projective camera with constant internal parameters, we show how to use the two independent Kruppa equations in order to explicitly cut down the number of parameters of the Kruppa matrix KKT by exactly two. Thus, we derive a procedure which results in a closed formula for the Kruppa matrix that depends on exactly three remaining parameters. This formula allows an easy incorporation of the positivity constraint and admits of an interpretation in terms of the image of the horopter. We focus on the general case where the camera motion is unknown and not restricted to some special type. Solutions of the Kruppa equations given three fundamental matrices have been attempted in the past by iterative numerical methods that are searching in multidimensional spaces. As an application of the reduced Kruppa matrix mentioned above we also outline how this problem can be analytically reduced to the determination of the real, positive roots of a polynomial of 14-th degree in one variable.