Abstract
We present a structured image compression scheme based on a u = v + w model, where the original image u is decomposed between a sketch v and a residue w. The sketch contains all the meaningful edge curves, and the geometry of these edges is precisely detected and coded using level lines. The residue w = u - v contains all the microtextures, and it is compressed by means of a wavelet packet representation. By splitting the information contained in natural images between sketch and microtextures, we can use the most adapted representation on each of these structures. Edges are not deteriorated by ringing artefacts on the contrary of what could be observed with standard wavelet or wavelet packet compression schemes.
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References
Alvarez, L., Gousseau, Y., and Morel, J.-M. (1999). Scales in natural images and a consequence on their bounded variation norm. In Scale Space Thcories in Computer Vision, pages 247–258. Lecture Notes in Computer Science 1682. Proc. of Sec. I nt. Conf. Sc ale-Space’ 99.
Ambrosio, L., Caselles, V., Masnou, S., and Morel, J.-M. (1999). Connected components of sets of finite perimeter and applications to image processing. Preprint.
Aronsson, G.(1967). Extension of functions satisfying lipschitz conditions. Ark. Math., 6:551–561.
Candès, E. and Donoho, D. (1999). Ridgelets: a key to higher-dimensional intermittency ? Phil. Trans. R. Soc. Lond. A., pages 2495–2509.
Cao, F. (1998). Absolutely minimizing lipschitz extension with discontinuous boundary data. Note aux C.R. Acad. Sci. Paris, t.327(I):563–568.
Carlsson, S. (1988). Sketch based coding of grey level images. Signal Processing North-Holland, 15(1):57–83.
Casas, J. (1996). Morphological interpolation for image coding. In Berger, M., Deriche, R., Herlin, I., J. Jaffré, and Morel, J.-M., editors, 12th Int. Conf. on Analysis and Optimization of Systems. Images, Wavelets and PDEs. Springer.
Caselles, V., Coll, B., and Morel, J.-M. (1996). A kanizsa programme. In Progress in Nonlinear Differential Equs. and their Applications, pages 35–55.
Caselles, V., Coll, B., and Morel, J.-M. (1999). Topographic maps and local contrast changes in natural images. Int. J. Comp. Vision, 33 (1) :5–27.
Caselles, V., Morel, J.-M., and Sbert, C. (1998). An axiomatic approach to image interpolation. IEEE Trans. on Imaqe Proc., 7(3):376–386.
Cohen, A., Daubechies, I., and Feauveau, J.-C. (1992). Biorthogonal bases of compactly supported wavelets. Commun. in Pure and Appl. Math., 45(5).
Coifman, R. and Meyer, Y. (1992). Size properties of wavelet packets. In et al., B. R., editor, Wavelets and their Applications, pages 125–150. Jones and Bartlett.
Coifman, R. and Wickerhauser, M. (1992). Entropy-based algorithms for best basis selection. IEEE Trans. on Info. Theory, 38(2):713–718.
Crandall, M., Ishii, H., and Lions, P.-L. (1992). User’s guide to viscosity solution of second order partial differential equations. Bull. Amer. Math. Soc, 27:1–67.
D’Alès, J.-P., Froment, J., and Morel, J.-M. (1999) . Reconstruction visuelle et généricité. Intellectica, 1(8) :11–35.
Do, M. N. and Vetterli, M. (2000). Orthonormal finite ridgelet transform for image compression. In Proc. of I CIP’2000, volume 2, pages 367–370.
Donolio, D. (1997). Wedlets: nearly-minimax estimation of edges. Tech. Rep. no 515, Statistics Dep., Stanford Univ.
Froment, J. (1999a). A compact and multiscale image model based on levels sets. In Nielsen, M., Johansen, P., Olsen, O. F., and Weickert, J., editors, Lecture Notes in Computer Science, number 1682, pages 152–163. Springer. Proc. Sec. Int. Conf. Scale-Space’99.
Froment, J. (1999b). A functional analysis model for natural images permitting structured compression. ESAIM:COCV Control, Opt. and Cal. of Var., 4:473–495.
Froment, J. (2000). Perceptible level lines and isoperimetric ratio. In IEEE 7th Int. Conf. on Image Proc., volume 2, pages 112–115.
Froment, J. and Mallat, S. (1992). Second generation compact image coding with wavelets. In Chui, C., editor, Wavelets - A Tutorial in Theory and Applications, pages 655–678. Academic Press.
Froment, J. and Moisan, L. (2000). Megawave2 v.2.00. A free and opensource Unix image processing software for reproducible research, available at http://www.cmla.ens-cachan.fr.
Gorrnish, M., Lee, D., and Marcellin, M. (2000). Jpeg 2000: overview, architecture and applications. In Proc. of ICIP’2000, volume 2, pages 29–32.
Kanisza, G. (1980). Grammatica del Vedere. Il Mulino, Bologna.
Landau, H. and Pollak, H. (1962). Prolate spheroidal wave functions, fourier analysis and uncertainty (iii) : the dimension of the space of essentially time and bandlimited signals. Bell System Technical Journal, 41:1295–1336.
Mallat, S. (1997). A wavelet tour of signal processing. Academic Press.
Mallat, S. and Zhong, S. (1992). Characterization of signals from multiscale edges. IEEE Trans. Pattern Recog. and Machine Intell., 14(7):710–732.
Marr, D. (1982). Vision. W.H.Freeman and Co.
Mertins, A. (1999). Image compression via edge-based wavelet transform. Opt. Eng., 38(6):991–1000.
Meyer, F. (1999). Wavelet packet coder and decoder. Binaries available for Linux on Pentium processors at http://ece-www.colorado.edu/fineyer/distrib.html.
Meyer, F., Averbuch, A., and Stromberg, J.-O. (2000). Fast adaptive wavelet packet image compression. IEEE Trans. on Image Proc., 9(5).
Meyer, F. and Coifnan, R. (1997). Brushlets: a tool for directional image analysis and image compression. Applied and Comput. Harmonic Ana., pages 147–187.
Monasse, P. and Guichard, F. (1999). Scale-space from a level lines tree. In Scale-Space Theories in Computer Vision, pages 175–186. Lecture Notes in Computer Science 1682. Proc. of Sec. Int. Conf. Scale-Space’99.
Morel, J.-M. and Solimini, S. (1995). Variational Methods in Image Segmentation. Birkhauser.
Pennec, E. L. and Mallat, S. (2000). Image compression with geometrical wavelets. In Proc. of ICIP’2000, volume 1, pages 661–664.
Shapiro, J. (1993). Embedded image coding using zerotrees of wavelet coefficients. IEEE Trans. on Signal Processing, 41(12) :3445–3462.
Wallace, G. (1991). Jpeg. Communications of the ACM, 34(4):31–44.
Wertheimer, M. (1923). Untersuchungen zur lehre der gestalt. Psychologische Forschung. IV:301–350.
Witten, I., Neal, R., and Cleary, J. (1987). Arithmetic coding for data compression. Communications of the ACM, 30(6):520–540.
Xiong, Z., Ramchandran, K., and Orchard, M. (1998). Wavelet packets coding using space-frequency quantization. IEEE Trans. on Image Proc., 7(6) :892–898.
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Froment, J. (2001). Image Compression Through Level Lines and Wavelet Packets. In: Petrosian, A.A., Meyer, F.G. (eds) Wavelets in Signal and Image Analysis. Computational Imaging and Vision, vol 19. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-9715-9_11
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DOI: https://doi.org/10.1007/978-94-015-9715-9_11
Publisher Name: Springer, Dordrecht
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