Skip to main content
SpringerLink
Log in

Image watermarking techniques based on Schur decomposition and various image invariant moments: a review

  • Published:
Multimedia Tools and Applications Aims and scope Submit manuscript

Abstract

Digital image watermarking provides security, copyright protection, and authenticity to multimedia content by embedding digital content like text, image, and video. In the modern digital age, watermarking of digital images is an essential aspect of providing authenticity to digital content. Digital image watermarking is also used for the authenticity of the medical image in telemedicine applications. In these applications, digital image watermarking provides security to various medical images like Computerized tomography (CT) scans, Magnetic resonance imaging (MRI) images, and X-radiation (X-ray) images. In the past decades, many intellectuals have been working in the field of image watermarking to provide various characteristics features to watermarking like sufficient embedding capacity, strong robustness, and better imperceptibility. This paper covers watermarking techniques based on Schur decomposition and various types of moments like Zernike moment, Fourier harmonic moments, polar harmonic moments, etc. A survey on watermarking techniques suitable for telemedicine applications which include various medical images like CT-scan, MRI image, and X-ray images, is also presented. Various performance measures proposed by different researchers are also discussed, and the suitability of these measures for watermarking schemes is analysed under various attacks. In this paper, novel classification of watermarking schemes, recent essential requirements for different categories of image watermarking applications are covered. A tabular comparison of various watermarking schemes based on different families of moments are presented and also a comparative analysis of outcomes of different categories of moment based watermarking schemes is included. Various challenges and opportunities are also included to make this review more comprehensive.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4

Similar content being viewed by others

Data availability

My manuscript has no associated data.

References

  1. Akhaee MA, Sahraeian SME, Marvasti F (2009) Contourlet-based image watermarking using optimum detector in a noisy environment. IEEE Trans Image Process 19(4):967–980

    MathSciNet  Google Scholar 

  2. Alshanbari HS (2021) Medical image watermarking for ownership & tamper detection. Multimed Tools Appl 80:16549–16564

    Google Scholar 

  3. Aparna JR, Ayyappan S (2015) Image watermarking using Diffie Hellman key exchange algorithm. Proc Comput Sci 46:1684–1691

    Google Scholar 

  4. Awasthi D, Srivastava VK (2022) LWT-DCT-SVD and DWT-DCT-SVD based watermarking schemes with their performance enhancement using Jaya and Particle swarm optimization and comparison of results under various attacks. Multimed Tools Appl 81:25075–25099. https://doi.org/10.1007/s11042-022-12456-4

    Article  Google Scholar 

  5. Awasthi D, Srivastava VK (2023) Robust, imperceptible and optimized watermarking of DICOM image using Schur decomposition, LWT-DCT-SVD and its authentication using SURF. Multimed Tools Appl 82:16555–16589. https://doi.org/10.1007/s11042-022-14002-8

    Article  Google Scholar 

  6. Awasthi D, Srivastava VK (2023) Hessenberg Decomposition-Based Medical Image Watermarking with Its Performance Comparison by Particle Swarm and JAYA Optimization Algorithms for Different Wavelets and Its Authentication Using AES. Circuits Syst Signal Process. https://doi.org/10.1007/s00034-023-02344-z

    Article  Google Scholar 

  7. Awasthi D, Srivastava VK (2023) Performance enhancement of SVD based dual image watermarking in wavelet domain using PSO and JAYA optimization and their comparison under hybrid attacks. Multimed Tools Appl. https://doi.org/10.1007/s11042-023-14723-4

    Article  Google Scholar 

  8. Awasthi D, Khare P, Srivastava VK (2023) BacterialWmark: telemedicine watermarking technique using bacterial foraging for smart healthcare system. J Electron Imaging 32(4):042107

    Google Scholar 

  9. Belkasim SO, Shridhar M, Ahmadi M (1991) Pattern recognition with moment invariants: a comparative study and new results. Pattern Recogn 24(12):1117–1138

    Google Scholar 

  10. Cedillo-Hernández M, García-Ugalde F, Nakano-Miyatake M, Pérez-Meana HM (2014) Robust hybrid color image watermarking method based on DFT domain and 2D histogram modification. SIViP 8:49–63

    Google Scholar 

  11. Chun-peng W, Xing-yuan W, Zhi-qiu X (2016) Geometrically invariant image watermarking based on fast radial harmonic Fourier moments. Signal Process Image Commun 45:10–23

    Google Scholar 

  12. Das C, Panigrahi S, Sharma VK, Mahapatra KK (2014) A novel blind robust image watermarking in DCT domain using inter-block coefficient correlation. AEU-Int J Electron Commun 68(3):244–253

    Google Scholar 

  13. Ernawan F, Kabir MN (2020) A block-based RDWT-SVD image watermarking method using human visual system characteristics. Vis Comput 36(1):19–37

    Google Scholar 

  14. Favorskaya M, Savchina E, Popov A (2018) Adaptive visible image watermarking based on Hadamard transform. In: IOP conference series: materials science and engineering (vol 450, no 5, p 052003). IOP Publishing

  15. Gao G, Jiang G (2015) Bessel-Fourier moment-based robust image zero-watermarking. Multimed Tools Appl 74:841–858

    Google Scholar 

  16. Golub GH, Van Loan CF (2013) Matrix computations. JHU Press

    Google Scholar 

  17. Hamidi M, Haziti ME, Cherifi H, Hassouni ME (2018) Hybrid blind robust image watermarking technique based on DFT-DCT and Arnold transform. Multimed Tools Appl 77:27181–27214

    Google Scholar 

  18. Heidari S, Naseri M (2016) A novel LSB based quantum watermarking. Int J Theor Phys 55:4205–4218

    Google Scholar 

  19. Hosny KM, Darwish MM (2018) Robust color image watermarking using invariant quaternion Legendre-Fourier moments. Multimed Tools Appl 77:24727–24750

    Google Scholar 

  20. Hosny KM, Darwish MM (2019) Resilient color image watermarking using accurate quaternion radial substituted Chebyshev moments. ACM Trans Multimed Comput Commun Appl (TOMM) 15(2):1–25

    Google Scholar 

  21. Hsu LY, Hu HT (2015) Blind image watermarking via exploitation of inter-block prediction and visibility threshold in DCT domain. J Vis Commun Image Represent 32:130–143

    Google Scholar 

  22. Hsu CS, Tu SF (2020) Enhancing the robustness of image watermarking against cropping attacks with dual watermarks. Multimed Tools Appl 79(17-18):11297–11323

    Google Scholar 

  23. Ismail IA, Shouman MA, Hosny KM, Salam HM (2010) Invariant image watermarking using accurate Zernike moments. J Comput Sci 6(1):52

    Google Scholar 

  24. Khare P, Srivastava VK (2021) A secured and robust medical image watermarking approach for protecting integrity of medical images. Trans Emerg Telecommun Technol 32(2):e3918

    Google Scholar 

  25. Khare P, Srivastava VK (2021) A reliable and secure image watermarking algorithm using homomorphic transform in DWT domain. Multidim Syst Sign Process 32:131–160

    MathSciNet  Google Scholar 

  26. Kishore PVV, Venkatram N, Sarvya C, Reddy LSS (2014) Medical image watermarking using RSA encryption in wavelet domain. In: 2014 first international conference on Networks & Soft Computing (ICNSC2014). IEEE, pp 258-262

  27. Ko HJ, Huang CT, Horng G, Shiuh-Jeng WANG (2020) Robust and blind image watermarking in DCT domain using inter-block coefficient correlation. Inf Sci 517:128–147

    Google Scholar 

  28. Lakrissi Y, Saaidi A, Essahlaoui A (2018) Novel dynamic color image watermarking based on DWT-SVD and the human visual system. Multimed Tools Appl 77:13531–13555

    Google Scholar 

  29. Li J, Yu C, Gupta BB, Ren X (2018) Color image watermarking scheme based on quaternion Hadamard transform and Schur decomposition. Multimed Tools Appl 77:4545–4561

    Google Scholar 

  30. Liao X, Yu Y, Li B, Li Z, Qin Z (2019) A new payload partition strategy in color image steganography. IEEE Trans Circ Syst Video Technol 30(3):685–696

    Google Scholar 

  31. Liao X, Yin J, Chen M, Qin Z (2020) Adaptive payload distribution in multiple images steganography based on image texture features. IEEE Trans Dependable Secure Comput 19(2):897–911

    Google Scholar 

  32. Liu P, Yang J, Wei J, Chen F (2010) A novel watermarking scheme in contourlet domain based on schur factorization. In: 2010 2nd international conference on information engineering and computer science. IEEE, pp 1-4

  33. Liu X, Han G, Wu J, Shao Z, Coatrieux G, Shu H (2017) Fractional Krawtchouk transform with an application to image watermarking. IEEE Trans Signal Process 65(7):1894–1908

    MathSciNet  Google Scholar 

  34. Liu D, Yuan Z, Su Q (2020) A blind color image watermarking scheme with variable steps based on Schur decomposition. Multimed Tools Appl 79:7491–7513

    Google Scholar 

  35. Maheshkar S (2017) Region-based hybrid medical image watermarking for secure telemedicine applications. Multimed Tools Appl 76:3617–3647

    Google Scholar 

  36. Maity SP, Kundu MK (2011) Perceptually adaptive spread transform image watermarking scheme using Hadamard transform. Inf Sci 181(3):450–465

    Google Scholar 

  37. Makbol NM, Khoo BE (2013) Robust blind image watermarking scheme based on redundant discrete wavelet transform and singular value decomposition. AEU-Int J Electron Commun 67(2):102–112

    Google Scholar 

  38. Mishra A, Agarwal C, Sharma A, Bedi P (2014) Optimized gray-scale image watermarking using DWT–SVD and firefly algorithm. Expert Syst Appl 41(17):7858–7867

    Google Scholar 

  39. Mohammad AA (2012) A new digital image watermarking scheme based on Schur decomposition. Multimed Tools Appl 59:851–883

    Google Scholar 

  40. Mohan BC, Swamy KV (2010) On the use of Schur decomposition for copyright protection of digital images. Int J Comput Electr Eng 2(4):1793–8163

    Google Scholar 

  41. Mousavi SM, Naghsh A, Manaf AA, Abu-Bakar SAR (2017) A robust medical image watermarking against salt and pepper noise for brain MRI images. Multimed Tools Appl 76:10313–10342

    Google Scholar 

  42. Munib S, Khan A (2017) Robust image watermarking technique using triangular regions and Zernike moments for quantization based embedding. Multimed Tools Appl 76:8695–8710

    Google Scholar 

  43. Najafi E, Loukhaoukha K (2019) Hybrid secure and robust image watermarking scheme based on SVD and sharp frequency localized contourlet transform. J Inf Secur Appl 44:144–156

    Google Scholar 

  44. Nasir I, Weng Y, Jiang J (2007) A new robust watermarking scheme for color image in spatial domain. In: 2007 third international IEEE conference on signal-image technologies and internet-based system. IEEE, pp 942-947

  45. Niu PP, Wang P, Liu YN, Yang HY, Wang XY (2016) Invariant color image watermarking approach using quaternion radial harmonic Fourier moments. Multimed Tools Appl 75:7655–7679

    Google Scholar 

  46. Papakostas GA (2014) Over 50 Years of Image Moments and Moment Invariants. Gate to Computer Science & Research 1

  47. Parah SA, Sheikh JA, Ahad F, Loan NA, Bhat GM (2017) Information hiding in medical images: a robust medical image watermarking system for E-healthcare. Multimed Tools Appl 76:10599–10633

    Google Scholar 

  48. Ren H, Ping Z, Bo W, Wu W, Sheng Y (2003) Multidistortion-invariant image recognition with radial harmonic Fourier moments. JOSA A 20(4):631–637

    MathSciNet  Google Scholar 

  49. Roy S, Pal AK (2017) A robust blind hybrid image watermarking scheme in RDWT-DCT domain using Arnold scrambling. Multimed Tools Appl 76(3):3577–3616

    Google Scholar 

  50. Roy S, Pal AK (2017) A blind DCT based color watermarking algorithm for embedding multiple watermarks. AEU-Int J Electron Commun 72:149–161

    Google Scholar 

  51. Ruanaidh JJÒ, Pun T (1998) Rotation, scale and translation invariant spread spectrum digital image watermarking. Signal Process 66(3):303–317

    Google Scholar 

  52. Sabbane F, Tairi H (2019) Medical image watermarking technique based on polynomial decomposition. Multimed Tools Appl 78:34129–34155

    Google Scholar 

  53. Santhi V, Arulmozhivarman P (2013) Hadamard transform based adaptive visible/invisible watermarking scheme for digital images. J Inf Secur Appl 18(4):167–179

    Google Scholar 

  54. Savelonas MA, Chountasis S (2010) Noise-resistant watermarking in the fractional Fourier domain utilizing moment-based image representation. Signal Process 90(8):2521–2528

    Google Scholar 

  55. Shao Z, Shang Y, Zhang Y, Liu X, Guo G (2016) Robust watermarking using orthogonal Fourier–Mellin moments and chaotic map for double images. Signal Process 120:522–531

    Google Scholar 

  56. Singh S, Rathore VS, Singh R (2017) Hybrid NSCT domain multiple watermarking for medical images. Multimed Tools Appl 76:3557–3575

    Google Scholar 

  57. Soualmi A, Alti A, Laouamer L (2018) A new blind medical image watermarking based on weber descriptors and Arnold chaotic map. Arab J Sci Eng 43:7893–7905

    Google Scholar 

  58. Soualmi A, Alti A, Laouamer L (2021) A novel blind watermarking approach for medical image authentication using MinEigen value features. Multimed Tools Appl 80:2279–2293

    Google Scholar 

  59. Su Q, Chen B (2017) An improved color image watermarking scheme based on Schur decomposition. Multimed Tools Appl 76:24221–24249

    Google Scholar 

  60. Su Q, Chen B (2018) Robust color image watermarking technique in the spatial domain. Soft Comput 22:91–106

    Google Scholar 

  61. Su Q, Niu Y, Liu X, Zhu Y (2012) Embedding color watermarks in color images based on Schur decomposition. Opt Commun 285(7):1792–1802

    Google Scholar 

  62. Su Q, Wang G, Lv G, Zhang X, Deng G, Chen B (2017) A novel blind color image watermarking based on Contourlet transform and Hessenberg decomposition. Multimed Tools Appl 76:8781–8801

    Google Scholar 

  63. Su Q, Yuan Z, Liu D (2018) An approximate Schur decomposition-based spatial domain color image watermarking method. IEEE Access 7:4358–4370

    Google Scholar 

  64. Su Q, Zhang X, Wang G (2020) An improved watermarking algorithm for color image using Schur decomposition. Soft Comput 24(1):445–460

    Google Scholar 

  65. Swaraja K (2018) Medical image region based watermarking for secured telemedicine. Multimed Tools Appl 77(21):28249–28280

    Google Scholar 

  66. Tan J, Liao X, Liu J, Cao Y, Jiang H (2021) Channel attention image steganography with generative adversarial networks. IEEE Trans Netw Sci Eng 9(2):888–903

    Google Scholar 

  67. Thakkar FN, Srivastava VK (2017) A blind medical image watermarking: DWT-SVD based robust and secure approach for telemedicine applications. Multimed Tools Appl 76:3669–3697

    Google Scholar 

  68. Thakkar FN, Srivastava VK (2019) Performance comparison of recent optimization algorithm Jaya with particle swarm optimization for digital image watermarking in complex wavelet domain. Multidim Syst Sign Process 30:1769–1791

    Google Scholar 

  69. Thakur S, Singh AK, Ghrera SP, Mohan A (2020) Chaotic based secure watermarking approach for medical images. Multimed Tools Appl 79:4263–4276

    Google Scholar 

  70. Thanki R, Borra S (2019) Fragile watermarking for copyright authentication and tamper detection of medical images using compressive sensing (CS) based encryption and contourlet domain processing. Multimed Tools Appl 78:13905–13924

    Google Scholar 

  71. Thanki R, Kothari A (2021) Multi-level security of medical images based on encryption and watermarking for telemedicine applications. Multimed Tools Appl 80(3):4307–4325

    Google Scholar 

  72. Tirkel AZ, Osborne CF, Van Schyndel RG (1996) Image watermarking-a spread spectrum application. In: Proceedings of ISSSTA'95 international symposium on spread spectrum techniques and applications (Vol. 2, pp. 785-789). IEEE

  73. Tiwari A, Srivastava VK (2022) A chaotic encrypted reliable image watermarking scheme based on integer wavelet transform-Schur transform and singular value decomposition. In: 2022 international conference on computing, communication, and intelligent systems (ICCCIS). IEEE, pp 581-586

  74. Tiwari A, Srivastava VK (2022) Imperceptible digital image watermarking based on discrete wavelet transform and Schur decomposition. In: Sustainable technology and advanced computing in electrical engineering. Springer, Singapore, pp 119-128

  75. Tiwari A, Srivastava VK (2022) Integer wavelet transform and dual decomposition based image watermarking scheme for reliability of DICOM medical image. In: 2022 IEEE 9th Uttar Pradesh section international conference on electrical, electronics and computer engineering (UPCON). IEEE, pp 1-6

  76. Tiwari A (2023) Srivastava, VK (2023) Novel schemes for the improvement of lifting wavelet transform-based image watermarking using Schur decomposition. J Supercomput 79:13142–13179. https://doi.org/10.1007/s11227-023-05167-6

    Article  Google Scholar 

  77. Tiwari N, Ramaiya MK, Sharma M (2013) Digital watermarking using DWT and DES. In: 2013 3rd IEEE international advance computing conference (IACC). IEEE, pp 1100-1102

  78. Urvoy M, Goudia D, Autrusseau F (2014) Perceptual DFT watermarking with improved detection and robustness to geometrical distortions. IEEE Trans Inf Forensics Secur 9(7):1108–1119

    Google Scholar 

  79. Vaidya S P, PVSSR CM (2017) A robust semi-blind watermarking for color images based on multiple decompositions. Multimed Tools Appl 76:25623–25656

    Google Scholar 

  80. Vaishnavi D, Subashini TS (2015) Robust and invisible image watermarking in RGB color space using SVD. Proc Comput Sci 46:1770–1777

    Google Scholar 

  81. Van Loan CF, Golub G (1996) Matrix computations (Johns Hopkins studies in mathematical sciences). Matrix Computations 5

  82. von F, Z. (1934) Beugungstheorie des schneidenver-fahrens und seiner verbesserten form, der phasenkontrastmethode. physica 1(7-12):689–704

    Google Scholar 

  83. Wang XY, Hou LM (2010) A new robust digital image watermarking based on Pseudo-Zernike moments. Multidim Syst Sign Process 21(2):179–196

    MathSciNet  Google Scholar 

  84. Wang XY, Yang YP, Yang HY (2010) Invariant image watermarking using multi-scale Harris detector and wavelet moments. Comput Electr Eng 36(1):31–44

    Google Scholar 

  85. Wang XY, Niu PP, Yang HY, Wang CP, Wang AL (2014) A new robust color image watermarking using local quaternion exponent moments. Inf Sci 277:731–754

    Google Scholar 

  86. Wang XY, Wang CP, Wang AL, Yang HY (2014) SVM correction based geometrically invariant digital watermarking algorithm. Multimed Tools Appl 72:1933–1960

    Google Scholar 

  87. Wang CP, Wang XY, Chen XJ, Zhang C (2017) Robust zero-watermarking algorithm based on polar complex exponential transform and logistic mapping. Multimed Tools Appl 76:26355–26376

    Google Scholar 

  88. Wang C, Wang X, Li Y, Xia Z, Zhang C (2018) Quaternion polar harmonic Fourier moments for color images. Inf Sci 450:141–156

    MathSciNet  Google Scholar 

  89. Wong PW, Memon N (2001) Secret and public key image watermarking schemes for image authentication and ownership verification. IEEE Trans Image Process 10(10):1593–1601

    Google Scholar 

  90. Xia Z, Wang X, Li X, Wang C, Unar S, Wang M, Zhao T (2019) Efficient copyright protection for three CT images based on quaternion polar harmonic Fourier moments. Signal Process 164:368–379

    Google Scholar 

  91. Xia Z, Wang X, Wang M, Unar S, Wang C, Liu Y, Li X (2019) Geometrically invariant color medical image null-watermarking based on precise quaternion polar harmonic Fourier moments. IEEE Access 7:122544–122560

    Google Scholar 

  92. Xia Z, Wang X, Zhou W, Li R, Wang C, Zhang C (2019) Color medical image lossless watermarking using chaotic system and accurate quaternion polar harmonic transforms. Signal Process 157:108–118

    Google Scholar 

  93. Xin Y, Liao S, Pawlak M (2007) Circularly orthogonal moments for geometrically robust image watermarking. Pattern Recogn 40(12):3740–3752

    Google Scholar 

  94. Xu H, Kang X, Chen Y, Wang Y (2019) Rotation and scale invariant image watermarking based on polar harmonic transforms. Optik 183:401–414

    Google Scholar 

  95. Yamni M, Daoui A, Karmouni H, Sayyouri M, Qjidaa H, Flusser J (2020) Fractional Charlier moments for image reconstruction and image watermarking. Signal Process 171:107509

    Google Scholar 

  96. Yamni M, Karmouni H, Sayyouri M, Qjidaa H (2021) Image watermarking using separable fractional moments of Charlier–Meixner. J Frankl Inst 358(4):2535–2560

    MathSciNet  Google Scholar 

  97. Yang Y, Sun X, Yang H, Li CT, Xiao R (2009) A contrast-sensitive reversible visible image watermarking technique. IEEE Trans Circ Syst Video Technol 19(5):656–667

    Google Scholar 

  98. Yang HY, Wang P, Wang XY, Niu PP, Miao EN, Zhang Y (2015) Robust digital watermarking based on local invariant radial harmonic Fourier moments. Multimed Tools Appl 74:10559–10579

    Google Scholar 

  99. Yang HY, Wang XY, Niu PP, Wang AL (2015) Robust color image watermarking using geometric invariant quaternion polar harmonic transform. ACM Trans Multimed Comput Commun Appl (TOMM) 11(3):1–26

    Google Scholar 

  100. Yeo IK, Kim HJ (2003) Generalized patchwork algorithm for image watermarking. Multimedia Systems 9:261–265

    Google Scholar 

  101. Yuan XC, Pun CM (2014) Feature extraction and local Zernike moments based geometric invariant watermarking. Multimed Tools Appl 72:777–799

    Google Scholar 

  102. Zear A, Singh AK, Kumar P (2018) A proposed secure multiple watermarking technique based on DWT, DCT and SVD for application in medicine. Multimed Tools Appl 77:4863–4882

    Google Scholar 

  103. Zhang H, Shu H, Coatrieux G, Zhu J, Wu QJ, Zhang Y, ... Luo L (2011) Affine Legendre moment invariants for image watermarking robust to geometric distortions. IEEE Trans Image Process, 20(8):2189-2199

Download references

Author information

Authors and Affiliations

  1. Electronics and Communication Engineering Department, Motilal Nehru National Institute of Technology, Prayagraj, Uttar Pradesh, 211004, India

    Anurag Tiwari & Vinay Kumar Srivastava

Authors
  1. Anurag Tiwari
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Vinay Kumar Srivastava
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Anurag Tiwari.

Ethics declarations

Conflict of interest

There is no conflict of Interest.

Additional information

Publisher’s note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Tiwari, A., Srivastava, V.K. Image watermarking techniques based on Schur decomposition and various image invariant moments: a review. Multimed Tools Appl 83, 16447–16483 (2024). https://doi.org/10.1007/s11042-023-16109-y

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11042-023-16109-y

Keywords

Search

Navigation