Congruences and Concurrent Lines in Multi-View Geometry

Jean Ponce; Bernd Sturmfels; Matthew Trager

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arXiv · 1608.05924

Congruences and Concurrent Lines in Multi-View Geometry

Jean Ponce·Bernd Sturmfels·Matthew Trager

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Abstract

We present a new framework for multi-view geometry in computer vision. A camera is a mapping between $\mathbb{P}^3$ 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 $\mathbb{P}^3$ 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 $\mathbb{P}^3$ to $\mathbb{P}^2$ or $\mathbb{P}^1\times \mathbb{P}^1$.

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math.AG cs.CV cs.SC

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BibTeX RIS

Jean Ponce, Bernd Sturmfels, Matthew Trager. 2016-08-21. Congruences and Concurrent Lines in Multi-View Geometry. https://arxiv.org/abs/1608.05924

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