Computer Vision and Image Understanding
Multiple view geometry in computer vision
Multiple view geometry in computer vision
Optimization Criteria and Geometric Algorithms for Motion and Structure Estimation
International Journal of Computer Vision
A Mathematical Introduction to Robotic Manipulation
A Mathematical Introduction to Robotic Manipulation
Theory of Reconstruction from Image Motion
Theory of Reconstruction from Image Motion
Properties of the Catadioptric Fundamental Matrix
ECCV '02 Proceedings of the 7th European Conference on Computer Vision-Part II
Generalized Rank Conditions in Multiple View Geometry with Applications to Dynamical Scenes
ECCV '02 Proceedings of the 7th European Conference on Computer Vision-Part II
Rank Conditions on the Multiple-View Matrix
International Journal of Computer Vision
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Based upon an axiomatic formulation of vision system in a general Riemannian manifold, this paper provides a unified framework for the study of multiple view geometry in three dimensional spaces of constant curvature, including Euclidean space, spherical space, and hyperbolic space. It is shown that multiple view geometry for Euclidean space can be interpreted as a limit case when (sectional) curvature of a non-Euclidean space approaches to zero. In particular, we show that epipolar constraint in the general case is exactly the same as that known for the Euclidean space but should be interpreted more generally when being applied to triangulation in non-Euclidean spaces. A special triangulation method is hence introduced using trigonometry laws from Absolute Geometry. Based on a common rank condition, we give a complete study of constraints among multiple images as well as relationships among all these constraints. This idealized geometric framework may potentially extend extant multiple view geometry to the study of astronomical imaging where the effect of space curvature is no longer negligible, e.g., the so-called “gravitational lensing” phenomenon, which is currently active study in astronomical physics and cosmology.