Open Access
Issue
ESAIM: M2AN
Volume 56, Number 2, March-April 2022
Page(s) 485 - 504
DOI https://doi.org/10.1051/m2an/2022014
Published online 24 February 2022
  1. M. Agueh, G. Carlier and N. Igbida, On the minimizing movement with the 1-Wasserstein distance. ESAIM Control Optim. Calc. Var. 24 (2018) 1415–1427. [CrossRef] [EDP Sciences] [MathSciNet] [Google Scholar]
  2. A. Ahmed and A. Farag, A new formulation for shape from shading for non-Lambertian surfaces. In: IEEE Computer Society Conference on Computer Vision and Pattern Recognition. Vol. 2 (2006) 1817–1824. [Google Scholar]
  3. L. Ambrosio, N. Fusco and D. Pallara, Functions of Bounded Variation and Free Discontinuity Problems. Clarendon Press, Oxford (2000). [Google Scholar]
  4. M. Bardi and M. Falcone, Discrete approximation of the minimal time function for systems with regular optimal trajectories. In: Analysis and Optimization of Systems. Lect. Notes Control Inf. Sci. Vol. 144 (1990) 103–112. [CrossRef] [Google Scholar]
  5. J.-D. Benamou and G. Carlier, Augmented Lagrangian methods for transport optimization, mean field games and degenerate elliptic equations. J. Optim. Theory Appl. 167 (2015) 1–26. [CrossRef] [MathSciNet] [Google Scholar]
  6. F. Boyer and P. Fabrie, Mathematical Tools for the Study of the Incompressible Navier-Stokes Equations and Related Models. Vol. 183 of Applied Mathematical Sciences. Springer, New York (2013). [Google Scholar]
  7. F. Camilli and L. Grüne, Numerical approximation of the maximal solutions for a class of degenerate Hamilton-Jacobi equations. SIAM J. Numer. Anal. 38 (2000) 1540–1560. [CrossRef] [MathSciNet] [Google Scholar]
  8. F. Camilli and A. Siconolfi, Maximal subsolutions for a class of degenerate Hamilton-Jacobi problems. Indiana Univ. Math. J. 48 (1999) 1111–1131. [Google Scholar]
  9. F. Camilli and S. Tozza, A unified approach to the well-posedness of some non-Lambertian models in shape-from-shading theory. SIAM J. Imaging Sci. 10 (2017) 26–46. [CrossRef] [MathSciNet] [Google Scholar]
  10. A. Chambolle, An algorithm for total variation minimization and applications. J. Math. Imaging Vis. 20 (2004) 89–97. [Google Scholar]
  11. A. Chambolle and T. Pock, A first-order primal-dual algorithm for convex problems with applications to imaging. J. Math. Imaging Vis. 40 (2011) 120–145. [CrossRef] [Google Scholar]
  12. F. Courteille, A. Crouzil, J.-D. Durou and P. Gurdjos, Towards shape from shading under realistic photographic conditions. In: Proceedings of the 17th International Conference on Pattern Recognition. Vol. 2 (2004) 277–280. [Google Scholar]
  13. M.G. Crandall and P.-L. Lions, Viscosity solutions of Hamilton-Jacobi equations. Trans. Am. Math. Soc. 277 (1983) 1–42. [Google Scholar]
  14. M.G. Crandall, H. Ishii and P.-L. Lions, User’s guide to viscosity solutions of second order partial differential equations. Bull. Am. Math. Soc. New Ser. 27 (1992) 1–67. [CrossRef] [Google Scholar]
  15. A. Crouzil, X. Descombes and J.-D. Durou, A multiresolution approach for shape from shading coupling deterministic and stochastic optimization. IEEE Trans. Pattern Anal. Mach. Intell. 25 (2003) 1416–1421. [CrossRef] [Google Scholar]
  16. P. Daniel and J.-D. Durou, From deterministic to stochastic methods for shape from shading. In: Proc. 4th Asian Conf. Comp. Vis. (2000). [Google Scholar]
  17. J.-D. Durou, M. Falcone and M. Sagona, Numerical methods for shape-from-shading: a new survey with benchmarks. Comput. Vis. Image. Underst. 109 (2008) 22–43. [CrossRef] [Google Scholar]
  18. S. Dweik and F. Santambrogio, Summability estimates on transport densities with Dirichlet regions on the boundary via symmetrization techniques. ESAIM Control Optim. Calc. Var. 24 (2018) 1167–1180. [CrossRef] [EDP Sciences] [MathSciNet] [Google Scholar]
  19. H. Ennaji, N. Igbida and V.T. Nguyen, Augmented Lagrangian methods for degenerate Hamilton-Jacobi equations. Calc. Var. Part. Differ. Equ. 60 (2021) 238. [CrossRef] [Google Scholar]
  20. H. Ennaji, N. Igbida and V.T. Nguyen, Beckmann-type problem for degenerate Hamilton-Jacobi equations. Quart. Appl. Math. (2021) (in press) DOI: 10.1090/qam/1606. [Google Scholar]
  21. M. Falcone, T. Giorgi and P. Loreti, Level sets of viscosity solutions: some applications to fronts and Rendez-Vous problems. SIAM J. Appl. Math. 54 (1994) 1335–1354. [CrossRef] [MathSciNet] [Google Scholar]
  22. M. Falcone, M. Sagona and A. Seghini, A scheme for the shape-from-shading model with black shadows. In: Numerical Mathematics and Advanced Applications (2003) 503–512. [CrossRef] [Google Scholar]
  23. A. Fathi and A. Siconolfi, PDE aspects of Aubry-Mather theory for quasiconvex Hamiltonians. Calc. Var. Partial Differ. Equ. 22 (2005) 185–228. [CrossRef] [MathSciNet] [Google Scholar]
  24. A. Festa, Analysis and approximation of Hamilton Jacobi equations on irregular data. Ph.D. thesis, University of Rome, Sapienza (2012). [Google Scholar]
  25. A. Festa and M. Falcone, An approximation scheme for an Eikonal equation with discontinuous coefficient. SIAM J. Numer. Anal. 52 (2014) 236–257. [CrossRef] [MathSciNet] [Google Scholar]
  26. H. Hayakawa, S. Nishida, Y. Wada and M. Kawato, A computational model for shape estimation by integration of shading and edge information. Neural Netw. 7 (1994) 1193–1209. [CrossRef] [Google Scholar]
  27. B.K. Horn, Shape from shading: a method for obtaining the shape of a smooth opaque object from one view. Technical report, USA (1970). [Google Scholar]
  28. B.K.P. Horn, Obtaining Shape from Shading Information, MIT Press, Cambridge, USA, (1989) 123–171. [Google Scholar]
  29. B.K.P. Horn and M.J. Brooks, The variational approach to shape from shading. Comput. Vis. Graph. Image Process. 33 (1986) 174–208. [CrossRef] [Google Scholar]
  30. N. Igbida and V.T. Nguyen, Augmented Lagrangian method for optimal partial transportation. IMA J. Numer. Anal. 38 (2018) 156–183. [CrossRef] [MathSciNet] [Google Scholar]
  31. N. Igbida, V.T. Nguyen and J. Toledo, On the uniqueness and numerical approximations for a matching problem. SIAM J. Optim. 27 (2017) 2459–2480. [CrossRef] [MathSciNet] [Google Scholar]
  32. R. Jordan, D. Kinderlehrer and F. Otto, The variational formulation of the Fokker-Planck equation. SIAM J. Math. Anal. 29 (1998) 1–17. [Google Scholar]
  33. P.-L. Lions, Generalized solutions of Hamilton-Jacobi equations. In: Research Notes in Mathematics. Vol. 69. Pitman Advanced Publishing Program, Boston – London – Melbourne (1982). [Google Scholar]
  34. P.L. Lions, E. Rouy and A. Tourin, Shape-from-shading, viscosity solutions and edges. Numer. Math. 64 (1993) 323–353. [CrossRef] [MathSciNet] [Google Scholar]
  35. R. Monneau, Introduction to the fast marching method (2010). https://hal.archives-ouvertes.fr/hal-00530910 [Google Scholar]
  36. A.P. Pentland, Local shading analysis. IEEE Trans. Pattern Anal. Mach. Intell. PAMI-6 (1984) 170–187. [CrossRef] [Google Scholar]
  37. T. Ping-Sing and M. Shah, Shape from shading using linear approximation. Image Vis. Comput. 12 (1994) 487–498. [CrossRef] [Google Scholar]
  38. T. Pock and A. Chambolle, Diagonal preconditioning for first order primal-dual algorithms in convex optimization. In: 2011 International Conference on Computer Vision (2011) 1762–1769. [Google Scholar]
  39. E. Prados, F. Camilli and O. Faugeras, A viscosity solution method for shape-from-shading without image boundary data. ESAIM: M2AN 40 (2006) 393–412. [CrossRef] [EDP Sciences] [Google Scholar]
  40. Y. Quéau, J. Mélou, F. Castan, D. Cremers and J.-D. Durou, A variational approach to shape-from-shading under natural illumination. In: International Conference on Energy Minimization Methods in Computer Vision and Pattern Recognition (2018) 342–357. [Google Scholar]
  41. E. Rouy and A. Tourin, A viscosity solutions approach to shape-from-shading. SIAM J. Numer. Anal. 29 (1992) 867–884. [CrossRef] [MathSciNet] [Google Scholar]
  42. A. Tankus, N. Sochen and Y. Yeshurun, Shape-from-shading under perspective projection. Int. J. Comput. Vision 63 (2005) 21–43. [CrossRef] [Google Scholar]
  43. S. Tozza and M. Falcone, Analysis and approximation of some shape-from-shading models for non-Lambertian surfaces. J. Math. Imaging Vision 55 (2016) 153–178. [CrossRef] [MathSciNet] [Google Scholar]
  44. R. Zhang, P.-S. Tsai, J.E. Cryer and M. Shah, Shape from shading: a survey. IEEE Trans. Pattern Anal. Mach. Intell. 21 (1999) 690–706. [CrossRef] [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.

Recommended for you