Abstract
Fuzzy transform is a relatively recent fuzzy approximation method, mainly used for image and general data processing. Due to the growing interest in the application of fuzzy transform over the last years, it seems proper providing a review of the technique. In this paper, we recall F-transform-based compression methods for data and images. The related works are examined, their motivations are explained, and the theoretical foundations are described. To test practical abilities of the related works, benchmark with emphasis to quality and processing time is established and the corresponding graphs are commented.
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References
Abdelaal M, Theel O (2013) An efficient and adaptive data compression technique for energy conservation in wireless sensor networks. In: 2013 IEEE conference on wireless sensor (ICWISE). IEEE, pp 124–129
Abdelaal M, Theel O, Kuka C, Zhang P, Gao Y, Bashlovkina V, Nicklas D, Fränzle M (2016) Improving energy efficiency in qos-constrained wireless sensor networks. Int J Distrib Sensor Netw. https://doi.org/10.1155/2016/1576038
Alikhani R, Zeinali M, Bahrami F, Shahmorad S, Perfilieva I (2017) Trigonometric \(f^m\)-transform and its approximative properties. Soft Comput 21(35673577 21):3567–3577
Antia HM (2002) Numerical methods for scientists and engineers, I. Birkhauser Verlag, Basel
Bashlovkina V, Abdelaal M, Theel O (2015) Fuzzycat: a novel procedure for refining the f-transform based sensor data compression. In: Proceedings of the 14th international conference on information processing in sensor networks. ACM, pp 340–341
Bede B, Rudas IJ (2011) Approximation properties of fuzzy transforms. Fuzzy Sets Syst 180(1):20–40
Christopoulos C, Skodras A, Ebrahimi T (2000) The jpeg2000 still image coding system: an overview. IEEE Trans Consum Electron 46(4):1103–1127
Deutsch P, Gailly J-L (1996) Zlib compressed data format specification version 3.3, Technical report
Di Martino F, Sessa S (2007) Compression and decompression of images with discrete fuzzy transforms. Inf Sci 177(11):2349–2362
Di Martino F, Sessa S (2018) Multi-level fuzzy transforms image compression. J Ambient Intell Humaniz Comput. https://doi.org/10.1007/s12652-018-0971-4
Di Martino F, Loia V, Perfilieva I, Sessa S (2008) An image coding/decoding method based on direct and inverse fuzzy transforms. Int J Approx Reason 48(1):110–131
Di Martino F, Loia V, Sessa S (2010) Fuzzy transforms for compression and decompression of color videos. Inf Sci 180(20):3914–3931
Di Martino F, Loia V, Perfilieva I, Sessa S (2013) Fuzzy transform for coding/decoding images: a short description of methods and techniques. Stud Fuzziness Soft Comput 298:139–146
Di Martino F, Hurtik P, Perfilieva I, Sessa S (2014) A color image reduction based on fuzzy transforms. Inf Sci 266:101–111
Di Martino F, Sessa S, Perfilieva I (2017) First order fuzzy transform for images compression. J Signal Inf Process 8(03):178
Gaeta M, Loia V, Tomasiello S (2015) Multisignal 1-d compression by f-transform for wireless sensor networks applications. Appl Soft Comput 30:329–340
Gaeta M, Loia V, Tomasiello S (2016) Cubic b-spline fuzzy transforms for an efficient and secure compression in wireless sensor networks. Inf Sci 339:19–30
Gambhir D, Rajpal N (2015) Improved fuzzy transform based image compression and fuzzy median filter based its artifact reduction: pairfuzzy. Int J Mach Learn Cybern 6(6):935–952
Gambhir D, Rajpal N (2017) Edge and fuzzy transform based image compression algorithm: Edgefuzzy, In: Artificial intelligence and computer vision. Springer, pp 115–142
Ghofrani F, Helfroush MS (2011) A modified approach for image compression based on fuzzy transform. In: 2011 19th Iranian conference on electrical engineering (ICEE). IEEE, pp 1–6
Gibbs NE, Poole WG, Stockmeyer PK (1976) An algorithm for reducing the bandwidth and profile of a sparse matrix. SIAM J Numer Anal 13(2):236–250
Horn RA, Johnson CR (1985) Matrix analysis. Cambridge University Press, Cambridge
Huffman DA (1952) A method for the construction of minimum-redundancy codes. Proc IRE 40(9):1098–1101
Hurtik P, Perfilieva I (2013a) Image compression methodology based on fuzzy transform using block similarity. In: 8th conference of the European society for fuzzy logic and technology, EUSFLAT 2013—advances in intelligent systems research. pp 521–526
Hurtik P, Perfilieva I (2013b) Image compression methodology based on fuzzy transform. In: International joint conference CISIS12-ICEUTE’ 12-SOCO’ 12 special sessions. Springer, pp 525–532
Hurtik P, Perfilieva I (2017) A hybrid image compression algorithm based on jpeg and fuzzy transform. In: 2017 IEEE international conference on fuzzy systems (FUZZ-IEEE). IEEE, pp 1–6
Hurtik P, Perfilieva I (2018) Noise influence in fzt+jpeg image compression: accepted. In: FLINS 2018. pp 1–7
Hyndman RJ, Koehler AB (2006) Another look at measures of forecast accuracy. Int J Forecast 22(4):679–688
Jahedi S, Javadi F, Mehdipour M (2018) Compression and decompression based on discrete weighted transform. Appl Math Comput 335:133–145
Khastan A (2017) A new representation for inverse fuzzy transform and its application. Soft Comput 21(13):3503–3512
Loia V, Tomasiello S, Vaccaro A (2017) Fuzzy transform based compression of electric signal waveforms for smart grids. IEEE Trans Syst Man Cybern Syst 47(1):121–132
Luo JC (1992) Algorithms for reducing the bandwidth and profile of a sparse matrix. Comput Struct 44(3):535–548
Miano J (1999) Compressed image file formats: Jpeg, png, gif, xbm, bmp. Addison-Wesley Professional, Boston
Novák V, Perfilieva I, Holčapek M, Kreinovich V (2014) Filtering out high frequencies in time series using f-transform. Inf Sci 274:192–209
Patanè G (2011) Fuzzy transform and least-squares approximation: analogies, differences, and generalizations. Fuzzy Sets Syst 180(1):41–54
Paternain D, Jurio A, Ruiz-Aranguren J, Minárová M, Takáč Z, Bustince H (2017) Optimized fuzzy transform for image compression. In: Advances in fuzzy logic and technology 2017. Springer, pp 118–128
Pennebaker WB, Mitchell JL (1992) JPEG: Still image data compression standard. Springer, Berlin
Perfilieva I (2004) Fuzzy transform: application to the reef growth problem. In: Demicco RV, Klir GJ (eds) Fuzzy logic in geology. Elsevier, pp 275–300
Perfilieva I (2005) Fuzzy transforms and their applications to image compression, In: International Workshop on Fuzzy Logic and Applications, Springer, pp. 19–31
Perfilieva I (2006a) Fuzzy transforms: theory and applications. Fuzzy Sets Syst 157:993–1023
Perfilieva I (2006b) Fuzzy transforms: theory and applications. Fuzzy Sets Syst 157(8):993–1023
Perfilieva I, De Beats B (2010) Fuzzy transforms of monotone functions with application to image compression. Inf Sci 180:3304–3315
Perfilieva I, Haldeeva E (2001) Fuzzy transformation. In: IFSA world congress and 20th NAFIPS international conference, 2001. Joint 9th, vol 4. IEEE, pp 1946–1948
Perfilieva I, Valásek R (2005) Data compression on the basis of fuzzy transforms. In: EUSFLAT conference, Citeseer. pp 663–668
Perfilieva I, Vlašánek P (2013) Influence of various types of basic functions on image reconstruction using f-transform. In: 8th conference of the european society for fuzzy logic and technology, EUSFLAT 2013—advances in intelligent systems research. pp 497–502
Perfilieva I, Daňková M, Bede B (2011) Towards a higher degree f-transform. Fuzzy Sets Syst 180(1):3–19
Perfilieva I, Hodáková P, Hurtík P (2016a) Differentiation by the f-transform and application to edge detection. Fuzzy Sets Syst 288:96–114
Perfilieva I, Holčapek M, Kreinovich V (2016b) A new reconstruction from the f-transform components. Fuzzy Sets Syst 288:3–25
Perfilieva I, Hurtik P, Di Martino F, Sessa S (2017) Image reduction method based on the f-transform. Soft Comput 21(7):1847–1861
Perfilieva I, Pavliska V, Vajgl M, De Baets B et al (2008) Advanced image compression on the basis of fuzzy transforms. In: Proceedings of the conference on IPMU. pp 1167–1174
Rao KR, Yip P (2014) Discrete cosine transform: algorithms, advantages, applications. Academic press, New York
Rashedi E, Nezamabadi-Pour H, Saryazdi S (2009) Gsa: a gravitational search algorithm. Inf Sci 179(13):2232–2248
Sztyber A (2014) Analysis of usefulness of a fuzzy transform for industrial data compression. In: Journal of physics: conference series, vol 570. IOP Publishing, p 042002
Vlašánek P (2013) Generating suitable basic functions used in image reconstruction by f-transform. Adv Fuzzy Syst 4:1–6
Wang Z, Bovik AC, Simoncelli EP (2004) Image quality assessment: from error visibility to structural similarity. IEEE Trans Image Process 13(4):600–612
Yamamoto T, Ikebe Y (1979) Inversion of band matrices. Linear Algebra Appl 24:105–111
Zeinali M, Alikhani R, Shahmorad S, Bahrami F, Perfilieva I (2018) On the structural properties of fm-transform with applications. Fuzzy Sets Syst 342:32–52
Ziv J, Lempel A (1977) A universal algorithm for sequential data compression. IEEE Trans Inf Theory 23(3):337–343
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This research was supported by the project “LQ1602 IT4Innovations excellence in science”.
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Hurtik, P., Tomasiello, S. A review on the application of fuzzy transform in data and image compression. Soft Comput 23, 12641–12653 (2019). https://doi.org/10.1007/s00500-019-03816-8
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DOI: https://doi.org/10.1007/s00500-019-03816-8