In this paper, we present a new image compression method based on the direct and inverse F1-transform, a generalization of the concept of fuzzy transform. Under weak compression rates, this method improves the quality of the images with respect to the classical method based on the fuzzy transform.
References
[1]
Perfilieva, I. and Hodáková, P. (2013) F1-Transform of Functions of Two Variables. Proceedings of EUSFLAT 2013, Advances in Intelligent Systems Research, Milano, 32, 547-553.
[2]
Perfilieva, I., Hodáková, P. and Hurtik, P. (2014) Differentiation by the F-Transform and Application for Edge Detection. Fuzzy Sets and Systems, 288, 96-114.
https://doi.org/10.1016/j.fss.2014.12.013
[3]
Perfilieva, I. (2006) Fuzzy Transform: Theory and Application. Fuzzy Sets and Systems, 157, 993-1023. https://doi.org/10.1016/j.fss.2005.11.012
[4]
Di Martino, F., Loia, V. and Sessa, S. (2003) A Method in the Compression/Decompression of Images Using Fuzzy Equations and Fuzzy Similarities. Proceedings of the 10th IFSA World Congress, Istanbul, 30 June-2 July 2003, 524-527.
[5]
Di Martino, F., Loia, V., Perfilieva, I. and Sessa, S. (2008) An Image Coding/Decoding Method Based on Direct and Inverse Fuzzy Transforms. International Journal of Approximate Systems, 48, 110-131.
https://doi.org/10.1016/j.ijar.2007.06.008
[6]
Di Martino, F. and Sessa, S. (2007) Compression and Decompression of Images with Discrete Fuzzy Transforms. Information Sciences, 177, 2349-2362.
https://doi.org/10.1016/j.ins.2006.12.027
[7]
Di Martino, F., Loia, V. and Sessa, S. (2010) A Segmentation Method for Images Compressed by Fuzzy Transforms. Fuzzy Sets and Systems, 161, 56-74.
https://doi.org/10.1016/j.fss.2009.08.002
[8]
Di Martino, F., Loia, V. and Sessa, S. (2010) Fuzzy Transforms for Compression and Decompression of Colour Videos. Information Sciences, 180, 3914-3931.
https://doi.org/10.1016/j.ins.2010.06.030
[9]
Di Martino, F., Hurlik, P., Perfilieva, I. and Sessa, S. (2014) A Color Image Reduction Based on Fuzzy Transforms. Information Sciences, 266, 101-111.
https://doi.org/10.1016/j.ins.2014.01.014
[10]
Di Martino, F. and Sessa, S. (2013) Coding B-Frames on Color Videos with Fuzzy Transforms. Advances on Fuzzy Systems, 2013, Article ID: 652429.
https://doi.org/10.1155/2013/652429
[11]
Di Martino, F., Loia, V. and Sessa, S. (2012) Fragile Watermarking Tamper Detection with Images Compressed by Fuzzy Transform. Information Sciences, 195, 62-90. https://doi.org/10.1016/j.ins.2012.01.014
[12]
Di Martino, F., Loia, V. and Sessa, S. (2013) Image Matching by Using Fuzzy Transform. Advances on Fuzzy Systems, 2013, Article ID: 760705, 10 p.
[13]
Loia, V. and Sessa, S. (2005) Fuzzy Relation Equations for Coding/Decoding Processes of Images and Videos. Information Sciences, 171, 145-172.
https://doi.org/10.1016/j.ins.2004.04.003
[14]
Nobuhara, H., Pedrycz, W. and Hirota, K. (2000) Fast Solving Method of Fuzzy Relational Equation and Its Application to Lossy Image Compression. IEEE Transactions on Fuzzy Systems, 8, 325-334. https://doi.org/10.1109/91.855920
[15]
Nobuhara, H., Pedrycz, W. and Hirota, K. (2005) Relational Image Compression: Optimizations through the Design of Fuzzy Coders and YUV Color Space. Soft Computing, 9, 471-479. https://doi.org/10.1007/s00500-004-0366-7
[16]
Nobuhara, H., Hirota, K., Di Martino, F., Pedrycz, W. and Sessa, S. (2005) Fuzzy Relation Equations for Compression/Decompression Processes of Colour Images in the RGB and YUV Colour Spaces. Fuzzy Optimization and Decision Making, 4, 235-246. https://doi.org/10.1007/s10700-005-1892-1
[17]
Perfilieva, I. and De Baets, B. (2010) Fuzzy Transforms of Monotone Functions with Application to Image Compression. Information Sciences, 180, 3304-3315.
https://doi.org/10.1016/j.ins.2010.04.029
[18]
Vajgl, M., Perfilieva, I. and Hodáková, P. (2012) Advanced F-Transform Based Image Fusion. Advances in Fuzzy Systems, 2012, Article ID: 125086, 9 p.
https://doi.org/10.1155/2012/125086
[19]
Di Martino, F., Loia, V. and Sessa, S. (2010) Fuzzy Transforms Method and Attribute Dependency in Data Analysis. Information Sciences, 180, 493-505.
https://doi.org/10.1016/j.ins.2009.10.012
[20]
Di Martino, F., Loia, V. and Sessa, S. (2011) Fuzzy Transforms Method in Prediction Data Analysis. Fuzzy Sets and Systems, 180, 146-163.
https://doi.org/10.1016/j.fss.2010.11.009
[21]
Holcapek, M. (2011) A Smoothing Filter Based on Fuzzy Transform. Fuzzy Sets and Systems, 180, 69-97. https://doi.org/10.1016/j.fss.2011.05.028
[22]
Perfilieva, I., Novak, V. and Dvorak, A. (2008) Fuzzy Transforms in the Analysis of Data. International Journal of Approximate Reasoning, 40, 26-46.
https://doi.org/10.1016/j.ijar.2007.06.003
[23]
Stěpnicka, M. and Polakovic, O. (2009) A Neural Network Approach to the Fuzzy Transform. Fuzzy Sets and Systems, 160, 1037-1047.
https://doi.org/10.1016/j.fss.2008.11.029
[24]
Stěpnieka, M., Dvorák, A., Pavliska, V. and Vavrícková, L. (2011) A Linguistic Approach to Time Series Modeling with the Help of F-Transform. Fuzzy Sets and Systems, 180, 164-184. https://doi.org/10.1016/j.fss.2011.02.017
[25]
Troiano, L. and Ktriptani, P. (2011) Supporting Trading Strategies by Inverse Fuzzy Transform. Fuzzy Sets and Systems, 180, 121-145.
https://doi.org/10.1016/j.fss.2011.05.004
[26]
Bede, B. and Rudas, I.J. (2011) Approximation Properties of Fuzzy Transforms. Fuzzy Sets and Systems, 180, 20-40. https://doi.org/10.1016/j.fss.2011.03.001
[27]
Perfilieva, I., Dankova, M. and Bede, B. (2011) Towards a Higher Degree F-Transform. Fuzzy Sets Systems, 180, 3-19.
https://doi.org/10.1016/j.fss.2010.11.002
[28]
Di Martino, F., Loia, V. and Sessa, S. (2003) A Method for Coding/Decoding Images by Using Fuzzy Relation Equations. In: Bilgic, T., De Baets, B. and Kaynak, O., Eds., Fuzzy Sets and Systems—IFSA 2003, Lecture Notes in Artificial Intelligence, Vol. 2715, Springer, Berlin, 436-441. https://doi.org/10.1007/3-540-44967-1_52
