On a variational theory of image amodal completion

 Access to full text

 Full (PDF)

1. [1] L. ALVAREZ - Y. GOUSSEAU - J.-M. MOREL, The size of objects in natural and artificial images, Advances in Imaging and Electron Physics, 111 (1999) pp. 167-242. 
2. [2] L. AMBROSIO - V. CASELLES - S. MASNOU - J.-M. MOREL, Connected components of sets of finite perimeter and applications to image processing, J. Eur. Math. Soc., 3 (2001), pp. 39-92. Zbl0981.49024MR1812124
3. [3] L. AMBROSIO - N. FUSCO - D. PALLARA, Functions of Bounded Variation and Free Discontinuity Problems, Oxford University Press, 2000. Zbl0957.49001MR1857292
4. [4] L. AMBROSIO - S. MASNOU, A direct variational approach to a problem arising in image reconstruction, Interfaces and Free Boundaries, 5 (2003), pp. 63-81. Zbl1029.49037MR1959769
5. [5] C. BALLESTER - M. BERTALMIO - V. CASELLES - G. SAPIRO - J. VERDERA, Filling-in by joint interpolation of vector fields and gray levels, IEEE Trans. On Image Processing, 10(8) (2001), pp. 1200-1211. Zbl1037.68771MR1851781
6. [6] G. BELLETTINI, Variational approximation of functionals with curvatures and related properties, J. of Conv. Anal., 4(1) (1997), pp. 91-108. Zbl0882.49013MR1459883
7. [7] G. BELLETTINI - G. DAL MASO - M. PAOLINI, 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. Zbl0797.49013MR1233638
8. [8] G. BELLETTINI - L. MUGNAI, 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. Zbl1110.49014MR2097034
9. [9] G. BELLETTINI - L. MUGNAI, A varifolds representation of the relaxed elastica functional, Submitted. Zbl1127.49032
10. [10] M. BERTALMIO - A. BERTOZZI - G. SAPIRO, Navier-Stokes, fluid dynamics, and image and video inpainting, In Proc. IEEE Int. Conf. on Comp. Vision and Pattern Recog., HawaõÈ, 2001. 
11. [11] M. BERTALMIO - G. SAPIRO - V. CASELLES - C. BALLESTER, Image inpainting, In Proc. ACM Conf. Comp. Graphics (SIGGRAPH), New Orleans, USA (2000), pp. 417-424. 
12. [12] M. BERTALMIO - L. VESE - G. SAPIRO - S. OSHER, Simultaneous structure and texture image inpainting, IEEE Transactions on Image Processing, 12(8) (2003), pp. 882-889. 
13. [13] R. BORNARD - E. LECAN - L. LABORELLI - J.-H. CHENOT, Missing data correction in still images and image sequences, In Proc. 10th ACM Int. Conf. on Multimedia, (2002), pp. 355-361. 
14. [14] T.F. CHAN - S.H. KANG - J. SHEN, Euler's elastica and curvature based inpainting, SIAM Journal of Applied Math., 63 (2) (2002), pp. 564-592. Zbl1028.68185MR1951951
15. [15] T.F. CHAN - J. SHEN, Mathematical models for local deterministic inpaintings, SIAM Journal of Applied Math., 62(3) (2001), pp. 1019-1043. Zbl1050.68157MR1897733
16. [16] T.F. CHAN - J. SHEN, Non-texture inpainting by curvature-driven diffusion (CDD), Journal of Visual Comm. and Image Rep., 12(4) (2001), pp. 436-449. 
17. [17] G. CITTI - A. SARTI, A cortical based model of perceptual completion in the roto-translation space, Submitted. Zbl1088.92008
18. [18] A. CRIMINISI - P. PÉREZ - K. TOYAMA, Object removal by exemplar-based inpainting, In IEEE Int. Conf. Comp. Vision and Pattern Recog., vol. 2, (2003), pp. 721-728. 
19. [19] G. DAL MASO, An Introduction to G-convergence, Birkhaüser, 1993. Zbl0816.49001MR1201152
20. [20] A. EFROS - T. LEUNG, Texture synthesis by non-parametric sampling, In Proc. Int. Conf. on Comp. Vision, vol. 2, Kerkyra, Greece (1999), pp. 1033-1038. 
21. [21] M. ELAD - J.-L. STARCK - D. DONOHO - P. QUERRE, Simultaneous cartoon and texture image inpainting using Morphological Component Analysis, Applied and Comp. Harmonic Analysis, 2005, to appear. Zbl1081.68732MR2186449
22. [22] S. ESEDOGLU - S. RUUTH - R. TSAI, 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. [23] S. ESEDOGLU - J. SHEN, Digital image inpainting by the Mumford-ShahEuler image model, European J. Appl. Math., 13 (2002), pp. 353-370. Zbl1017.94505MR1925256
24. [24] C. FANTONI - W. GERBINO, Contour interpolation by vector field combination, Journal of Vision, 3 (2003), pp. 281-303. 
25. [25] Y. GOUSSEAU, La distribution des formes dans les images naturelles, PhD thesis, CEREMADE, Université Paris IX, 2000. 
26. [26] R. GRZIBOVSKIS - A. HEINTZ, A convolution-thresholding scheme for the Willmore flow, Preprint, 2003. Zbl1147.53054
27. [27] R. HLADKY - S. PAULS, Minimal surfaces in the roto-translation group with applications to a neuro-biological image completion model, Submitted. 
28. [28] G. KANIZSA, Organization in Vision: Essays on Gestalt Perception, Präger, 1979. 
29. [29] S. MASNOU, Filtrage et Désocclusion d'Images par Méthodes d'Ensembles de Niveau, PhD thesis, Université Paris-IX Dauphine, France, 1998. 
30. [30] S. MASNOU, Disocclusion: a variational approach using level lines, IEEE Trans. Image Processing, 11 (2002), pp. 68-76. MR1888912
31. [31] S. MASNOU, Euler spirals for image amodal completion, In preparation. 
32. [32] S. MASNOU - J.-M. MOREL, Level lines based disocclusion, In 5th IEEE Int. Conf. on Image Processing, Chicago, Illinois, October 4-7, 1998. 
33. [33] G. MATHERON, Random Sets and Integral Geometry, John Wiley, N.Y., 1975. Zbl0321.60009MR385969
34. [34] Y. MEYER, Oscillating patterns in image processing and nonlinear evolution equations, In Amer. Math. Soc., editor, University Lecture Series, volume Col. 22, 2001. Zbl0987.35003MR1852741
35. [35] D. MUMFORD, Elastica and computer vision, In C.L. Bajaj, editor, Algebraic Geometry and its Applications, Springer-Verlag, New-York (1994), pp. 491-506. Zbl0798.53003MR1272050
36. [36] M. NITZBERG - D. MUMFORD, The 2.1-D Sketch, In Proc. 3rd Int. Conf. on Computer Vision, Osaka, Japan (1990), pp. 138-144. 
37. [37] J. PETITOT, Neurogeometry of V1 and Kanizsa contours, Axiomathes, 13 (2003), pp. 347-363. 
38. [38] E. VILLÉGER - G. AUBERT - L. BLANC-FÉRAUD, Image Disocclusion Using a Probabilistic Gradient Orientation, In Proc. Int. Conf. on Pattern Recog. (ICPR), Cambridge, U.K., 2004. 
39. [39] L. YAROSLAVSKY - M. EDEN, Fundamentals of Digital Optics, Birkhäuser, 1996. Zbl0877.94006MR1430120
40. [40] W.P. ZIEMER, Weakly differentiable functions, Springer Verlag, 1989. Zbl0692.46022MR1014685