Parameter estimation and hypothesis testing in linear models
Parameter estimation and hypothesis testing in linear models
Three-dimensional computer vision: a geometric viewpoint
Three-dimensional computer vision: a geometric viewpoint
Generalized homogeneous coordinates for computational geometry
Geometric computing with Clifford algebras
Catadioptric Projective Geometry
International Journal of Computer Vision
Properties of the Catadioptric Fundamental Matrix
ECCV '02 Proceedings of the 7th European Conference on Computer Vision-Part II
Pose Estimation in Conformal Geometric Algebra Part I: The Stratification of Mathematical Spaces
Journal of Mathematical Imaging and Vision
Journal of Mathematical Imaging and Vision
Geometric Algebra for Computer Science: An Object-Oriented Approach to Geometry (The Morgan Kaufmann Series in Computer Graphics)
Estimation of geometric entities and operators from uncertain data
PR'05 Proceedings of the 27th DAGM conference on Pattern Recognition
Optimal computation of 3-D similarity: Gauss-Newton vs. Gauss-Helmert
Computational Statistics & Data Analysis
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We consider the epipolar geometry between two omnidirectional images acquired from a single viewpoint catadioptric vision sensor with parabolic mirror. This work in particular deals with the estimation of the respective epipoles. We use conformal geometric algebra to show the existence of a 3×3 essential matrix, which describes the underlying epipolar geometry. The essential matrix is preferable to the 4×4 fundamental matrix, which comprises the fixed intrinsic parameters, as it can be estimated from less data. We use the essential matrix to obtain a prior for a stochastic epipole computation being a key aspect of our work. The computation uses the well-tried amalgamation of a least-squares adjustment (LSA) technique, called the Gauss-Helmert method, with conformal geometric algebra. The imaging geometry enables us to assign distinct uncertainties to the image points which justifies the considerable advantage of our LSA method over standard estimation methods. Next to the stochastically optimal position of the epipoles, the method computes the rigid body motion between the two camera positions. In addition, our text demonstrates the effortlessness and elegance with which such problems integrate into the framework of geometric algebra.