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Congruences and Concurrent Lines in Multi-View Geometry

Abstract : We present a new framework for multi-view geometry in computer vision. A camera is a mapping between P 3 and a line congruence. This model, which ignores image planes and measurements, is a natural abstraction of traditional pinhole cameras. It includes two-slit cameras, pushbroom cameras, catadioptric cameras, and many more. We study the concurrent lines variety, which consists of n-tuples of lines in P 3 that intersect at a point. Combining its equations with those of various congruences, we derive constraints for corresponding images in multiple views. We also study photographic cameras which use image measurements and are modeled as rational maps from P^3 to P^2 or P^1 × P^1 .
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Contributor : Matthew Trager Connect in order to contact the contributor
Submitted on : Wednesday, December 28, 2016 - 11:14:14 AM
Last modification on : Friday, July 8, 2022 - 10:09:34 AM

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Jean Ponce, Bernd Sturmfels, Matthew Trager. Congruences and Concurrent Lines in Multi-View Geometry. Advances in Applied Mathematics, Elsevier, 2017, 88, pp.62-91. ⟨10.1016/j.aam.2017.01.001⟩. ⟨hal-01423057⟩



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