@article{RSMUP_2006__116__211_0, author = {Masnou, Simon and Morel, Jean-Michel}, title = {On a variational theory of image amodal completion}, journal = {Rendiconti del Seminario Matematico della Universit\`a di Padova}, volume = {115}, year = {2006}, pages = {211-252}, mrnumber = {2287348}, zbl = {1150.49023}, language = {en}, url = {http://dml.mathdoc.fr/item/RSMUP_2006__116__211_0} }
Masnou, Simon; Morel, Jean-Michel. On a variational theory of image amodal completion. Rendiconti del Seminario Matematico della Università di Padova, Tome 115 (2006) pp. 211-252. http://gdmltest.u-ga.fr/item/RSMUP_2006__116__211_0/
[1] The size of objects in natural and artificial images, Advances in Imaging and Electron Physics, 111 (1999) pp. 167-242.
- - ,[2] Connected components of sets of finite perimeter and applications to image processing, J. Eur. Math. Soc., 3 (2001), pp. 39-92. | MR 1812124 | Zbl 0981.49024
- - - ,[3] Functions of Bounded Variation and Free Discontinuity Problems, Oxford University Press, 2000. | MR 1857292 | Zbl 0957.49001
- - ,[4] A direct variational approach to a problem arising in image reconstruction, Interfaces and Free Boundaries, 5 (2003), pp. 63-81. | MR 1959769 | Zbl 1029.49037
- ,[5] Filling-in by joint interpolation of vector fields and gray levels, IEEE Trans. On Image Processing, 10(8) (2001), pp. 1200-1211. | MR 1851781 | Zbl 1037.68771
- - - - ,[6] Variational approximation of functionals with curvatures and related properties, J. of Conv. Anal., 4(1) (1997), pp. 91-108. | MR 1459883 | Zbl 0882.49013
,[7] Semicontinuity and relaxation properties of a curvature depending functional in 2D, Ann. Scuola Norm. Sup. Pisa Cl. Sci, (4) 20, no 2 (1993), pp. 247-297. | Numdam | MR 1233638 | Zbl 0797.49013
- - ,[8] Characterization and representation of the lower semicontinuous envelope of the elastica functional, Ann. Inst. H. Poincaré, Anal. Non Lin., 21(6) (2004), pp. 839-880. | Numdam | MR 2097034 | Zbl 1110.49014
- ,[9] A varifolds representation of the relaxed elastica functional, Submitted. | Zbl 1127.49032
- ,[10] Navier-Stokes, fluid dynamics, and image and video inpainting, In Proc. IEEE Int. Conf. on Comp. Vision and Pattern Recog., HawaõÈ, 2001.
- - ,[11] Image inpainting, In Proc. ACM Conf. Comp. Graphics (SIGGRAPH), New Orleans, USA (2000), pp. 417-424.
- - - ,[12] Simultaneous structure and texture image inpainting, IEEE Transactions on Image Processing, 12(8) (2003), pp. 882-889.
- - - ,[13] Missing data correction in still images and image sequences, In Proc. 10th ACM Int. Conf. on Multimedia, (2002), pp. 355-361.
- - - ,[14] Euler's elastica and curvature based inpainting, SIAM Journal of Applied Math., 63 (2) (2002), pp. 564-592. | MR 1951951 | Zbl 1028.68185
- - ,[15] Mathematical models for local deterministic inpaintings, SIAM Journal of Applied Math., 62(3) (2001), pp. 1019-1043. | MR 1897733 | Zbl 1050.68157
- ,[16] Non-texture inpainting by curvature-driven diffusion (CDD), Journal of Visual Comm. and Image Rep., 12(4) (2001), pp. 436-449.
- ,[17] A cortical based model of perceptual completion in the roto-translation space, Submitted. | Zbl 1088.92008
- ,[18] Object removal by exemplar-based inpainting, In IEEE Int. Conf. Comp. Vision and Pattern Recog., vol. 2, (2003), pp. 721-728.
- - ,[19] An Introduction to G-convergence, Birkhaüser, 1993. | MR 1201152 | Zbl 0816.49001
,[20] Texture synthesis by non-parametric sampling, In Proc. Int. Conf. on Comp. Vision, vol. 2, Kerkyra, Greece (1999), pp. 1033-1038.
- ,[21] Simultaneous cartoon and texture image inpainting using Morphological Component Analysis, Applied and Comp. Harmonic Analysis, 2005, to appear. | MR 2186449 | Zbl 1081.68732
- - - ,[22] Threshold dynamics for shape reconstruction and disocclusion, Technical report, UCLA CAM Report 05-22, April 2005, In Proc. of IEEE Int. Conf. on Image Processing 2005.
- - ,[23] Digital image inpainting by the Mumford-ShahEuler image model, European J. Appl. Math., 13 (2002), pp. 353-370. | MR 1925256 | Zbl 1017.94505
- ,[24] Contour interpolation by vector field combination, Journal of Vision, 3 (2003), pp. 281-303.
- ,[25] La distribution des formes dans les images naturelles, PhD thesis, CEREMADE, Université Paris IX, 2000.
,[26] A convolution-thresholding scheme for the Willmore flow, Preprint, 2003. | Zbl 1147.53054
- ,[27] Minimal surfaces in the roto-translation group with applications to a neuro-biological image completion model, Submitted.
- ,[28] Organization in Vision: Essays on Gestalt Perception, Präger, 1979.
,[29] Filtrage et Désocclusion d'Images par Méthodes d'Ensembles de Niveau, PhD thesis, Université Paris-IX Dauphine, France, 1998.
,[30] Disocclusion: a variational approach using level lines, IEEE Trans. Image Processing, 11 (2002), pp. 68-76. | MR 1888912
,[31] Euler spirals for image amodal completion, In preparation.
,[32] Level lines based disocclusion, In 5th IEEE Int. Conf. on Image Processing, Chicago, Illinois, October 4-7, 1998.
- ,[33] Random Sets and Integral Geometry, John Wiley, N.Y., 1975. | MR 385969 | Zbl 0321.60009
,[34] Oscillating patterns in image processing and nonlinear evolution equations, In Amer. Math. Soc., editor, University Lecture Series, volume Col. 22, 2001. | MR 1852741 | Zbl 0987.35003
,[35] Elastica and computer vision, In C.L. Bajaj, editor, Algebraic Geometry and its Applications, Springer-Verlag, New-York (1994), pp. 491-506. | MR 1272050 | Zbl 0798.53003
,[36] The 2.1-D Sketch, In Proc. 3rd Int. Conf. on Computer Vision, Osaka, Japan (1990), pp. 138-144.
- ,[37] Neurogeometry of V1 and Kanizsa contours, Axiomathes, 13 (2003), pp. 347-363.
,[38] Image Disocclusion Using a Probabilistic Gradient Orientation, In Proc. Int. Conf. on Pattern Recog. (ICPR), Cambridge, U.K., 2004.
- - ,[39] Fundamentals of Digital Optics, Birkhäuser, 1996. | MR 1430120 | Zbl 0877.94006
- ,[40] Weakly differentiable functions, Springer Verlag, 1989. | MR 1014685 | Zbl 0692.46022
,