Critical Loci for Two Views Reconstruction as Quadratic Transformations Between Images

1. Beltrametti, M., Carletti, E., Gallarati, D.: Lectures on Curves. Surfaces and Projective Varieties: A Classical View of Algebraic Geometry. EMS Textbooks in Mathematics, vol. 9. European Mathematical Society, Zürich (2009)

   Book  Google Scholar 

2. Bertolini, M., Besana, G.M., Turrini, C.: Instability of projective reconstruction from 1-view near critical configurations in higher dimensions. In: Alberto, C., Juan, M., Claudia, P. (eds.) Algebra Geometry and their Interactions. Contemporary Mathematics, vol. 448, pp. 1–12 (2007)

3. Bertolini, M., Besana, G.M., Turrini, C.: Instability of projective reconstruction of dynamic scenes near critical configurations. In: Proceedings of the International Conference on Computer Vision, ICCV (2007)

4. Bertolini, M., Besana, G.M., Turrini, C.: Applications of multiview tensors in higher dimensions. In: Aja-Fernández, S., de Luis Garcia, R., Tao, D., Li, X. (eds.) Tensors in Image Processing and Computer Vision. Advances in Pattern Recognition. Springer, Berlin (2009)

   MATH  Google Scholar 

5. Bertolini, M., Besana, G.M., Turrini, C.: Critical loci for projective reconstruction from multiple views in higher dimension: a comprehensive theoretical approach. Linear Algebra Appl. 469, 335–363 (2015)

   Article  MathSciNet  Google Scholar 

6. Bertolini, M., Notari, R., Turrini, C.: The Bordiga surface as critical locus for 3-view reconstructions. J. Symb. Comput. 91, 74–97 (2017). (Special Issue MEGA)

   Article  MathSciNet  Google Scholar 

7. Bertolini, M., Turrini, C.: Critical configurations for 1-view in projections from \({\mathbb{P}}^{k} \rightarrow {\mathbb{P}}^{2}\). J. Math. Imaging Vis. 27, 277–287 (2007)

   Article  Google Scholar 

8. Buchanan, T.: The twisted cubic and camera calibration. Comput. Vis. Graph. Image Process. 42, 130–132 (1988)

   Article  MathSciNet  Google Scholar 

9. Dolgachev, I.V.: Classical Algebraic Geometry: A Modern View. Cambridge University Press, Cambridge (2012). https://doi.org/10.1017/CBO9781139084437

   Book  MATH  Google Scholar 

10. Faugeras, O.: Three-Dimensional Computer Vision. A Geometric Viewpoint. MIT Press, Cambridge (1993)

    Google Scholar 

11. Hartley, R., Kahl, F.: Critical configurations for projective reconstruction from multiple views. Int. J. Comput. Vis. 71(1), 5–47 (2007)

    Article  Google Scholar 

12. Hartley, R., Zisserman, A.: Multiple View Geometry in Computer Vision, 2nd edn. Cambridge University Press, Cambridge (2003). (With a foreword by Olivier Faugeras)

    MATH  Google Scholar 

13. Hudson, H.P.: Cremona Transformation in Plane and Space. Cambridge University Press, Cambridge (1927)

    MATH  Google Scholar 

14. Krames, J.: Zur ermittlung eines objectes aus zwei perspectiven (ein beitrag zur theorie der gefhrlichen rter). Monatsh. Math. Phys. 49, 327–354 (1940)

    Article  Google Scholar 

15. Maybank, S.: Theory of Reconstruction from Image Motion. Springer, Secaucus (1992)

    MATH  Google Scholar 

16. Semple, J.G., Kneebone, G.T.: Algebraic Projective Geometry. Oxford University Press, Oxford (1952)

    MATH  Google Scholar 

17. Sturm, P.: Critical motion sequences for the self-calibration of cameras and stereo systems with variable focal length. Image Vis. Comput. 20, 415–426 (2002)

    Article  Google Scholar 

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