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Critical configurations for three projective views (2112.05478v4)
Published 10 Dec 2021 in math.AG and cs.CV
Abstract: The problem of structure from motion is concerned with recovering the 3-dimensional structure of an object from a set of 2-dimensional images taken by unknown cameras. Generally, all information can be uniquely recovered if enough images and point correspondences are provided, yet there are certain cases where unique recovery is impossible; these are called critical configurations. We use an algebraic approach to study the critical configurations for three projective cameras. We show that all critical configurations lie on the intersection of quadric surfaces, and classify exactly which intersections constitute a critical configuration.
- Sameer Agarwal, Andrew Pryhuber and Rekha R. Thomas “Ideals of the Multiview Variety” In IEEE Transactions on Pattern Analysis and Machine Intelligence 43.4, 2021, pp. 1279–1292 DOI: 10.1109/TPAMI.2019.2950631
- “Critical Configurations for 1-View in Projections from ℙk→ℙ2→superscriptℙ𝑘superscriptℙ2\mathbb{P}^{k}\to\mathbb{P}^{2}blackboard_P start_POSTSUPERSCRIPT italic_k end_POSTSUPERSCRIPT → blackboard_P start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT” In Journal of Mathematical Imaging and Vision 27, 2007, pp. 277–287 DOI: 10.1007/s10851-007-0649-6
- Marina Bertolini, Cristina Turrini and GianMario Besana “Instability of Projective Reconstruction of Dynamic Scenes near Critical Configurations” In 2007 IEEE 11th International Conference on Computer Vision, 2007, pp. 1–7 DOI: 10.1109/ICCV.2007.4409100
- “Critical loci in computer vision and matrices dropping rank in codimension one” In Journal of Pure and Applied Algebra 224.12 Elsevier, 2020, pp. 106439
- Martin Bråtelund “Critical configurations for two projective views, a new approach” In Journal of Symbolic Computation, 2023, pp. 102226 DOI: https://doi.org/10.1016/j.jsc.2023.102226
- Martin Bråtelund “A Classification of Critical Configurations for any Number of Projective Views” In arXiv e-prints, 2024, pp. arXiv:2401.03450 DOI: 10.48550/arXiv.2401.03450
- “Compatibility of Fundamental Matrices for Complete Viewing Graphs” In arXiv e-prints, 2023, pp. arXiv:2303.10658 DOI: 10.48550/arXiv.2303.10658
- Thomas Buchanan “The twisted cubic and camera calibration” In Computer Vision, Graphics, and Image Processing 42.1, 1988, pp. 130–132 DOI: https://doi.org/10.1016/0734-189X(88)90146-6
- Thomas Buchanan “Critical sets for 3D reconstruction using lines” In Computer Vision — ECCV’92 Berlin, Heidelberg: Springer Berlin Heidelberg, 1992, pp. 730–738
- Harold Scott Macdonald Coxeter and Samuel L Greitzer “Geometry revisited” In Geometry revisited, New mathematical library ; 19 Washington: Mathematical Association of America, 1967
- “Critical Curves and Surfaces for Euclidean Reconstruction” In Computer Vision — ECCV 2002 Berlin, Heidelberg: Springer Berlin Heidelberg, 2002, pp. 447–462
- “Critical Configurations for Projective Reconstruction from Multiple Views” In International Journal of Computer Vision 71.1, 2007, pp. 5–47 DOI: doi:10.1007/s11263-005-4796-1
- “Multiple View Geometry in Computer Vision” Cambridge University Press, 2004 DOI: 10.1017/CBO9780511811685
- Richard I. Hartley “Ambiguous Configurations for 3-View Projective Reconstruction” In Computer Vision - ECCV 2000 Berlin, Heidelberg: Springer Berlin Heidelberg, 2000, pp. 922–935
- F. Kahl, R. Hartley and K. Astrom “Critical configurations for n-view projective reconstruction” In Proceedings of the 2001 IEEE Computer Society Conference on Computer Vision and Pattern Recognition. CVPR 2001 2, 2001, pp. II-158–II-164 DOI: 10.1109/CVPR.2001.990945
- J. Krames “Zur Ermittlung eines Objektes aus zwei Perspektiven. (Ein Beitrag zur Theorie der “gefährlichen Örter”.)” In Monatshefte für Mathematik und Physik 49, 1941, pp. 327–354
- “A stability analysis of the Fundamental matrix” In Computer Vision — ECCV ’94 Berlin, Heidelberg: Springer Berlin Heidelberg, 1994, pp. 577–588
- S. Maybank “Theory of Reconstruction from Image Motion”, Springer Series in Information Sciences Springer Berlin Heidelberg, 1993 DOI: https://doi.org/10.1007/978-3-642-77557-4
- Stephen J Maybank and Amnon Shashua “Ambiguity in reconstruction from images of six points” In Sixth International Conference on Computer Vision (IEEE Cat. No.98CH36271), 1998, pp. 703–708 DOI: 10.1109/ICCV.1998.710794
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