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Fuzzy relation equations for coding/decoding processes of images and videos. (English) Zbl 1078.68815
Summary: We adopt fuzzy relation equations with continuous triangular norms for compression/decompression processes of grey images, colour images in the RGB space and frames of videos, by comparing the results of the reconstructed images with standard methods like JPEG and MPEG-4. Any image is subdivided in blocks and each block is coded/decoded using arbitrary fuzzy sets as coders in the fuzzy equations. We evaluate the peak signal to noise ratio on the decompressed images for several values of the compression rates as measure of the quality of images and frames reconstructed. The original frames of a video are classified in Intra-frames and Predictive frames by using a similarity measure based on the well known Lukasiewicz t-norm.

MSC:
68U10 Computing methodologies for image processing
68P30 Coding and information theory (compaction, compression, models of communication, encoding schemes, etc.) (aspects in computer science)
03E72 Theory of fuzzy sets, etc.
94A08 Image processing (compression, reconstruction, etc.) in information and communication theory
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[1] F. Di Martino, V. Loia, S. Sessa, A method in the compression/decompression of images using fuzzy equations and fuzzy similarities, in: Proceedings of Conference IFSA 2003, (29/6-2/7/2003, Istanbul, Turkey), 2003, pp. 524-527
[2] F. Di Martino, V. Loia, S. Sessa, A method for coding/decoding images by using fuzzy relation equations, Selected papers from IFSA 2003 (29/6-2/7/2003, Istanbul, Turkey), in: T. Bilgic, B.De Baets and O.Kaynak, (Eds.), Lecture Notes in Artificial Intelligence, Vol. 2715, Springer, Berlin, Germany, pp. 436-441, 2003 · Zbl 1037.68773
[3] Di Nola, A.; Pedrycz, W.; Sanchez, E.; Sessa, S., Fuzzy relations equations and its applications to knowledge engineering, (1989), Kluwer Academic Publications Dordrecht, The Netherlands
[4] Hirota, K.; Pedrycz, W., Fuzzy relational compression, IEEE transactions on systems, man and cybernetics, part B, 29, 3, 407-415, (1999)
[5] Kerre, E., Fuzzy techniques in image processing, Studies in fuzziness and soft computing, (2000), (Physica-Verlag), Springer-Verlag Co Heidelberg, Germany · Zbl 0956.68152
[6] Klement, E.P.; Mesiar, R.; Pap, E., Triangular norms, (2000), Kluwer Academic Publications Dordrecht, The Netherlands · Zbl 0972.03002
[7] Loia, V.; Pedrycz, W.; Sessa, S., Fuzzy relation calculus in the compression and decompression of fuzzy relations, International journal of image and graphics, 2, 4, 617-631, (2002)
[8] Nachtegael, M.; Weken, D.; Ville, D.; Kerre, E.E., Fuzzy filters for image processing, Studies in fuzziness and soft computing, (2000), (Physica-Verlag), Springer-Verlag Co Heidelberg (Germany)
[9] Nobuhara, H.; Hirota, K.; Pedrycz, W., Fast solving method of fuzzy relational equations and its application to lossy image compression, IEEE transactions of fuzzy systems, 8, 3, 325-334, (2000)
[10] H. Nobuhara, K. Hirota, W. Pedrycz, A Digital Watermarking Algorithm Using Image Compression Method Based on Fuzzy Relational Equations, in: Proceedings of IEEE International Conference on Fuzzy Systems (12-17/5/2002, Honolulu, Hawaii, USA), Vol. 2, pp. 1568-1573, 2002
[11] H. Nobuhara, K. Hirota, W. Pedrycz, Relational Image Compression: Optimizations through the Design of Fuzzy Coders and YUV Color Space, Soft Computing Journal, in press
[12] H. Nobuhara, K. Hirota, W. Pedrycz, S. Sessa, A motion compression/reconstruction method based on max T-norm composite fuzzy relational equations, submitted · Zbl 1102.68698
[13] Pennebaker, W.B.; Mitchell, J.L., JPEG: still image data compression standard, (1993), Van Nostrand Reinhold New York, USA
[14] Sikora, T., MPEG digital video coding standards, digital electronics handbook, (1995), McGraw-Hill, Inc New York, USA
[15] Turunen, E., Mathematics behind fuzzy logic, Advances in soft computing, (1999), (Physica-Verlag), Springer-Verlag Co Heidelberg (Germany) · Zbl 0940.03029
[16] Ziv, J.; Lempel, A., A universal algorithm for sequential data compression, IEEE transaction on information theory, 23, 3, 337-343, (1977) · Zbl 0379.94010
[17] http://sampl.eng.ohio-state.edu/ sampl/database.htm
[18] http://jj2000.epfl.ch
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