A Robust image watermarking for copyright protection using Multiresolution Walsh-Hadamard transform and Schur using Differential evolution

Swaraja K; Meenakshi K; Ushakumari Ch; Kishore D

doi:10.12688/f1000research.124720.1

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Research Article

A Robust image watermarking for copyright protection using Multiresolution Walsh-Hadamard transform and Schur using Differential evolution

[version 1; peer review: 2 approved with reservations, 1 not approved]

Swaraja K¹, Meenakshi K ¹, Ushakumari Ch¹, Kishore D²

PUBLISHED 16 Nov 2022

Author details Author details

¹ Electronics and Communication Engineering, Gokaraju Rangaraju Institute of Engineering and Technology, Hyderabad, Telangana, 500090, India
² Electronics and Communication Engineering, Aditya College of Engineering and Technology, Surampalem, Andhra pradesh, India

Swaraja K
Roles: Conceptualization, Methodology, Software, Supervision, Visualization, Writing – Original Draft Preparation

Meenakshi K
Roles: Conceptualization, Project Administration, Supervision, Visualization, Writing – Review & Editing

Ushakumari Ch
Roles: Conceptualization, Formal Analysis, Investigation, Methodology, Visualization

Kishore D
Roles: Data Curation, Investigation, Resources, Visualization

OPEN PEER REVIEW

REVIEWER STATUS

This article is included in the Computational Modelling and Numerical Aspects in Engineering collection.

Abstract

\textit{Background} The proposed watermarking framework is based on the multi-resolution Walsh-Hadamard Transform (MR-WHT) along with Schur factorization. For embedding, the cover image is converted into a frequency domain using MR-WHT before Schur factorization is applied. \textit{Methods} The upper triangle's highest stable eigenvalues in the Schur factorization are employed as reliable embedding locations for the watermark. The singular values of these coefficients are updated with the singular values of the watermark, and the matrix array generated by the biggest eigenvalues is further factorised by singular value decomposition using multiple scaling factors and Differential evolution (DE). Later, an inverse SVD, inverse Schur, and inverse multiresolution Walsh-Hadamard transform is executed to obtain a watermarked image. \textit{Results} The simulation results show that the proposed method is imperceptible and robust against existing watermarking algorithms used in the literature.

Keywords

MR-WHT, Singular Value Decomposition, Schur factorization, PSNR, SSIM, NCC, Transparancy, Robustness

Corresponding author: Meenakshi K

Competing interests: No competing interests were disclosed.

Grant information: The author(s) declared that no grants were involved in supporting this work.

Copyright: © 2022 K S et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

How to cite: K S, K M, Ch U and D K. A Robust image watermarking for copyright protection using Multiresolution Walsh-Hadamard transform and Schur using Differential evolution [version 1; peer review: 2 approved with reservations, 1 not approved]. F1000Research 2022, 11:1333 (https://doi.org/10.12688/f1000research.124720.1) First published: 16 Nov 2022, 11:1333 (https://doi.org/10.12688/f1000research.124720.1) Latest published: 16 Nov 2022, 11:1333 (https://doi.org/10.12688/f1000research.124720.1)

Introduction

The enormous progress in digital technology and the advancement in processor speed, combined with internet access, augmented the ease with which multimedia content including audio, images, and videos were reproduced and duplicated. As a result, owners of associated metadata must contend with the challenge of safeguarding their digital property against copyright violations and other forms of exploitation. As a result, owners of multimedia content must overcome the challenge of preventing copyright infringement and other types of exploitation of their digital content. Digital watermarking provided an effective method of preventing fraudulent and illegal replication of digital media. However, better and more advanced watermarking techniques are required as the use of multimedia documents grows at an exponential rate. Thus, digital watermarking has evolved into a multidisciplinary research field involving communications theory, signal processing, and multimedia coding.

Digital watermarking¹ is a technique for concealing information that is embedded in a multimedia object. The object could be any type of multimedia, such as an invisible signal embedded directly in digital media. Spatial and spectral domain methods are the two most commonly used methods for digital watermarking. The first type of algorithm embeds a watermark by modifying image pixels. The second category, for example the Discrete Cosine Transform, embed watermarks in spectrum coefficients (DCT)²^–⁵ and other different transforms.⁶^–¹⁸ Techniques in the spectrum domain are considered to be superior compared with those of the spatial domain. In the least perpetually significant coefficients of a transform of an image in the spectral domain, one can insert a watermark. The watermark can be spread across various transform coefficient bands. This will increase the watermarks’ transparency and prevent watermarked image visual degradation. Additionally, the watermark is distributed unevenly, making it extremely challenging for the hacker to remove it.

One issue with current watermarking techniques is that they struggle with the optimization of imperceptibility and robustness because it has been discovered that these two parameters are incompatible. As a result, many techniques to optimize transparency and robustness¹⁹^–²² are used in the literature. Genetic-algorithms (GA),²³^–²⁷ Differential-evolution,²⁸^–³⁰ Particle-swarm optimization (PSO),³¹^–³⁴ and fuzzy-logic³⁵^,³⁶ are currently used in literature for optimizing the transparency and robustness. A GA was used to find optimum thresholds for quantizing wavelet coefficients.³² Oguz FindiK et al.³³ used PSO for watermarking color images. Shieh et al.³⁷ identified a fitness function depending on factors related to robustness and imperceptibility. After DCT transformation, the transformed image is segmented into 8 × 8 and four bands are randomly selected for watermark embedding and given to a fitness function. Following GA, the four robust bands with the highest fitness are used for embedding the watermark. Their performance metrics are found to be improved. Another use of GA is demonstrated by aslantas et al.,⁹ who used GA to investigate the best watermarking strategy based on SVD. To embed the watermark, multiple scaling factors were applied to the singular values of the original image. Additionally, a GA was used in an embedded method based on the quantization index modulation (QIM) technique.³⁸

Much research has been focused on achieving HVS image characteristics and it has been demonstrated that the DHT has a poor threshold difference for noise processing at low compression quality.³⁹ These facts may aid DHT-based schemes in achieving simultaneous optimum performance, as well as achieving optimal robustness against low quality compression while also having a higher embedding capacity, resulting in better performance than DCT or wavelet-based schemes. As a result, we believe that using Walsh-Hadamard characteristics to design optimal data hiding schemes with a high degree of robustness and imperceptibility is a worthwhile endeavor.

Preliminaries

Using a hybridized multiresolution fast Walsh-Hadamard transform and Schur transform with differential evolution, a reliable hybrid watermarking is developed in this paper.

Walsh-Hadamard transform (WHT)

Of all the orthogonal transforms that are currently in use, it has the lowest computational complexity. Functionally identical kernels serve as the foundation for the Walsh-Hadamard transform. The kernel of forward Walsh-Hadamard transform is found by:

(1)

k (e, f, p, q) = \sum_{j = 0}^{m} {(- 1)}^{[b_{j} (e) b_{m - 1 - j} (p) + b_{j} (f) b_{m - 1 - j} (q)]}

The inverse kernel of WHT is given by:

(2)

l (e, f, p, q) = \sum_{j = 0}^{m} {(- 1)}^{[b_{j} (e) b_{m - 1 - j} (p) + b_{j} (f) b_{m - 1 - j} (q)]}

The Walsh-Hadamard transform⁴⁰ is a square array with orthogonal rows and columns of ones with plus and minus signs. The transform is computed quickly using the successive doubling method and has the advantage of having almost identical forward and inverse kernels and less computational complexity. The algorithm exhibits resilience to compression at low quality levels. Compared to other popular transforms, Walsh-Hadamard is more resilient to image manipulation because the multivalued kernels make it such that the values of the pixels in the block alter by various amounts.⁴¹ Therefore, real-time hardware implementation is better suited for it.

Schur decomposition

If a square matrix A has all linearly independent eigenvectors, then an invertible matrix P exists with the property that P⁻¹AP = Λ, where Λ is a diagonal matrix. However, not all square matrices can be diagonalized. QR factorization or Schur factorization can help to address this weakness. Schur asserts that any invertible matrix can be expressed as the multiplication of the upper triangle matrix (T) with the unitary matrix (U).

(3)

T = U^{H} A U

For some unitary matrix U and upper triangular matrix T. In matrix T, the diagonal entries of T are the eigenvalues of A.

Singular value decomposition

SVD is a mathematical tool that is frequently used in image watermarking, compression, and retrieval. Every real matrix A, according to this theory, can be broken down into a multiplication of 3 matrices, W, D, F where WW^T = I, FF^T = I and the largest singular values are contained in the diagonal matrix, S. Zero is the singular value of the matrix above rank r.

(4)

G = {WDF}^{T}

In SVD, singular values stand in for the layer’s luminance and singular vectors for the image’s geometry. The largest singular values of the SVD have the greatest energy preservation and resistance to small perturbations, making them immune to the majority of signal processing as well as image compression operations.⁴²

Differential evolution

A generation is the term used to describe the population in each iteration of the evolution, which typically begins with a population of randomly chosen individuals. Every member of the population has their fitness assessed once every generation; in most optimization algorithms, the fitness is the value of the objective function. The current population is stochastically selected for the fittest individuals, and each individual’s genome is altered (through crossover and possibly through random mutation) to create a new generation. The following algorithm iteration uses the new generation of candidate solutions. The central concept of DE is a method for generating trial parameter vectors. A vector with weighted difference within two members of the population is accumulated to a third member by DE to create new parameter vectors. If the newly produced vector has a relatively low objective function when compared to the population of predefined member, it will be replaced in the next generation by the vector to which it was compared. The aforementioned generation process can, but does not have to, include the comparison vector. Furthermore, to maintain the record of the growth made during the minimization procedure, the parameter vector x_best, G, which is best is calculated for each generation G, is measured. Consider the watermarking system with real valued properties

(5)

P_{m}; m = 0, 1, 2, \dots L - 1;

The watermarking system has constraints in the form of:

(6)

P_{m}; m = L, L + 1, L + 2, L + 3, \dots, L + C;

System optimization implies varying the D-dimensional parameter vector.

(7)

y = (y_{0} y_{1} \dots y_{D - 1})

According to scheme DE1 of Ref. 43 for all vectors X_{i, G} for j = 0,1,2, …, N − 1, a trial vector (v) is produced in accordance to:

(8)

V_{j, G} = Y_{s 1, G} + F \times (Y_{s 2, G} - Y_{s 3, G})

where s₁,s₂,s₃ are mutually distinct. In DE, a fixed number of vectors are randomly generated to create a population of potential solutions within an n-d search space, which are then exploited in the search space and find the objective function minima. New vectors are produced by the amalgamation of vectors randomly selected from the present population at each iteration, referred to as a generation (mutation). A predetermined target vector is then combined with the incoming vectors. The trial vector is created during this process, which is known as recombination. Finally, if, and only if, the trial vector results in a decrease in the result of the objective function, it is accepted for the following generation. This final operator is known as a selection.

Proposed watermarking algorithm

Most emerging watermarking methods employ a single transformation function that must be fine-tuned. Moreover, multiple scaling components are recommended in the literature for fine adjusting because singular values reveal different tolerances to different scaling factors. So multiple scaling factors are proposed in the literature.⁹ The proposed algorithm contains three steps: a watermark concealing algorithm, a watermark extraction algorithm, and a computation of multiple scaling factor.

Watermark concealing algorithm

This subsection describes the proposed watermarking algorithm based on the hybridized multiresolution fast Walsh-Hadamard transform and Schur transform using DE as shown in Figure 1.

Figure 1. Watermark embedding algorithm of proposed algorithm.

1. The cover image A is subjected to a FWHT2 transform.
(9)
$B = FWHT 2 (A)$
The significant coefficients of WHT2 lie in the mid and upper bands of frequency of the translated image. Therefore, the watermark is implanted in the mid and high frequency zones of the image.
2. Apply MR-WHT2 to B, given in Equations 10–13. Multiresolution is applied by row followed by column modification. Row-wise modification results from Equations 10–13:
(10)
$B 1 (: x) = [\frac{B (: 2 x - 1) + B (: 2 x - 1)}{2}]$
(11)
$B 1 (: width / 2 + x) = B 1 (: 2 x - 1) - B 1 (: 2 x)$

Column-wise modification results:

(12)

B 1 (y :) = [\frac{B (2 y - 1 :) + B (2 y :)}{2}]

(13)

B 1 (height / 2 + x :) = B 1 (2 y - 1 :) - B 1 (2 y :)

3. The multiresolution Walsh-Hadamard transform decomposes image into LL, LH, HL and HH bands.
4. Extract the HH band for watermark embedding.
5. Suppose that the cover image size is R × S. The size of HH band after the MR-WHT2 transform is R × S, where P and Q are $\frac{M}{2}$ and $\frac{N}{2}$ . The HH band is segmented into 8 × 8 blocks and the number of R × S is 0 to m-1 and 0 to n-1, where m and n are $\frac{R}{8}$ and $\frac{S}{8}$ .
6. Apply Schur factorization to each 8 × 8 block of HH band. Schur factorization decomposes images into unitary matrix (U) and upper traingular matrix (T).
7. Employ HEBS (high eigenvalue block selection) to obtain the largest eigenvalue of each each 8 × 8 block and its size is the same as the watermark and denotes it array (C). Apply SVD to array B and w, as given in Equation 14.
(14)
$\begin{array}{l} [U_{c}, w_{c}, V_{c}] = SVD (B) \\ [U_{w}, w_{w}, V_{w}] = SVD (w) \end{array}$
8. Amended singular values are obtained from w_c and w_w given in the equation below:
(15)
$w_{wa} = S_{c} + \frac{k}{max (max (k))} \times w_{w}$
9. Apply the inverse SVD.
(16)
$B_{new} = U_{c} S_{wa} V_{c}^{T}$
10. Replace the coefficients in B_new with high eigenvalue blocks in the T matrix of Schur factorization. The modified upper traingular matrix is denoted by T_new.
11. Apply the inverse Schur transform.
(17)
$G = {UT}_{new} U^{T}$
12. Merge all 8 × 8 blocks to form H_new.
13. Remap all bands LL,LH, HL and HH_new to form Q.
14. Apply the inverse multiresolution to the Q obtained from the column and row transformation. Undo column-wise modification results.
(18)
$Q 1 (2 y - 1 :) = Q (y :) + [\frac{Q (\frac{Height}{2} + y :) + 1}{2}]$
(19)
$Q 1 (2 y :) = Q 1 (2 y - 1 :) - Q (\frac{Height}{2} + y :)$
15. Undo row-wise modification.
(20)
$Q 2 (: 2 x - 1) = Q 1 (: x) + [\frac{Q 1 (: \frac{width}{2} + x) + 1}{2}]$
(21)
$Q 1 (: 2 x) = Q 1 (: 2 x - 1) + (\frac{Q 2 (: \frac{Height}{2} + x) + 1}{2})$
16. Perform inverse FWHT2D to obtain the watermarked image D.

Watermark extraction

The proposed watermarking framework is based on non-blind watermarking, which requires an original image for extraction. The host and the watermarked image are subjected to FWHT2D followed by forward multiresolution to obtain LL, LH, HL, and HH bands, as well as LLW, LHW, HLW, and HHW bands, respectively.

1. Apply Schur factorization to HH and HHW bands.
2. Compute the HEBS in upper triangular matrix of Schur factorization to form a matrix array of M and M_W, respectively.
3. Apply forward SVD to M and M_W to obtain singular values.
(22)
$S_{wnew} = (w_{wa} - w_{c}) * \frac{max (max (k))}{k}$
4. Obtain singular values of the watermark from w_wa and w_c by using Equation 22.
5. Obtain the inverse SVD to extract the watermark.
(23)
$Extracted watermark = U_{w} S_{wnew} V_{w}^{T}$

Computing multiple scaling factor from random population

The proposed work utilizes the DE to search for multiple scaling factors (msfs) in order to strengthen the robustness of the proposed scheme. The logo embedded size is 32 × 32. Therefore, the size of msf’s is 32. If the input population size is 100, then 100 strings of 32 variables is stochastically generated, out of which each 32 string represents a possible solution. The fitness function is computed with the structural similarity (S.S.I.M) among A and D and cross correlation is computed between the original and the extracted watermark.

(24)

f_{i} = S . S . I . M (A, D) - \frac{\sum_{i = 1}^{t} (NCC (w, w_{ext}))}{t}

where t is the count of attacks applied. The objective function of DE is given by:

(25)

{fitness}_{i} = \frac{1}{f_{i}}

The strings that provided the higher fitness values after all strings in a generation have been examined are chosen for the upcoming generation. Then, using genetic operators crossover and mutation operators from these strings, the population of the upcoming generation is produced. The aforementioned procedures are repeated until a predetermined stopping criterion, such as the maximum generation number, is met.

Simulation results and discussion

The proposed algorithm implements on benchmark images airplane, Zelda, Lena, and Baboon, each 512 × 512 in size. The watermark used is a java cup. The algorithm is implemented on Matlab-2013 (RRID:SCR 001622), 4GB RAM, duo core processor. The transparency of the image which is watermarked is judged by peak signal to noise ratio and is given by:

(26)

PSNR = 10 log 10 (\frac{I_{\max}^{2}}{MSE})

Here, MSE is the mean square within the original and reconstructed image given in Equation 27.

(27)

MSE = \frac{\sum_{j = 1}^{N} \sum_{i = 1}^{M} {(X_{i, j} - Y_{i, j})}^{2}}{MN}

where, X and Y stand for the gray values of the host and watermarked image; I_max is the maximum intensity of the 8 bit image i.e. 255, and M and N are the height and width of the image. The PSNR values of the watermarked image is compared to algorithms developed by Refs. 44–46, with the proposed algorithm as shown in Figure 3. The high PSNR of the proposed algorithm reveals that the proposed watermarking scheme offers high imperceptibility. As shown in Figure 2, the distortion introduced by watermark is negligible and there is no distinction seen between the host and watermarked images of Zelda, Lena and Baboon.

Figure 2. a. Airplane as cover image, e. watermarked airplane having P.S.N.R = 47.4735, b. The cover image Zelda, f. watermarked Zelda having P.S.N.R = 46.5037, c. The cover image Lena, g.watermarked Lena having P.S.N.R = 47.1501, d. Baboon as cover image, h. The watermarked Baboon P.S.N.R = 46.4414.

Figure 3. Comparision of proposed algorithm with algorithms developed by Refs. 44–46.

The high peak signal to noise ratio and N.C.C close to 1 signifies that the proposed method is highly imperceptible, as well as robust to attacks.

The settings of the parameter of DE are, F = 0.5, Cr = 0.5, NP = 32, population = 10, maximum number of generations = 200. This section describes the performance of the projected watermarking framework for the various experiments. The Watermarked image is altered when various attacks are considered.

The robustness of proposed framework is contrasted with other methods based on normalized cross correlation. The normalized cross correlation (N.C.C) lies between 0 to 1. If the N.C.C is nearer to 1, the more similar the extorted watermark will be to the embedded one. The proposed algorithm is compared with a pure SVD, simple genetic algorithm, SVD based on a micro genetic algorithm, multiresolution Walsh-Hadamard tranform, and proposed algorithm multiresolution Walsh-Hadamard transform and Schur transform with DE.

The different attacks utilized in the framework of watermarking are:

1. Average filtering: The image which is watermarked is subjected to a low pass mask of 3 × 3 neighborhood. Averaging removes sharp variations in the image such as edges and noise. The extorted watermark is 100% identical to the inserted watermark.
2. Rotation is the important attack during image watermarking. The size of the image typically increases when it is rotated. Therefore, some of the useful information is lost in order to return to its original form. The extracted watermark is 94.48% identical to the inserted watermark.
3. Symmetric cropping: the watermarked image is cropped on both sides. The extracted watermark is 95.55% identical to the original watermark.
4. Histogram equalization: histogram equalization is used to adjust the contrast of the image. The extracted watermark is 99.99% identical to the inserted watermark.
5. Gaussian noise: the marked image is subjected to Gaussian noise, having a zero mean with a normalized variance of 0.01. The extracted watermark is 99.50% identical to the original watermark.
6. JPEG compression: the watermarked image is compressed to a specified ratio of compression of 60%. The extracted watermark is 99.65% identical to the original watermark.
7. A significant attack on image watermarking is scaling. High frequency components are eliminated. Thus, important information could be lost. The image is reduced in size to one-fourth of its original size and placed back in its original location before the extraction process in the proposed watermarking. The proposed watermarking is 99.99% identical to the original watermark. The original watermark and the extracted watermark from the above attacks is shown in Figure 4.

Figure 4. Extracted watermark from watermarked image Lena and airplane after different types of attacks.

The proposed algorithm is compared with existing optimization algorithms like pure SVD, SVD+GA, SVD+SGA, SVD+μ GA, DCT+DE. The N.C.C values are compared in Table 1.

Table 1. Comparison of different optimization algorithms.

Attack	SVD+GA	SVD+SGA	SVD+μ GA	SVD+DE	DCT+DE	Proposed method
Averaging	0.9992	0.9819	0.9819	0.984	0.999	0.9999
Rotation	0.9822	0.9903	0.9917	0.9936	0.985	0.9948
Cropping	0.9944	0.9944	0.9911	0.9925	0.995	0.9955
Histogram equalization	0.9944	0.9844	0.9963	0.9971	0.998	0.9999
Gaussian noise	0.9878	0.9677	0.9787	0.9717	0.974	0.9952
JPEG compression	0.9812	0.9911	0.9925	0.9951	0.996	0.9965
Rescaling	0.9612	0.9812	0.9912	0.9934	0.944	0.999

Author contributions

K. Meenakshi, K. Swaraja: Conception and design of study. Ch. Ushakumari, K. Swaraja: Acquisition, analysis and/or interpretation of data. D. Kishore, K. Meenakshi: Drafting the manuscript and revising.

Data availability

Figshare:[copyright protection using Multiresolution Walsh Hadamard transform] DOI: 10.6084/m9.figshare.20408937

Data are available under the terms of the Creative Commons Attribution 4.0 International license (CC-BY 4.0).

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36. Hsieh M-S: Perceptual copyright protection using multiresolution wavelet-based watermarking and fuzzy logic. arXiv preprint arXiv:1007.5136. 2010.
37. Shieh C-S, Huang H-C, Wang F-H, et al.: Genetic watermarking based on transform-domain techniques. Pattern Recogn. 2004; 37(3): 555–565. Publisher Full Text
38. Kumsawat P, Attakitmongcol K, Srikaew A: A new approach for optimization in image watermarking by using genetic algorithms. Signal Processing, IEEE Transactions on. 2005; 53(12): 4707–4719. Publisher Full Text
39. Ramkumar M, Akansu AN: Capacity estimates for data hiding in compressed images. Image Processing, IEEE Transactions on. 2001; 10(8): 1252–1263. PubMed Abstract | Publisher Full Text
40. Pratt W, Kane J, Andrews HC: Hadamard transform image coding. Proc. IEEE. 1969; 57(1): 58–68. Publisher Full Text
41. Gonzalez RC, Richard E: Woods, digital image processing. Prentice Hall Press;2002.0-201-18075-8.
42. Run R-S, Horng S-J, Lai J-L, et al.: An improved svd-based watermarking technique for copyright protection. Expert Syst. Appl. 2012; 39(1): 673–689. Publisher Full Text
43. Storn R, Price K: Differential evolution–a simple and efficient heuristic for global optimization over continuous spaces. J. Glob. Optim. 1997; 11(4): 341–359. Publisher Full Text
44. Veeraswamy K, Srinivaskumar S, Chatterji BN: Designing quantization table for hadamard transform based on human visual system for image compression. ICGST-GVIP Journal. 2007; 7(3): 31–38.
45. Bhatnagar G, Raman B: Robust watermarking in multiresolution walsh-hadamard transform. Advance Computing Conference, 2009. IACC 2009. IEEE International. IEEE;2009; pp. 894–899.
46. Santhi V, Arulmozhivarman P: Hadamard transform based adaptive visible/invisible watermarking scheme for digital images. Inf. Secur. Tech. Rep. 2013; 5: 202. Publisher Full Text

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Version 1

VERSION 1 PUBLISHED 16 Nov 2022

Author details Author details

¹ Electronics and Communication Engineering, Gokaraju Rangaraju Institute of Engineering and Technology, Hyderabad, Telangana, 500090, India
² Electronics and Communication Engineering, Aditya College of Engineering and Technology, Surampalem, Andhra pradesh, India

Swaraja K
Roles: Conceptualization, Methodology, Software, Supervision, Visualization, Writing – Original Draft Preparation

Meenakshi K
Roles: Conceptualization, Project Administration, Supervision, Visualization, Writing – Review & Editing

Ushakumari Ch
Roles: Conceptualization, Formal Analysis, Investigation, Methodology, Visualization

Kishore D
Roles: Data Curation, Investigation, Resources, Visualization

Competing interests

No competing interests were disclosed.

Grant information

The author(s) declared that no grants were involved in supporting this work.

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Published: 16 Nov 2022, 11:1333

https://doi.org/10.12688/f1000research.124720.1

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K S, K M, Ch U and D K. A Robust image watermarking for copyright protection using Multiresolution Walsh-Hadamard transform and Schur using Differential evolution [version 1; peer review: 2 approved with reservations, 1 not approved]. F1000Research 2022, 11:1333 (https://doi.org/10.12688/f1000research.124720.1)

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ApprovedThe paper is scientifically sound in its current form and only minor, if any, improvements are suggested

Approved with reservations A number of small changes, sometimes more significant revisions are required to address specific details and improve the papers academic merit.

Not approvedFundamental flaws in the paper seriously undermine the findings and conclusions

Version 1

VERSION 1

PUBLISHED 16 Nov 2022

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Reviewer Report 06 Nov 2023

Amine Khaldi, Universite Kasdi Merbah Ouargla, Ouargla, Ouargla Province, Algeria

Approved with Reservations

https://doi.org/10.5256/f1000research.136944.r192201

The paper presentation is not clear. What is the objective of the conducted research? What is the novelty related scientific literature?
It seems to me that the authors have conducted some experiments

The paper presentation is not clear. What is the objective of the conducted research? What is the novelty related scientific literature?
It seems to me that the authors have conducted some experiments on a dataset without really proposing a "system"
The paper is not well organized and lack of numerous descriptions that makes it hard to read and understand. Several key points of the literature, strongly related to this paper has been forgotten.
Please, clearly explain how your solution advances existing approaches,
Redraw the graphs with high resolution (at least 300 dpi)
There is a need to strengthen the Abstract. The author should improve the abstract to include the following in its body: a brief background, brief description of methods and results, and finally conclusions.
Add detailed related work section. Discuss the motivation and limitations of previous works
Every time a method/formula is used for something, it needs to be justified by either (a) prior work showing the superiority of this method, or (b) by your experiments showing its advantage over prior work methods - comparison is needed, or (c) formal proof of optimality. Please consider more prior works.
The descriptions given in this proposed scheme are not sufficient that this manuscript only adopted a variety of existing methods to complete the experiment where there are no strong hypothesis and methodical theoretical arguments. Therefore, the reviewer considers that this paper needs more works
More experiments, especially comparative experiments, should be involved to verify the performances of the proposed algorithm.
The author should justify and discuss in more details the obtained results
There was no discussion for the full paper and future works. I suggest the authors expand the discussion of the whole work in the last section, then point out the shortcomings of the work, and finally discuss possible future work.

Is the work clearly and accurately presented and does it cite the current literature?

Partly
Is the study design appropriate and is the work technically sound?

Yes
Are sufficient details of methods and analysis provided to allow replication by others?

Partly
If applicable, is the statistical analysis and its interpretation appropriate?

Yes
Are all the source data underlying the results available to ensure full reproducibility?

Yes
Are the conclusions drawn adequately supported by the results?

No

Competing Interests: No competing interests were disclosed.

Reviewer Expertise: Watermarking

I confirm that I have read this submission and believe that I have an appropriate level of expertise to confirm that it is of an acceptable scientific standard, however I have significant reservations, as outlined above.

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Reviewer Report 06 Nov 2023

Ankit Rajpal, Department of Computer Science, University of Delhi, New Delhi, Delhi, India

Approved with Reservations

https://doi.org/10.5256/f1000research.136944.r214541

Using the multi-resolution Walsh-Hadamard transform (MR-WHT) and Schur factorization, the authors came up with a framework for watermarking. The paper has the following shortcomings:

The motivation and objective of the proposed work are not clear.

Using the multi-resolution Walsh-Hadamard transform (MR-WHT) and Schur factorization, the authors came up with a framework for watermarking. The paper has the following shortcomings:

The motivation and objective of the proposed work are not clear.
The related research work is not recent. Moreover, a comparison with state-of-the-art methods is not provided.
The block diagram and the algorithmic steps for both watermark embedding and extraction lack coherence. For example, there is no mention of differential evolution in the algorithm.
Eqs. (1) and (2) have the same RHS.
The standard images used for the experimentation are limited.
The discussion section highlighting the strengths and limitations of the proposed work may be included.

Is the work clearly and accurately presented and does it cite the current literature?

No
Is the study design appropriate and is the work technically sound?

Partly
Are sufficient details of methods and analysis provided to allow replication by others?

Yes
If applicable, is the statistical analysis and its interpretation appropriate?

No
Are all the source data underlying the results available to ensure full reproducibility?

No source data required
Are the conclusions drawn adequately supported by the results?

Yes

Competing Interests: No competing interests were disclosed.

Reviewer Expertise: Image and Video Watermarking, Explainable AI, and Medical Image Analysis

I confirm that I have read this submission and believe that I have an appropriate level of expertise to confirm that it is of an acceptable scientific standard, however I have significant reservations, as outlined above.

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3

Reviewer Report 17 Oct 2023

Ledya Novamizanti, Telkom University, Bandung, West Java, Indonesia

Not Approved

https://doi.org/10.5256/f1000research.136944.r202814

This work presents a robust image watermarking for copyright protection using Multiresolution Walsh-Hadamard transform and Schur transform using differential evolution. The paper is not clear, not innovative enough and insufficient experiments. Besides, some problems are listed as follows:

This work presents a robust image watermarking for copyright protection using Multiresolution Walsh-Hadamard transform and Schur transform using differential evolution. The paper is not clear, not innovative enough and insufficient experiments. Besides, some problems are listed as follows:

The problem definition of this work is not clear. In introduction or in related work section, the drawbacks of each conventional technique should be described clearly. The authors should emphasize the difference with other methods to clarify the position of this work further.
Don’t use acronym without explanation. e.g. DHT, etc. All acronyms must be defined before use.
The language needs improvement, and there are confusions in formulae and character descriptions. For instance, on the page 5, it's unclear whether " FWHT2", "WHT2" and the term " FWHT2D" in page 7 refer to the same element. Furthermore, many variable are not specified.
Duplicate formulas in Eq. (1) and (2).
Distinguish mathematical expression from programming code. Don’t use “:” in equations. For instance, see Eq. (10), (11), (12), 13), etc.
Comparative literature is too scarce and older.
The experimental section is not convincing. With only four test images, the sample size is inadequate. Although the paper claims to propose a robust watermarking algorithm, it fails to demonstrate the robustness in the experimental comparison.
The statement "it has been demonstrated that the DHT has a poor threshold difference for noise processing at low compression quality" should be supported by specific references or citations to studies that have demonstrated this. Adding such evidence would enhance the credibility of this claim.
While the introduction suggests that using Walsh-Hadamard characteristics is a "worthwhile endeavor," it would be beneficial to explicitly state the research gap or problem the study aims to address. This would provide clarity on the study's objectives and what it seeks to contribute to the existing literature.
It would be helpful to explicitly state the research hypothesis or objectives in the introduction. This would provide a clear sense of what the study aims to investigate or demonstrate.
The sentence "These facts may aid DHT-based schemes in achieving simultaneous optimum performance..." could be rephrased for greater clarity.
Provide an illustration related to MR-WHT.

Is the work clearly and accurately presented and does it cite the current literature?

Partly
Is the study design appropriate and is the work technically sound?

No
Are sufficient details of methods and analysis provided to allow replication by others?

No
If applicable, is the statistical analysis and its interpretation appropriate?

Not applicable
Are all the source data underlying the results available to ensure full reproducibility?

No
Are the conclusions drawn adequately supported by the results?

No

Competing Interests: No competing interests were disclosed.

Reviewer Expertise: Image Processing, watermarking

I confirm that I have read this submission and believe that I have an appropriate level of expertise to state that I do not consider it to be of an acceptable scientific standard, for reasons outlined above.

CITE

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VERSION 1 PUBLISHED 16 Nov 2022

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Version 1 16 Nov 22	read	read	read

Ledya Novamizanti, Telkom University, Bandung, Indonesia
Ankit Rajpal, University of Delhi, New Delhi, India
Amine Khaldi, Universite Kasdi Merbah Ouargla, Ouargla, Algeria

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Reviewer Report

2 Views

06 Nov 2023 | for Version 1

Amine Khaldi, Universite Kasdi Merbah Ouargla, Ouargla, Ouargla Province, Algeria

2 Views Cite this report Responses(0)

Approved With Reservations

The paper presentation is not clear. What is the objective of the conducted research? What is the novelty related scientific literature?
It seems to me that the authors have conducted some experiments on a dataset without really proposing a "system"
The paper is not well organized and lack of numerous descriptions that makes it hard to read and understand. Several key points of the literature, strongly related to this paper has been forgotten.
Please, clearly explain how your solution advances existing approaches,
Redraw the graphs with high resolution (at least 300 dpi)
There is a need to strengthen the Abstract. The author should improve the abstract to include the following in its body: a brief background, brief description of methods and results, and finally conclusions.
Add detailed related work section. Discuss the motivation and limitations of previous works
Every time a method/formula is used for something, it needs to be justified by either (a) prior work showing the superiority of this method, or (b) by your experiments showing its advantage over prior work methods - comparison is needed, or (c) formal proof of optimality. Please consider more prior works.
The descriptions given in this proposed scheme are not sufficient that this manuscript only adopted a variety of existing methods to complete the experiment where there are no strong hypothesis and methodical theoretical arguments. Therefore, the reviewer considers that this paper needs more works
More experiments, especially comparative experiments, should be involved to verify the performances of the proposed algorithm.
The author should justify and discuss in more details the obtained results
There was no discussion for the full paper and future works. I suggest the authors expand the discussion of the whole work in the last section, then point out the shortcomings of the work, and finally discuss possible future work.

Is the work clearly and accurately presented and does it cite the current literature?

Partly
Is the study design appropriate and is the work technically sound?

Yes
Are sufficient details of methods and analysis provided to allow replication by others?

Partly
If applicable, is the statistical analysis and its interpretation appropriate?

Yes
Are all the source data underlying the results available to ensure full reproducibility?

Yes
Are the conclusions drawn adequately supported by the results?

No

Competing Interests

No competing interests were disclosed.

Reviewer Expertise

Watermarking

I confirm that I have read this submission and believe that I have an appropriate level of expertise to confirm that it is of an acceptable scientific standard, however I have significant reservations, as outlined above.

Respond to this report

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Reviewer Report

9 Views

06 Nov 2023 | for Version 1

Ankit Rajpal, Department of Computer Science, University of Delhi, New Delhi, Delhi, India

9 Views Cite this report Responses(0)

Approved With Reservations

Using the multi-resolution Walsh-Hadamard transform (MR-WHT) and Schur factorization, the authors came up with a framework for watermarking. The paper has the following shortcomings:

The motivation and objective of the proposed work are not clear.
The related research work is not recent. Moreover, a comparison with state-of-the-art methods is not provided.
The block diagram and the algorithmic steps for both watermark embedding and extraction lack coherence. For example, there is no mention of differential evolution in the algorithm.
Eqs. (1) and (2) have the same RHS.
The standard images used for the experimentation are limited.
The discussion section highlighting the strengths and limitations of the proposed work may be included.

Is the work clearly and accurately presented and does it cite the current literature?

No
Is the study design appropriate and is the work technically sound?

Partly
Are sufficient details of methods and analysis provided to allow replication by others?

Yes
If applicable, is the statistical analysis and its interpretation appropriate?

No
Are all the source data underlying the results available to ensure full reproducibility?

No source data required
Are the conclusions drawn adequately supported by the results?

Yes

Competing Interests

No competing interests were disclosed.

Reviewer Expertise

Image and Video Watermarking, Explainable AI, and Medical Image Analysis

I confirm that I have read this submission and believe that I have an appropriate level of expertise to confirm that it is of an acceptable scientific standard, however I have significant reservations, as outlined above.

Respond to this report

Responses (0)

Back to all reports

Reviewer Report

3 Views

17 Oct 2023 | for Version 1

Ledya Novamizanti, Telkom University, Bandung, West Java, Indonesia

3 Views Cite this report Responses(0)

Not Approved

This work presents a robust image watermarking for copyright protection using Multiresolution Walsh-Hadamard transform and Schur transform using differential evolution. The paper is not clear, not innovative enough and insufficient experiments. Besides, some problems are listed as follows:

The problem definition of this work is not clear. In introduction or in related work section, the drawbacks of each conventional technique should be described clearly. The authors should emphasize the difference with other methods to clarify the position of this work further.
Don’t use acronym without explanation. e.g. DHT, etc. All acronyms must be defined before use.
The language needs improvement, and there are confusions in formulae and character descriptions. For instance, on the page 5, it's unclear whether " FWHT2", "WHT2" and the term " FWHT2D" in page 7 refer to the same element. Furthermore, many variable are not specified.
Duplicate formulas in Eq. (1) and (2).
Distinguish mathematical expression from programming code. Don’t use “:” in equations. For instance, see Eq. (10), (11), (12), 13), etc.
Comparative literature is too scarce and older.
The experimental section is not convincing. With only four test images, the sample size is inadequate. Although the paper claims to propose a robust watermarking algorithm, it fails to demonstrate the robustness in the experimental comparison.
The statement "it has been demonstrated that the DHT has a poor threshold difference for noise processing at low compression quality" should be supported by specific references or citations to studies that have demonstrated this. Adding such evidence would enhance the credibility of this claim.
While the introduction suggests that using Walsh-Hadamard characteristics is a "worthwhile endeavor," it would be beneficial to explicitly state the research gap or problem the study aims to address. This would provide clarity on the study's objectives and what it seeks to contribute to the existing literature.
It would be helpful to explicitly state the research hypothesis or objectives in the introduction. This would provide a clear sense of what the study aims to investigate or demonstrate.
The sentence "These facts may aid DHT-based schemes in achieving simultaneous optimum performance..." could be rephrased for greater clarity.
Provide an illustration related to MR-WHT.

Is the work clearly and accurately presented and does it cite the current literature?

Partly
Is the study design appropriate and is the work technically sound?

No
Are sufficient details of methods and analysis provided to allow replication by others?

No
If applicable, is the statistical analysis and its interpretation appropriate?

Not applicable
Are all the source data underlying the results available to ensure full reproducibility?

No
Are the conclusions drawn adequately supported by the results?

No

Competing Interests

No competing interests were disclosed.

Reviewer Expertise

Image Processing, watermarking

I confirm that I have read this submission and believe that I have an appropriate level of expertise to state that I do not consider it to be of an acceptable scientific standard, for reasons outlined above.

Respond to this report

Responses (0)

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[2] 2. Liu J-C, Chen S-Y: Fast two-layer image watermarking without referring to the original image and watermark. Image Vis. Comput. 2001; 19(14): 1083–1097. Publisher Full Text

[3] 3. Briassouli A, Strintzis MG: Locally optimum nonlinearities for dct watermark detection. Image Processing, IEEE Transactions on. 2004; 13(12): 1604–1617. PubMed Abstract | Publisher Full Text

[4] 4. Lin SD, Shie S-C, Guo JY: Improving the robustness of dct-based image watermarking against jpeg compression. Comput. Stand. Interfaces. 2010; 32(1): 54–60. Publisher Full Text

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[9] 9. Aslantas V: An optimal robust digital image watermarking based on svd using differential evolution algorithm. Opt. Commun. 2009; 282(5): 769–777. Publisher Full Text

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[14] 14. Ganic E, Eskicioglu AM: Robust embedding of visual watermarks using discrete wavelet transform and singular value decomposition. J. Electron. Imaging. 2005; 14(4): 043004–043004. Publisher Full Text

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[17] 17. Falkowski BJ: Properties and ways of calculation of multi-polarity generalized walsh transforms. Circuits and Systems II: Analog and Digital Signal Processing. IEEE Transactions on. 1994; 41(6): 380–391. Publisher Full Text

[18] 18. Kutter M, Voloshynovskiy SV, Herrigel A:Watermark copy attack. Electronic Imaging. International Society for Optics and Photonics;2000; pp. 371–380.

[19] 19. Shen H, Zhu Y, Zhou X, et al.:Bacterial foraging optimization algorithm with particle swarm optimization strategy for global numerical optimization. Proceedings of the first ACM/SIGEVO Summit on Genetic and Evolutionary Computation. ACM;2009; pp. 497–504.

[20] 20. Hanmandlu M, Verma OP, Kumar NK, et al.: A novel optimal fuzzy system for color image enhancement using bacterial foraging. Instrumentation and Measurement, IEEE Transactions on. 2009; 58(8): 2867–2879. Publisher Full Text

[21] 21. Bakwad KM, Pattnaik SS, Sohi BS, et al.: Multimodal function optimization using synchronous bacterial foraging optimization technique. IETE J. Res. (Medknow Publications & Media Pvt. Ltd.). 2010; 56(2): 80. Publisher Full Text

[22] 22. Agarwal C, Mishra A, Sharma A: Gray-scale image watermarking using ga-bpn hybrid network. J. Vis. Commun. Image Represent. 2013; 24(7): 1135–1146. Publisher Full Text

[23] 23. Wang C, Ni J, Huang J: An informed watermarking scheme using hidden markov model in the wavelet domain. Information Forensics and Security, IEEE Transactions on. 2012; 7(3): 853–867. Publisher Full Text

[24] 24. Shih FY, Yi-Ta W: Enhancement of image watermark retrieval based on genetic algorithms. J. Vis. Commun. Image Represent. 2005; 16(2): 115–133. Publisher Full Text

[25] 25. Shih FY, Yi-Ta W: Robust watermarking and compression for medical images based on genetic algorithms. Inf. Sci. 2005; 175(3): 200–216. Publisher Full Text

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[34] 34. Naheed T, Usman I, Khan TM, et al.: Intelligent reversible watermarking technique in medical images using ga and pso. Optik-International Journal for Light and Electron Optics. 2014; 125(11): 2515–2525. Publisher Full Text

[35] 35. Santi P: Maity and Seba Maity. Multistage spread spectrum watermark detection technique using fuzzy logic. Signal Processing Letters, IEEE. 2009; 16(4): 245–248. Publisher Full Text

[36] 36. Hsieh M-S: Perceptual copyright protection using multiresolution wavelet-based watermarking and fuzzy logic. arXiv preprint arXiv:1007.5136. 2010.

[37] 37. Shieh C-S, Huang H-C, Wang F-H, et al.: Genetic watermarking based on transform-domain techniques. Pattern Recogn. 2004; 37(3): 555–565. Publisher Full Text

[38] 38. Kumsawat P, Attakitmongcol K, Srikaew A: A new approach for optimization in image watermarking by using genetic algorithms. Signal Processing, IEEE Transactions on. 2005; 53(12): 4707–4719. Publisher Full Text

[39] 39. Ramkumar M, Akansu AN: Capacity estimates for data hiding in compressed images. Image Processing, IEEE Transactions on. 2001; 10(8): 1252–1263. PubMed Abstract | Publisher Full Text

[40] 40. Pratt W, Kane J, Andrews HC: Hadamard transform image coding. Proc. IEEE. 1969; 57(1): 58–68. Publisher Full Text

[41] 41. Gonzalez RC, Richard E: Woods, digital image processing. Prentice Hall Press;2002.0-201-18075-8.

[42] 42. Run R-S, Horng S-J, Lai J-L, et al.: An improved svd-based watermarking technique for copyright protection. Expert Syst. Appl. 2012; 39(1): 673–689. Publisher Full Text

[43] 43. Storn R, Price K: Differential evolution–a simple and efficient heuristic for global optimization over continuous spaces. J. Glob. Optim. 1997; 11(4): 341–359. Publisher Full Text

[44] 44. Veeraswamy K, Srinivaskumar S, Chatterji BN: Designing quantization table for hadamard transform based on human visual system for image compression. ICGST-GVIP Journal. 2007; 7(3): 31–38.

[45] 45. Bhatnagar G, Raman B: Robust watermarking in multiresolution walsh-hadamard transform. Advance Computing Conference, 2009. IACC 2009. IEEE International. IEEE;2009; pp. 894–899.

[46] 46. Santhi V, Arulmozhivarman P: Hadamard transform based adaptive visible/invisible watermarking scheme for digital images. Inf. Secur. Tech. Rep. 2013; 5: 202. Publisher Full Text

A Robust image watermarking for copyright protection using Multiresolution Walsh-Hadamard transform and Schur using Differential evolution

Abstract

Keywords

Introduction

Preliminaries

Walsh-Hadamard transform (WHT)

(1)

(2)

Schur decomposition

(3)

Singular value decomposition

(4)

Differential evolution

(5)

(6)

(7)

(8)

Proposed watermarking algorithm

Watermark concealing algorithm

Figure 1. Watermark embedding algorithm of proposed algorithm.

(9)

(10)

(11)

(12)

(13)

(14)

(15)

(16)

(17)

(18)

(19)

(20)

(21)

Watermark extraction

(22)

(23)

Computing multiple scaling factor from random population

(24)

(25)

Simulation results and discussion

(26)

(27)

Figure 3. Comparision of proposed algorithm with algorithms developed by Refs. 44–46.

Figure 4. Extracted watermark from watermarked image Lena and airplane after different types of attacks.

Table 1. Comparison of different optimization algorithms.

Author contributions

Data availability

References

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