Fragile watermarking tamper detection via bilinear fuzzy relation equations

  • Ferdinando Di Martino
  • Salvatore SessaEmail author
Original Research


We present a fragile color image watermarking based on the greatest solution of a bilinear fuzzy relation equation. The original image is coded with fuzzy transforms and divided in sub-images of sizes 2 × 2 called blocks. The watermark is applied on these blocks. A pre-processing phase is used to determine the best compression rate for the coding process. We test this scheme in tamper detection analysis on a sample of color images having different sizes. The results show that the proposed algorithm is better than that one obtained by using our previous method. Furthermore comparisons with various block-based fragile watermarking methods are made in our tests.


Fragile watermarking Block-wise Scheme Bilinear fuzzy relation equation Fuzzy transform Tamper detection Tamper localization 



This paper was performed under the auspices of INDAM-GCNS.


This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors.


  1. Al-Otum HA, Al-Taba’a AO (2009) Adaptive color image watermarking based on a modified improved pixel-wise masking technique. Comput Electr Engin 5:673–695. CrossRefzbMATHGoogle Scholar
  2. Ansari IA, Pant M, Ahn CW (2016) SVD based fragile watermarking scheme for tamper localization and self-recovery. J Mach Learn Cyber 7:1225–1239. CrossRefGoogle Scholar
  3. Barni M (2002) Improved wavelet-based watermarking through pixel-wise making. IEEE Trans Image Process 10(5):783–791. CrossRefzbMATHGoogle Scholar
  4. Bezdek JC (1981) Pattern recognition with fuzzy objective function algorithms. Plenum Press, New York, ISBN:0306406713CrossRefzbMATHGoogle Scholar
  5. Celik MU, Sharma G, Saber E, Tekalp AM (2002) Hierarchical watermarking for secure image authentication with localization. IEEE Trans Image Process 11(6):585–595. CrossRefGoogle Scholar
  6. Chang YF, Tai WL (2013) A block-based watermarking scheme for image tamper detection and self-recovery. OPTO Electron Rev 21(2):182–190. MathSciNetCrossRefGoogle Scholar
  7. Chang CC, Hu YS, Lu TC (2006) A watermarking-based image ownership and tampering authentication scheme. Pattern Recogn Lett 27(5):439–446. CrossRefGoogle Scholar
  8. Chen WC, Wang MS (2009) A fuzzy C-means clustering-based fragile watermarking scheme for image authentication. Expert Syst Appl 36:1300–1307. CrossRefGoogle Scholar
  9. Cox IJ, Miller M, Bloom J, Fridrich J, Kalker T (2008) Digital watermarking and stenography. Morgan Kaufmann, San Francisco, ISBN: 9780123725851Google Scholar
  10. Di Martino F, Sessa S (2006) Digital watermarking in coding/decoding processes with fuzzy relation equations. Soft Comput 10:238–243. CrossRefGoogle Scholar
  11. Di Martino F, Sessa S (2012a) Digital watermarking strings with images compressed by fuzzy relation equations. In: Chatterjee PA (eds) Computational intelligence in image processing siarry. Springer, Berlin, pp 173–186. Google Scholar
  12. Di Martino F, Sessa S (2012b) Fragile watermarking tamper detection with images compressed by fuzzy transform. Inf Sci 195:62–90. CrossRefGoogle Scholar
  13. Di Martino F, Sessa S (2017) Comparison between images via bilinear fuzzy relation equations. J Ambient Intell Humaniz Comput. Google Scholar
  14. Hirota K, Pedrycz W (2002) Data compression with fuzzy relational equations. Fuzzy Sets Syst 126(3):325–335. MathSciNetCrossRefzbMATHGoogle Scholar
  15. Holliman M, Memon N (2000) Counterfeiting attacks on oblivious block-wise independent invisible watermarking schemes. IEEE Trans Image Process 9(3):432–441. CrossRefGoogle Scholar
  16. Li JX (1992) A new algorithm for the greatest solution of fuzzy bilinear equation. Fuzzy Sets Syst 46:193–210. MathSciNetCrossRefzbMATHGoogle Scholar
  17. Li CT (2004) Digital fragile watermarking scheme for authentication of JPEG images. IEE Proc Vision Image Signal Process 151(6):460–466. CrossRefGoogle Scholar
  18. Li CT, Yuan Y (2006) Digital watermarking scheme exploiting non deterministic dependence for image authentication. Opt Eng 45(12):127001. CrossRefGoogle Scholar
  19. Li X, Zhang H, Chen M (2012) Self-recovery fragile watermarking based on superior block-wise tamper detection. In:Proceedings of 11th IEEE International Conference on Signal Processing, Beijng, pp. 1697–1700.
  20. MeenakshiDevi P, Venkatesan M, Duraiswamy K (2009) Fragile watermarking scheme for image authentication with tamper localization using integer wavelet transform. J Comput Sci 5(11):831–837. CrossRefGoogle Scholar
  21. Ni R, Zhao Y, Yang L, Qiao X (2013) Irregular region-wise watermarking scheme for image tampering detection and recovery. Res Notes Inform Sci 14:471–476. Google Scholar
  22. Nobuhara H, Pedrycz W, Hirota K (2002) A digital watermarking algorithm using image compression method based on fuzzy relational equations. In: Proceedings of FUZZ-IEEE 2002, Vol. 2, IEEE Press, pp. 1568–1573.
  23. Perfilieva I (2006) Fuzzy transforms. Fuzzy Sets Syst 157 (8): 993 – 1023.
  24. Qin C, Ji P, Zhang X, Dong J, Wang J (2017) Fragile image watermarking with pixel-wise recovery based on overlapping embedding strategy. Sig Process 138:280–293. CrossRefGoogle Scholar
  25. Shih FY (2007) Digital watermarking and steganography: fundamentals and techniques. CRC Press (Taylor & Francis Group). Abingdon. ISBN: 9781420047578Google Scholar
  26. Singh D, Singh SK (2017) DCT based efficient fragile watermarking scheme for image authentication and restoration. Multimedia Tools Appl 76:953–977. CrossRefGoogle Scholar
  27. Suthaharan S (2004) Fragile image watermarking using a gradient image for improved localization and security. Pattern Recogn Lett 25(16):1893–1903. CrossRefGoogle Scholar
  28. Tong X, Liu Y, Zhang M, Chen Y (2013) A novel chaos-based fragile watermarking for image tampering detection and self-recovery. Signal Process Image Comm 28:301–308. CrossRefGoogle Scholar
  29. Walton S (1995) Information authentification for a slippery new age. Dr Dobbs J 20(4):18–26Google Scholar
  30. Wolfgang RB, Podilciuk CI, Delp EJ (1998) The effect of the matching watermark and compression transforms in compressed color images. In: Proceedings IEEE International conference in image processing (ICIP1), Chicago, pp. 440–444.

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Authors and Affiliations

  1. 1.Dipartimento di ArchitetturaUniversità degli Studi di Napoli Federico IINapoliItaly
  2. 2.Centro Interdipartimentale di Ricerca “A. Calza Bini”Università degli Studi di Napoli Federico IINapoliItaly

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