An Atlas for the Pinhole Camera
Algebraic Geometry
2022-10-05 v2 Computer Vision and Pattern Recognition
Commutative Algebra
Abstract
We introduce an atlas of algebro-geometric objects associated with image formation in pinhole cameras. The nodes of the atlas are algebraic varieties or their vanishing ideals related to each other by projection or elimination and restriction or specialization respectively. This atlas offers a unifying framework for the study of problems in 3D computer vision. We initiate the study of the atlas by completely characterizing a part of the atlas stemming from the triangulation problem. We conclude with several open problems and generalizations of the atlas.
Keywords
Cite
@article{arxiv.2206.13468,
title = {An Atlas for the Pinhole Camera},
author = {Sameer Agarwal and Timothy Duff and Max Lieblich and Rekha Thomas},
journal= {arXiv preprint arXiv:2206.13468},
year = {2022}
}
Comments
47 pages with references and appendices, final version