Free Access
Volume 20, Number 3, July-September 2014
Page(s) 748 - 770
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˜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]

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