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Register a new userA clever elimination strategy for efficient minimal solvers
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Added by
Joe Kileel
Publication date
2017
fields
Informatics Engineering
and research's language is
English
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We present a new insight into the systematic generation of minimal solvers in computer vision, which leads to smaller and faster solvers. Many minimal problem formulations are coupled sets of linear and polynomial equations where image measurements enter the linear equations only. We show that it is useful to solve such systems by first eliminating all the unknowns that do not appear in the linear equations and then extending solutions to the rest of unknowns. This can be generalized to fully non-linear systems by linearization via lifting. We demonstrate that this approach leads to more efficient solvers in three problems of partially calibrated relative camera pose computation with unknown focal length and/or radial distortion. Our approach also generates new interesting constraints on the fundamental matrices of partially calibrated cameras, which were not known before.
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This paper introduces minimal solvers that jointly solve for radial lens undistortion and affine-rectification using local features extracted from the image of coplanar translated and reflected scene texture, which is common in man-made environments. The proposed solvers accommodate different types of local features and sampling strategies, and three of the proposed variants require just one feature correspondence. State-of-the-art techniques from algebraic geometry are used to simplify the formulation of the solvers. The generated solvers are stable, small and fast. Synthetic and real-image experiments show that the proposed solvers have superior robustness to noise compared to the state of the art. The solvers are integrated with an automated system for rectifying imaged scene planes from coplanar repeated texture. Accurate rectifications on challenging imagery taken with narrow to wide field-of-view lenses demonstrate the applicability of the proposed solvers.
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