A functional analysis model for natural images permitting structured compression
ESAIM: Control, Optimisation and Calculus of Variations, Tome 4 (1999), pp. 473-495.
@article{COCV_1999__4__473_0,
     author = {Froment, Jacques},
     title = {A functional analysis model for natural images permitting structured compression},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     pages = {473--495},
     publisher = {EDP-Sciences},
     volume = {4},
     year = {1999},
     zbl = {0924.68201},
     mrnumber = {1713526},
     language = {en},
     url = {http://www.numdam.org/item/COCV_1999__4__473_0/}
}
TY  - JOUR
AU  - Froment, Jacques
TI  - A functional analysis model for natural images permitting structured compression
JO  - ESAIM: Control, Optimisation and Calculus of Variations
PY  - 1999
DA  - 1999///
SP  - 473
EP  - 495
VL  - 4
PB  - EDP-Sciences
UR  - http://www.numdam.org/item/COCV_1999__4__473_0/
UR  - https://zbmath.org/?q=an%3A0924.68201
UR  - https://www.ams.org/mathscinet-getitem?mr=1713526
LA  - en
ID  - COCV_1999__4__473_0
ER  - 
Froment, Jacques. A functional analysis model for natural images permitting structured compression. ESAIM: Control, Optimisation and Calculus of Variations, Tome 4 (1999), pp. 473-495. http://www.numdam.org/item/COCV_1999__4__473_0/

[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] 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. | MR 1225209 | Zbl 0788.68153

[3] F. Cao, Absolutely minimizing Lipschitz extension with discontinuous boundary data. C.R. Acad. Sci. Paris 327, Série I ( 1998) 563-568. | MR 1650611 | Zbl 0990.35048

[4] J. Canny, A computational approach to edge detection. IEEE Trans. Pattern Analysis and Machine Intelligence 8 ( 1986) 679-698.

[5] S. Carlsson, Sketch based coding of grey level images. Signal Processing North-Holland 15 ( 1998) 57-83.

[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). | Zbl 0960.68741

[7] V. Caselles, B. Coll and J.M. Morel, A Kanizsa programme. Progress in Nonlinear Differential Equs. and their Applications 25 ( 1996) 35-55. | MR 1414487 | Zbl 1077.68924

[8] V. Caselles, J.M. Morel and C. Sbert, An Axiomatic Approach to Image Interpolation. IEEE Trans. on Image Processing 7 ( 1998) 376-386. | MR 1669524 | Zbl 0993.94504

[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] V. Caselles, B. Coll and J.M. Morel, The Connected Components of Sets of Finite Perimeter in the Plane, Preprint ( 1998).

[11] A. Chambolle and P.L. Lions, Image Recovery via Total Variation Minimization and Related Problems. Numerische Mathematik 76 ( 1997) 167-188. | MR 1440119 | Zbl 0874.68299

[12] A. Cohen, I. Daubechies and J.C. Feauveau, Biorthogonal bases of compactly supported wavelets. Comm. in Pure & Appl. Math. 45 ( 1992). | MR 1162365 | Zbl 0776.42020

[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. | MR 1118699 | Zbl 0755.35015

[14] F. Dibos and G. Koepfler, Global Total Variation Minimization, TR 9801, CEREMADE, Université Paris-Dauphine, France ( 1998).

[15] L.C. Evans and R.F. Gariepy, Measure theory and fine properties of functions, Studies in Advanced Mathematics, CRC Press Inc. ( 1992). | MR 1158660 | Zbl 0804.28001

[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] 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] R. Hummel and R. Moniot, Reconstruction from zero-crossings in scale-space. IEEE Trans. on Acoustic, Speech and Signal Processing 37 ( 1989).

[19] G. Kanisza, Grammatica del Vedere, II Mulino, Bologna ( 1980).

[20] G. Kanisza, Vedere e pensare, II Mulino, Bologna ( 1991).

[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] 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] S. Mallat and S. Zhong, Characterization of signals from multiscale edges. IEEE Trans. Pattern Recognition and Machine Intelligence 14 ( 1992) 710-732.

[24] D. Marr, Vision, W.H. Freeman and Co. ( 1982).

[25] S. Masnou and J.M. Morel, Level lines based disocclusion, ICIP'98 IEEE Int. Conf. on Image Processing Chicago ( 1998).

[26] G. Matheron, Random Sets and Integral Geometry, John Wiley, N.Y. ( 1975). | MR 385969 | Zbl 0321.60009

[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] Y. Meyer, Wavelets: Algorithms and applications, SIAM ( 1993). | MR 1219953 | Zbl 0821.42018

[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] J.M. Morel, Perception visuelle et traitement d'images (I) et (II), Revue du Palais de la Découverte (novembre 1996et Février 1997).

[31] J.M. Morel and S. Solimini, Variational methods in image processing, Birkhäuser ( 1994).

[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] J. Serra, Image analysis and mathematical morphology, Academic Press ( 1982). | MR 753649 | Zbl 0565.92001

[34] J. Shapiro, Embedded Image Coding Using Zerotrees of Wavelet Coefficients. IEEE Trans. on Signal Processing 41 ( 1993) 3445-3462. | Zbl 0841.94020

[35] M. Wertheimer, Untersuchungen zur Lehre der Gestalt, Psychologische Forschung, IV ( 1923) 301-350.