Minimal Problems for the Calibrated Trifocal Variety

DOI10.1137/16M1104482zbMath1386.14185arXiv1611.05947MaRDI QIDQ5369250

Joe Kileel

Publication date: 16 October 2017

Published in: SIAM Journal on Applied Algebra and Geometry (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1611.05947

zbMATH Keywords

numerical algebraic geometryminimal problemscalibrated trifocal varietyhomotopy continuation software

Mathematics Subject Classification ID

Global methods, including homotopy approaches to the numerical solution of nonlinear equations (65H20) Rational and unirational varieties (14M20) Computational aspects of higher-dimensional varieties (14Q15) Multilinear algebra, tensor calculus (15A69) Machine vision and scene understanding (68T45) Projective and enumerative algebraic geometry (14N99)

Related Items (7)

Galois/Monodromy Groups for Decomposing Minimal Problems in 3D Reconstruction ⋮ An atlas for the pinhole camera ⋮ Nonlinear algebra and applications ⋮ Two Hilbert Schemes in Computer Vision ⋮ Unnamed Item ⋮ Necessary and sufficient polynomial constraints on compatible triplets of essential matrices ⋮ Reconstruction of Surfaces with Ordinary Singularities from Their Silhouettes

Uses Software

• Macaulay2
• Bertini

Cites Work

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• Witness sets of projections
• Numerical computation of Galois groups
• Theory of reconstruction from image motion
• Trace test
• On some properties of calibrated trifocal tensors
• A geometric approach to the trifocal tensor
• Trinocular geometry revisited
• A Hilbert Scheme in Computer Vision
• Regeneration homotopies for solving systems of polynomials
• The ideal of the trifocal variety
• Symmetric Functions Applied to Decomposing Solution Sets of Polynomial Systems
• The Numerical Solution of Systems of Polynomials Arising in Engineering and Science
• Critical motions for auto-calibration when some intrinsic parameters can vary

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