EDP Sciences logo
Subscriber Authentication Point
Search
Menu
All issues Volume 20 / No 3 (July-September 2014) ESAIM: COCV, 20 3 (2014) 748-770 References
Free Access
Issue
ESAIM: COCV
Volume 20, Number 3, July-September 2014
Page(s) 748 - 770
DOI https://doi.org/10.1051/cocv/2013082
Published online 27 May 2014
  1. A. Agrachev, Compactness for sub-Riemannian length-minimizers and subanalyticity. Rend. Sem. Mat. Univ. Politec. Torino 56 (2001) 1–12. [Google Scholar]
  2. A. Agrachev, Exponential mappings for contact sub-Riemannian structures. J. Dynam. Control Syst. 2 (1996) 321–358. [CrossRef] [Google Scholar]
  3. A. Agrachev, D. Barilari and U. Boscain, Introduction to Riemannian and Sub-Riemannian geometry, available at http://www.math.jussieu.fr/˜barilari/Notes.php [Google Scholar]
  4. A.A. Agrachev, Yu. L. Sachkov,Control Theory from the Geometric Viewpoint. Encyclopedia of Math. Sci., vol. 87. Springer (2004). [Google Scholar]
  5. A. Bellaiche, The tangent space in sub-Riemannian geometry. Sub-Riemannian Geometry, Progr. Math., vol. 144. Edited by A. Bellaiche and J.-J. Risler. Birkhäuser, Basel (1996) 1–78. [Google Scholar]
  6. U. Boscain, G. Charlot and F. Rossi, Existence planar curves minimizing length and curvature. Proc. Steklov Institute Math. 270 (2010) 43–56. [CrossRef] [Google Scholar]
  7. U. Boscain, R. Chertovskih, J.-P. Gauthier and A. Remizov, Hypoelliptic diffusion and human vision: a semi-discrete new twist on the Petitot theory. To appear in SIAM J. Imaging Sci. [Google Scholar]
  8. U. Boscain, J. Duplaix, J.P. Gauthier and F. Rossi, Anthropomorphic Image Reconstruction via Hypoelliptic Diffusion. SIAM J. Control Opt. 50 1309–1336. [Google Scholar]
  9. U. Boscain and F. Rossi, Projective Reeds-Shepp car on S2 with quadratic cost. ESAIM: COCV 16 (2010) 275–297. [CrossRef] [EDP Sciences] [Google Scholar]
  10. G. Citti and A. Sarti, A cortical based model of perceptual completion in the roto-translation space. J. Math. Imaging Vision 24 (2006) 307–326. [Google Scholar]
  11. R. Duits, U. Boscain, F. Rossi and Y. Sachkov, Association fields via cuspless sub-Riemannian geodesics in SE(2). To appear in J. Math. Imaging Vision. [Google Scholar]
  12. R. Duits and E.M. Franken, Left-invariant parabolic evolutions on SE(2) and contour enhancement via invertible orientation scores, Part I: Linear Left-Invariant Diffusion Equations on SE(2). Quart. Appl. Math. 68 (2010) 293–331. [MathSciNet] [Google Scholar]
  13. R. Duits and E.M. Franken, Left-invariant parabolic evolutions on SE(2) and contour enhancement via invertible orientation scores, Part II: nonlinear left-invariant diffusions on invertible orientation scores. Quart. Appl. Math. 68 (2010) 255–292. [MathSciNet] [Google Scholar]
  14. M. Gromov, Carnot–Caratheodory spaces seen from within, in Sub-Riemannian Geometry, in vol. 144 Progr. Math., edited by A. Bellaiche and J.-J. Risler (1996) 79–323. [Google Scholar]
  15. R.K. Hladky and S.D. Pauls, Minimal Surfaces in the Roto-Translation Group with Applications to a Neuro-Biological Image Completion Model. J Math Imaging Vis 36 (2010) 1–27. [CrossRef] [Google Scholar]
  16. W.C. Hoffman, The visual cortex is a contact bundle. Appl. Math. Comput. 32 (1989) 137–167. [CrossRef] [Google Scholar]
  17. L. Hörmander, Hypoelliptic Second Order Differential Equations. Acta Math. 119 (1967) 147–171. [CrossRef] [MathSciNet] [Google Scholar]
  18. D.H. Hubel and T.N. Wiesel, Receptive fields, binocular interaction and functional architecture in the cat’s visual cortex. The J. Phys. 160 (1962) 106. [Google Scholar]
  19. I. Moiseev and Yu. L. Sachkov, Maxwell strata in sub-Riemannian problem on the group of motions of a plane. ESAIM: COCV 16 (2010) 380–399. [CrossRef] [EDP Sciences] [Google Scholar]
  20. R. Montgomery, A Tour of Subriemannian Geometries, Their Geodesics and Applications. Vol. 91 of Math. Surveys and Monogr. AMS (2002). [Google Scholar]
  21. M. Nitzberg and D. Mumford, The 2.1-D sketch. ICCV (1990) 138–144. [Google Scholar]
  22. J. Petitot, Vers une Neuro-géomètrie. Fibrations corticales, structures de contact et contours subjectifs modaux. Math. Inform. Sci. Humaines 145 (1999) 5–101. [Google Scholar]
  23. J. Petitot, Neurogéomètrie de la vision – Modèles mathématiques et physiques des architectures fonctionnelles. Les Éditions de l’École Polytechnique (2008). [Google Scholar]
  24. J. Petitot, The neurogeometry of pinwheels as a sub-Riemannian contact structure. J. Phys. – Paris 97 (2003) 265–309. [CrossRef] [PubMed] [Google Scholar]
  25. Y. Sachkov, Conjugate and cut time in the sub-Riemannian problem on the group of motions of a plane. ESAIM: COCV 16 (2010) 1018–1039. [CrossRef] [EDP Sciences] [Google Scholar]
  26. Y.L. Sachkov, Cut locus and optimal synthesis in the sub-Riemannian problem on the group of motions of a plane. ESAIM: COCV 17 (2011) 293–321. [CrossRef] [EDP Sciences] [Google Scholar]
  27. Y.L. Sachkov, Discrete symmetries in the generalized Dido problem. Sb. Math. 197 (2006) 235–257. [CrossRef] [MathSciNet] [Google Scholar]
  28. G. Sanguinetti, G. Citti and A. Sarti, Image completion using a diffusion driven mean curvature flow in a sub-riemannian space, in Int. Conf. Comput. Vision Theory and Appl. (VISAPP’08), Funchal (2008) 22–25. [Google Scholar]
  29. A.V. Sarychev, First and Second-Order Integral Functionals of the Calculus of Variations Which Exhibit the Lavrentiev Phenomenon. J. Dyn. Control Syst. 3 (1997) 565–588. [Google Scholar]
  30. R. Vinter, Optimal Control. Birkhauser (2010). [Google Scholar]
  31. E.T. Whittaker and G.N. Watson, A Course of Modern Analysis. An introduction to the general theory of infinite processes and of analytic functions; with an account of principal transcendental functions. Cambridge University Press, Cambridge (1996). [Google Scholar]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.