Abstract
A series of extensive numerical experiments indicates that images, in general, possess a considerable degree of affine self-similarity, that is, blocks are well approximated by a number of other blocks – at the same or different scales – when affine greyscale transformations are employed. We introduce a simple model of affine image self-similarity which includes the method of fractal image coding (cross-scale, affine greyscale similarity) and the nonlocal means denoising method (same-scale, translational similarity) as special cases.
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References
Alexander, S.K.: Multiscale Methods in Image Modelling and Image Processing, Ph.D. Thesis, Dept. of Applied Mathematics, University of Waterloo (2005)
Barnsley, M.F.: Fractals Everywhere. Academic Press, New York (1988)
Buades, A., Coll, B., Morel, J.M.: A review of image denoising algorithms, with a new one. Multiscale Modelling and Simulation 4, 490–530 (2005)
Dabov, K., Foi, A., Katkovnik, V., Egiazarian, K.: Image denoising by sparse 3-D transform-domain collaborative filtering. IEEE Trans. Image Proc. 16, 2080–2095 (2007)
Ebrahimi, M., Vrscay, E.R.: Solving the Inverse Problem of Image Zooming Using “Self-Examples”. In: Kamel, M., Campilho, A. (eds.) ICIAR 2007. LNCS, vol. 4633, pp. 117–130. Springer, Heidelberg (2007)
Elad, M., Datsenko, D.: Example-based regularization deployed to super-resolution reconstruction of a single image. The Computer Journal 50, 1–16 (2007)
Etemoglu, C., Cuperman, V.: Structured vector quantization using linear transforms. IEEE Trans. Sig. Proc. 51, 1625–1631 (2003)
Fisher, Y. (ed.): Fractal Image Compression: Theory and Application. Springer, New York (1995)
Freeman, W.T., Jones, T.R., Pasztor, E.C.: Example-based super-resolution. IEEE Comp. Graphics Appl. 22, 56–65 (2002)
Ghazel, M., Freeman, G., Vrscay, E.R.: Fractal image denoising. IEEE Trans. Image Proc. 12, 1560–1578 (2003)
Ghazel, M., Freeman, G., Vrscay, E.R.: Fractal-wavelet image denoising. IEEE Trans. Image Proc. 15, 2669–2675 (preprint, 2006)
Gonzalez, R.C., Woods, R.E.: Digital Image Processing. Prentice-Hall, New Jersey (2002)
Hamzaoui, R.: Encoding and decoding complexity reduction and VQ aspects of fractal image compression, Ph.D. Thesis, University of Freiburg (1998)
Hamzaoui, R., Müller, M., Saupe, D.: VQ-enhanced fractal image compression. In: ICIP 1996. IEEE, Los Alamitos (1996)
Hamzaoui, R., Saupe, D.: Combining fractal image compression and vector quantization. IEEE Trans. Image Proc. 9, 197–207 (2000)
Lepsoy, S., Carlini, P., Oien, G.: On fractal compression and vector quantization. In: Fisher, Y. (ed.) Fractal Image Encoding and Analysis. NATO ASI Series F, vol. 159. Springer, Heidelberg (1998)
Lu, N.: Fractal Imaging. Academic Press, New York (1997)
Ruderman, D.L.: The statistics of natural images. Network: Computation in Neural Systems 5, 517–548 (1994)
Zhang, D., Wang, Z.: Image information restoration based on long-range correlation. IEEE Trans. Cir. Syst. Video Tech. 12, 331–341 (2002)
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Alexander, S.K., Vrscay, E.R., Tsurumi, S. (2008). A Simple, General Model for the Affine Self-similarity of Images. In: Campilho, A., Kamel, M. (eds) Image Analysis and Recognition. ICIAR 2008. Lecture Notes in Computer Science, vol 5112. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-69812-8_19
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DOI: https://doi.org/10.1007/978-3-540-69812-8_19
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