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Hybrid blind robust image watermarking technique based on DFT-DCT and Arnold transform

Mohamed Hamidi, Mohamed El Haziti, Hocine Cherifi, Mohammed El Hassouni

arXiv:1911.00753v1cs.MMcs.CR

TL;DR

The paper addresses the difficulty of protecting images with watermarks that are both imperceptible and robust. It proposes a blind hybrid DFT–DCT method with Arnold-transform encryption, and reports resistance to a wide variety of attacks while preserving high imperceptibility on natural and textured images.

  • Problem

    Copyright-protection watermarking faces difficulty balancing imperceptibility and robustness, while robust watermarks must remain detectable after distribution-related changes.

    Source: §1 · p. 2, §2 · p. 5

  • Method

    The blind method embeds a watermark in middle-band DCT coefficients of the DFT magnitude and applies Arnold transform to encrypt the watermark.

    Source: §1 · p. 3, §4.1 · p. 8

  • Results

    The proposed scheme is reported to resist a wide variety of attacks on natural and textured images while preserving high imperceptibility.

    Source: §7 · p. 32

  • Takeaways & Limitations

    The paper concludes that combining DFT and DCT provides good resistance to varied attacks while preserving high imperceptibility for natural and textured images.

    Source: §7 · p. 32

Abstract

from arXiv · show

In this paper, a robust blind image watermarking method is proposed for copyright protection of digital images. This hybrid method relies on combining two well-known transforms that are the discrete Fourier transform (DFT) and the discrete cosine transform (DCT). The motivation behind this combination is to enhance the imperceptibility and the robustness. The imperceptibility requirement is achieved by using magnitudes of DFT coefficients while the robustness improvement is ensured by applying DCT to the DFT coefficients magnitude. The watermark is embedded by modifying the coefficients of the middle band of the DCT using a secret key. The security of the proposed method is enhanced by applying Arnold transform (AT) to the watermark before embedding. Experiments were conducted on natural and textured images. Results show that, compared with state-of-the-art methods, the proposed method is robust to a wide range of attacks while preserving high imperceptibility.

1 Introduction

The introduction frames robust watermarking as a way to protect digital images from unauthorized use while balancing imperceptibility, robustness, capacity, and security. It proposes a blind DFT–DCT method with Arnold-transform encryption and outlines comparisons with other methods.

1 Introduction

  • Watermarking must balance imperceptibility, robustness, capacity, and security, with a secret key required for a minimum level of security.Robustness concerns detecting the watermark after distribution-related changes such as filtering, noise, compression, or cropping.Source: §1 · p. 2
  • Robust watermarking is presented as suited to copyright protection, while fragile schemes serve authentication and integrity checks and semi-fragile schemes tolerate some processing.The introduction distinguishes blind, semi-blind, and non-blind extraction by whether the original image or side information is needed.Source: §1 · pp. 2–3
  • The proposed blind method embeds a watermark in middle-band DCT coefficients of the DFT magnitude and uses Arnold transform to encrypt the watermark.The introduction attributes imperceptibility to using DFT magnitude and improved robustness to applying DCT to that magnitude.Source: §1 · p. 3
  • The evaluation compares the proposed scheme with its DFT counterpart and methods in,,,,, and.The introduction identifies imperceptibility and robustness as comparison criteria.Source: §1 · p. 3
  • The paper proceeds from related work and terminology to the proposed scheme, experimental setup, results, and conclusion.Source: §1 · p. 3

2 Related work

Prior work includes single-transform watermarking and hybrid transform schemes, while the paper identifies the imperceptibility–robustness tradeoff as the central challenge for copyright protection. Its proposed DFT–DCT combination uses DFT magnitude for imperceptibility and DCT for robustness, with Arnold transform for security.

2 Related work

  • The related-work section also cites DCT watermarking in and, Fourier-magnitude embedding in, and wavelet-based schemes in,, and.Source: §2 · pp. 3–4
  • Earlier hybrid methods combine DCT with SVD or DWT, and examples also use Arnold scrambling or adaptive watermark strength,,.The cited DWT–DCT method is reported to outperform DCT alone; the DWT–SVD–DCT method is described as secure, imperceptible, and robust to common signal-processing operations.Source: §2 · p. 4
  • Other hybrid approaches combine DWT, DCT, and SVD or add RDWT, NSCT, and MSVD, with reported goals or strengths including robustness, security, and capacity,,,,.The cited methods vary in embedding location and whether they are blind or semi-blind.Source: §2 · pp. 4–5
  • Existing copyright-watermarking schemes face difficulty achieving a good tradeoff between imperceptibility and robustness.The paper motivates combining transforms to exploit their different characteristics.Source: §2 · p. 5
  • The proposed approach combines DFT and DCT, using DFT magnitude for high imperceptibility and DCT to improve robustness to common signal-processing attacks, with Arnold transform for security.Source: §2 · p. 5

3 Preliminaries

The preliminaries describe the transform properties and scrambling operation used by the proposed watermarking scheme. DFT supplies a magnitude representation, DCT maps spatial values to frequency coefficients, and Arnold transform scrambles watermark pixels.

3.1 Discrete Fourier transform (DFT)

  • DFT represents an image through magnitude and phase; spatial shifts affect phase but not magnitude, and the text describes DFT as robust to cropping.When a watermark is embedded in the magnitude, the text says synchronization is unnecessary even if the spectrum is blurred.Source: §3.1 · pp. 5–6

3.2 Discrete cosine transform (DCT)

  • DCT transforms an image from the spatial domain to the frequency domain and is used for decorrelation and energy compaction.The section gives 2D-DCT and inverse 2D-DCT expressions; f(x, y) denotes spatial pixel values and C(u, v) the DCT coefficients, with m and n as block size.Source: §3.2 · p. 6

3.3 Arnold Transform

  • Arnold transform rearranges watermark pixels through repeated iterations, and its periodicity allows the original image to reappear after enough cycles.The transform parameters serve as an additional key, and the encrypted watermark can be decrypted by iterating the inverse transform.Source: §3.3 · p. 7
  • The paper illustrates Arnold encryption by comparing an original 64×64 watermark with its encrypted version after 50 iterations.Source: §3.3 · p. 7

4 Proposed scheme

The proposed blind watermarking method applies DCT to DFT magnitudes, embedding in middle-band coefficients to combine imperceptibility with robustness; Arnold scrambling adds security. Extraction regenerates keyed sequences and reverses the scrambling without requiring the original image.

4 Proposed scheme

  • The method applies DCT to DFT magnitudes and embeds the watermark in middle-band coefficients, using DFT magnitude for imperceptibility and DCT for robustness.The watermark is scrambled with Arnold transform to increase security.Source: §4 · pp. 7–8

4.1 Watermark embedding

  • Two keyed, statistically independent pseudo-random sequences encode watermark bits in middle-band coefficients of each 8×8 DCT block.The gain factor k trades robustness against imperceptibility, while the normally distributed sequences are motivated by resistance to averaging differently watermarked copies.Source: §4.1 · pp. 8–9

4.2 Watermark extraction

  • Blind extraction uses the two secret keys to regenerate the sequences, compare their correlations with middle-band coefficients, and apply inverse Arnold transform to recover the watermark.The watermarked image is processed through DFT magnitude and DCT before bit decisions are made.Source: §4.2 · pp. 10–11

5 Experimental setup

The experiments use natural grayscale and textured images with binary watermarks. Image quality and watermark robustness are assessed using PSNR, SSIM, and normalized correlation, alongside comparisons with selected methods.

5.1 Studied images

  • Experiments cover 10 natural 8-bit grayscale images of size 512×512 and 39 textured images, using binary logos of sizes 19×52 and 64×64.The watermark is Arnold-scrambled with n = 24; empirically selected embedding strength is k = 9600.Source: §5.1 · p. 11

5.2 Evaluation metrics

  • PSNR and SSIM assess image quality, while normalized correlation measures similarity between extracted and original watermarks as a robustness measure.PSNR is used for comparative purposes despite being recognized as not correlating with human perception; the experiments compare against methods in,, and.Source: §5.2 · pp. 12–13

6.1 Imperceptibility

The scheme reports high PSNR and SSIM, while visual checks indicate small, distributed changes. DFT-DCT yields better imperceptibility than DFT-only across all test images.

6.1 Imperceptibility

6.2 Robustness

The method is evaluated under noise, compression, filtering, cropping, and combined attacks, using normalized correlation (NC) to assess watermark extraction. Results report high robustness across natural and textured images, with DFT-DCT outperforming DFT-only in the reported comparisons.

5.2.2.1 Noising attack

  • For Gaussian noise variance below 0.02, NC is 1.0; at σ = 0.1, NC is 0.9417, while salt-and-pepper noise intensity 0.02 yields NC = 0.9843.The tests use zero-mean noise.Source: §5.2.2.1 · p. 22

5.2.2.2 Compression attack

  • For JPEG2000 compression, NC is close to 1 when CR < 5 and is 0.9 at CR = 10 for natural and textured images.Compression ratios were varied from 1 to 10.Source: §5.2.2.2 · pp. 23–24, Figure 15 · p. 25
  • For JPEG compression, NC is 1 when the quality factor is greater than 75; at quality factor 30, NC is 0.9344 for D9 and 0.9261 for Mandrill.The reported JPEG results show a small difference between natural and textured images; DFT-DCT outperforms DFT-only.Source: Figure 14 · p. 22, §5.2.2.2 · p. 25

5.2.2.3 Low-pass Gaussian filtering

  • With low-pass Gaussian filtering at σ = 0.6 and a 9 × 9 window, NC is 0.9765 for Mandrill and 0.9984 for D9.The Mandrill result also reports PSNR of 78.12 dB.Source: §5.2.2.3 · pp. 25–26

5.2.2.4 Gaussian smoothing

  • Under Gaussian smoothing with σ = 0.6 and a 9 × 9 window, NC is 0.9741; the method is reported to outperform DFT-only.The reported tests cover window sizes from 3 × 3 to 9 × 9.Source: §5.2.2.4 · p. 26, Figure 17 · p. 27

5.2.2.5 Cropping

  • After 50% cropping, NC is 1.0; the authors attribute cropping tolerance to spectrum blurring and the use of DFT magnitude, which removes the need for synchronization.Cropping proportions tested ranged from 10% to 50%.Source: §5.2.2.5 · pp. 27–28

5.2.2.6 Combined attacks

  • Across the combined-attack cases, NC exceeds 0.9694 regardless of image nature, and DFT-DCT outperforms DFT-only across attack types.The reported combined cases include multiple attacks; rotation results are described as encouraging.Source: Table 3 · p. 21, Table 4 · p. 23, §5.2.2.6 · p. 28

6.3 Computational complexity

The method’s global computational complexity is O(n^3), driven by matrix multiplication during embedding. Extraction is O(n^2), and average CPU time is reported separately.

6.3 Computational complexity

  • The method has global complexity O(n^3), with embedding at O(n^3) and extraction at O(n^2).Embedding complexity is attributed to matrix multiplication in equation 13; extraction complexity is attributed to inverse Arnold transform calculation.Source: §6.3 · p. 28
  • Average CPU times for watermark embedding and extraction are reported for 10 natural images of size 512 × 512.The measurements used MATLAB R2013a on an Intel Core i5-3470 at 3.2 GHz with 4 GB RAM.Source: §6.3 · p. 28, Table 6 · p. 28

6.4 Comparison with alternative methods

The paper compares imperceptibility, robustness, and computational complexity with alternative watermarking methods. It reports strong imperceptibility and robustness comparisons, while noting higher complexity than one compared method.

6.4.1 Imperceptibility

  • The proposed method’s PSNR is reported as superior to,, and, despite its larger capacity; it also outperforms Singh et al. at a capacity of 65536 bits.The comparisons use Lena for Table 7 and a 256 × 256 watermark across several images for Table 8.Source: §6.4.1 · p. 29, Table 7 · p. 29, Table 8 · p. 29

6.4.2 Robustness

  • For salt-and-pepper noise, the method is more robust than schemes,,, and; under histogram equalization, it outperforms,,,, and.Source: §6.4.2 · pp. 29–30
  • Against JPEG compression, the method outperforms,, and, but not,, and at quality factor 50; it performs best on cropping and exceeds listed methods for rotations above ±0.75°.Rotation NC is described as not so good above ±0.75°, though still better than the compared methods.Source: §6.4.2 · p. 30, Table 10 · p. 30, Table 11 · p. 31

6.4.3 Complexity analysis comparison

  • The proposed method has O(n^3) complexity, higher than at O(n^2); the paper reports better extraction accuracy and robustness than.Methods and are also described as cubic-complexity schemes.Source: §6.4.3 · p. 32

7 Conclusion

The conclusion presents a blind hybrid watermarking scheme that combines DFT and DCT, embedding in middle-band DCT coefficients of the cover image’s DFT magnitude. It reports resistance to a wide variety of attacks on natural and textured images while preserving high imperceptibility.

7 Conclusion

  • The blind scheme embeds in middle-band DCT coefficients of the cover image’s DFT magnitude, using secret keys for PN-sequence generation and Arnold-transform encryption.The paper concludes that the method resists a wide variety of attacks on natural and textured images while preserving high imperceptibility.Source: §7 · p. 32
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