A functional analysis model for natural images permitting structured compression

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1. [1] J.P. D'Alès, J. Froment and J.M. Morel, Reconstruction visuelle et généricité, Second European Workshop on Image Processing and Mean Curvature Motion, UIB, Spain ( 1995) 1_21. 
2. [2] L. Alvarez, F. Guichard, P.L. Lions and J.M. Morel, Axioms and fundamental equations of image processing. Arch. Rational Mechanics and Anal. 16 ( 1993) 200-257. Zbl0788.68153MR1225209
3. [3] F. Cao, Absolutely minimizing Lipschitz extension with discontinuous boundary data. C.R. Acad. Sci. Paris 327, Série I ( 1998) 563-568. Zbl0990.35048MR1650611
4. [4] J. Canny, A computational approach to edge detection. IEEE Trans. Pattern Analysis and Machine Intelligence 8 ( 1986) 679-698. 
5. [5] S. Carlsson, Sketch based coding of grey level images. Signal Processing North-Holland 15 ( 1998) 57-83. 
6. [6] J.R. Casas, Morphological Interpolation for Image Coding , 12th International Conference on Analysis and Optimization of systems. Images, Wavelets and PDEs. M.O. Berger, R. Deriche, I. Herlin, J. Jaffré, J.M. Morel, Eds., Springer, Paris ( 1996). Zbl0960.68741
7. [7] V. Caselles, B. Coll and J.M. Morel, A Kanizsa programme. Progress in Nonlinear Differential Equs. and their Applications 25 ( 1996) 35-55. Zbl1077.68924MR1414487
8. [8] V. Caselles, J.M. Morel and C. Sbert, An Axiomatic Approach to Image Interpolation. IEEE Trans. on Image Processing 7 ( 1998) 376-386. Zbl0993.94504MR1669524
9. [9] V. Caselles, B. Coll and J.M. Morel, Topographic maps and local contrast changes in natural images. Internat. J. Comput. Vision, to appear. 
10. [10] V. Caselles, B. Coll and J.M. Morel, The Connected Components of Sets of Finite Perimeter in the Plane, Preprint ( 1998). 
11. [11] A. Chambolle and P.L. Lions, Image Recovery via Total Variation Minimization and Related Problems. Numerische Mathematik 76 ( 1997) 167-188. Zbl0874.68299MR1440119
12. [12] A. Cohen, I. Daubechies and J.C. Feauveau, Biorthogonal bases of compactly supported wavelets. Comm. in Pure & Appl. Math. 45 ( 1992). Zbl0776.42020MR1162365
13. [13] M.G. Crandall, H. Ishii and P.L. Lions, User's Guide to Viscosity Solution of Second Order Partial Differential Equations. Bull. Amer. Math. Soc. 27 ( 1992) 1-67. Zbl0755.35015MR1118699
14. [14] F. Dibos and G. Koepfler, Global Total Variation Minimization, TR 9801, CEREMADE, Université Paris-Dauphine, France ( 1998). Zbl0957.49002
15. [15] L.C. Evans and R.F. Gariepy, Measure theory and fine properties of functions, Studies in Advanced Mathematics, CRC Press Inc. ( 1992). Zbl0804.28001MR1158660
16. [16] J. Froment and S. Mallat, Second Generation Compact Image Coding with Wavelets, Wavelets - A Tutorial in Theory and Applications, C.K. Chui, Ed., Academic Press ( 1992) 655-678. 
17. [17] J. Froment, Vol. 1: MegaWave2 User's Guide, Vol. 2: MegaWave2 System Library, Vol. 3: MegaWave2 User's Modules Library,, The Preliminary Guides to the MegaWave2 Software ( 1998). A version is available at http://www.cmla.ens-cachan.fr/Cmla/Megawave/ into the software package. 
18. [18] R. Hummel and R. Moniot, Reconstruction from zero-crossings in scale-space. IEEE Trans. on Acoustic, Speech and Signal Processing 37 ( 1989). 
19. [19] G. Kanisza, Grammatica del Vedere, II Mulino, Bologna ( 1980). 
20. [20] G. Kanisza, Vedere e pensare, II Mulino, Bologna ( 1991). 
21. [21] M. Kunt, M. Bénard and R. Leonardi, Recent Results in High-Compression Image Coding. IEEE Trans. on Circuits and Systems ( 1987) 1306-1336. 
22. [22] J. Li, P.Y. Cheng and C.C.J. Kuo, An embedded wavelet packed transform technique for texture compression. SPIE 2569 ( 1995) 602-613. 
23. [23] S. Mallat and S. Zhong, Characterization of signals from multiscale edges. IEEE Trans. Pattern Recognition and Machine Intelligence 14 ( 1992) 710-732. 
24. [24] D. Marr, Vision, W.H. Freeman and Co. ( 1982). 
25. [25] S. Masnou and J.M. Morel, Level lines based disocclusion, ICIP'98 IEEE Int. Conf. on Image Processing Chicago ( 1998). 
26. [26] G. Matheron, Random Sets and Integral Geometry, John Wiley, N.Y. ( 1975). Zbl0321.60009MR385969
27. [27] F.G. Meyer, A.Z. Averbuch, J-O. Strömberg and R.R. Coifman, Multi-layered image representation: Application to image compression, ICIP'98 IEEE Int. Conf. on Image Processing, Chicago ( 1998). 
28. [28] Y. Meyer, Wavelets: Algorithms and applications, SIAM ( 1993). Zbl0821.42018MR1219953
29. [29] P. Monasse and F. Guichard, Fast computation of a contrast-invariant image representation, TR 9815, CMLA, ENS Cachan, France, IEEE Trans, on image processing, submitted. 
30. [30] J.M. Morel, Perception visuelle et traitement d'images (I) et (II), Revue du Palais de la Découverte (novembre 1996et Février 1997). 
31. [31] J.M. Morel and S. Solimini, Variational methods in image processing, Birkhäuser ( 1994). Zbl0827.68111
32. [32] L.I. Rudin and S. Osher, Total Variation based image restoration with free local constraints, in Proc. IEEE Int. Conf. on Image Processing 1 ( 1994) 31-35. 
33. [33] J. Serra, Image analysis and mathematical morphology, Academic Press ( 1982). Zbl0565.92001MR753649
34. [34] J. Shapiro, Embedded Image Coding Using Zerotrees of Wavelet Coefficients. IEEE Trans. on Signal Processing 41 ( 1993) 3445-3462. Zbl0841.94020
35. [35] M. Wertheimer, Untersuchungen zur Lehre der Gestalt, Psychologische Forschung, IV ( 1923) 301-350.