mlsanityData to 7 Oct 2026

An Atlas for the Pinhole Camera

arXiv 2206.13468 ↗First posted 27 Jun 2022math.AG cs.CV math.ACcited by 5

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Abstract (arXiv)

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.

Key facts. Cited by 5 papers in the map (data through 7 Oct 2026). Builds on 5 of its 69 references that are in the map. First posted on arXiv 27 Jun 2022.

Builds on

5 of 69 references.

References · 5

  1. 2020PL1P -- Point-line Minimal Problems under Partial Visibility in Three Viewscited by 16
  2. 2013The Euclidean distance degree of an algebraic varietycited by 15
  3. 2016Minimal Problems for the Calibrated Trifocal Varietycited by 15
  4. 2015On the Existence of Epipolar Matricescited by 6
  5. 2015The Quadrifocal Varietycited by 4

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2022: 1; 2023: 1; 2024: 0; 2025: 2; 2026: 1.

5 papers.

  1. 2022Snapshot of Algebraic Visioncited by 9
  2. 2023Algebra and Geometry of Camera Resectioningcited by 2
  3. 2025Numerically Computing Galois Groups of Minimal Problemscited by 0
  4. 2025Universal Gr"obner Bases of (Universal) Multiview Idealscited by 0
  5. 2026Learning Fast Monomial Orders for Gr"obner Basis Computationscited by 0