The rapid development in the information technology field has introduced digital watermark technologies as a solution to prevent unauthorized copying and redistribution of data. This article introduces a self-embedded image verification and integrity scheme. The images are firstly split into dedicated segments of the same block sizes. Then, different Analytic Beta-Wavelet (ABW) orthogonal filters are utilized for embedding a self-segment watermark for image segment using a predefined method. ABW orthogonal filter coefficients are estimated to improve image reconstruction under different block sizes. We conduct a comparative study comparing the watermarked images using three kinds of ABW filters for block sizes 64 × 64, 128 × 128, and 256 × 256. We embed the watermark using the ABW-based image watermarking method in the 2-level middle frequency sub-bands of the ABW digital image coefficients. The imperceptibility and robustness of the ABW-based image watermarking method image is evaluated based on the Peak Signal to Noise Ratio (PSNR) and Correlation coefficient values. From the implementation results, we came to know that this ABW-based image watermarking method can withstand many image manipulations compared to other existing methods.

Data security becomes an essential issue in the digital world with the rapid growth of digital images and Internet technology accompanied by many security threats on the Internet. For this purpose, many image encryption technologies have emerged and proposed. The existing image encryption technologies use a simple structure and a small key space to reduce the time cost and complexity of algorithms and meet the requirements image information security [

To enhance the adaptive ability of image watermarking, we proposed the utilization of a new wavelet family named Beta Wavelet family for proposing an efficient image watermarking scheme. The main contribution of the proposed algorithm is as follows: It uses Beta wavelet family to tune many parameters related to the Beta function [

The rest of the paper is organized as follows: Section 2 presents the mathematical background of the parametric Beta Wavelets proposed in the schemas of protection and verification of the encrypted images. Section 3 exhibits the proposed schemes in both protection and verification steps. The results analysis is presented in Section 4. Section 5 concludes the paper with future trends.

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Beta Wavelet (BW) is a family of wavelets derived from beta function under certain conditions. Unlike other wavelet forms, BW can be generated based on a proper selection of beta function parameters. The beta distribution is given as follows [

where

Indeed, the beta function holds some properties as follows:

1. Beta distribution at the boundary of interval [

2. Beta distribution at the centroid,

3. Evaluation of the derivative of the beta function with respect to x at

4.

5. The second derivative of the beta function is given as follows:

where

Generally, the nth derivative of the beta function is given as the following:

with

The last property is crucial because the beta function's derivative is the essence of beta wavelets. Based on

Orthogonal multiresolution analysis is a powerful tool to create the basis of orthogonality. Multiresolution can be generated from interpolating scaling functions such as beta wavelet to ease the estimation of wavelet filter coefficients. To illustrate that, assume compact support wavelet in the interval [−N/2, N/2], and it is given as:

Let the interpolation scaling function is defined as follows:

Hence,

From

Generally, the other coefficients that construct filter g can be computed with the same procedure for each sample as follows:

Eventually, the wavelets are orthogonal, and the filter is a quadrature mirror filter if any sample of g creates an orthogonal base on

In this section, we study the suggested ABW-based image watermarking method in detail. The proposed method is with the potential of image integrity, verification, and tamper detection. It has two modules, watermark embedding module, and verification module. The two modules are explored and explained in detail. The Proposed ABW-based image watermarking method might be considered a fragile self-embedding watermarking process. It depends on segment-based self-watermarking instead of employing external watermarks.

The protection module of the suggested method is explored stepwise as follows, considering three different Analytic Beta-Wavelet (ABW) orthogonal filters.

Split the input image, f, into two equal sub-images, f1 and f2. Again, split the resulting parts into different non-overlapping segments. In our work, we try the block size of 64 × 64, 128 × 128, and 256 × 256. For example, given the original image of size (256 × 256), when splitting into two equal sub-images (f1, f2), their size will be (128 × 256) each. Each sub-image is then divided into 8 × 8 non-overlapped blocks. Therefore, the number of blocks per sub-image is (128 × 256)/(8 × 8) = 512.

Apply ABW transform to each block in the sub-image f1 starting from the upper-left corner block.

Embed the row and column of each block in sub-image f1 into the row and column of the corresponding transformed block in sub-image f2.

Apply inverse ABW transform to each block in sub-image f1 starting from the upper-left corner block.

Apply ABW transform to each block in sub-image f2, and repeat steps 3 and 4 for such an image.

Recompose the resulted two sub-images to obtain the block-based watermarked image.

The process of verification module can be digested in the following steps:

Receive the watermarked image.

Split the watermarked image, z, into two equal sub-images, z1 and z2. Again, split the resulting parts into different non-overlapping segments. In our work, we try the block size of 64 × 64, 128 × 128, and 256 × 256.

Apply ABW transform to each block in the sub-image z1 starting from the upper-left corner block.

Embed the row and column of each block in the transformed sub-image z1 into the row and column of the corresponding block in sub-image z2.

Apply inverse ABW transform to each block in sub-image z1 starting from the upper-left corner block.

Apply ABW transform to each block in sub-image z2, and repeat steps 4 and 5 for such an image.

Recompose the resulted two sub-images to obtain the extracted image.

We used four standard and widely used images to assess the performance and robustness of the beta wavelets in watermarking and forgery detection. These images are Barbara, Male, Cameraman, and Baboon, as shown in

The watermark is embedded into images by applying the safeguard method to the beta wavelets approximation coefficients at level 2. The non-sampled wavelet decomposition scheme is used in the experiments to preserve the quality of both the watermarked and the retrieved images.

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Consequently, along with the Daubechies (db2) and discrete Meyer (dmey) wavelets, 17 bi-orthogonal beta wavelet filters with different filter orders are generated and applied to the Barbara image with block sizes of 64 × 64, 128 × 128, and 256 × 256. The results of this study are provided in _{1} and I_{2}, the equations of these measures are:

where _{1} and I_{2}, respectively.

Beta wavelet filter | PSNR | C_{r} |
||||
---|---|---|---|---|---|---|

64 × 64 | 128 × 128 | 256 × 256 | 64 × 64 | 128 × 128 | 256 × 256 | |

Bior 1.3 | 28.0611 | 33.1331 | 33.1714 | 0.9337 | 0.9793 | 0.9791 |

Bior 1.5 | 28.0603 | 33.0822 | 33.1693 | 0.9339 | 0.9791 | 0.9792 |

Bior 1.7 | 28.0205 | 32.6380 | 33.0464 | 0.9343 | 0.9776 | 0.9790 |

Bior 2.1 | 27.9193 | 33.1370 | 33.0343 | 0.9316 | 0.9793 | 0.9790 |

Bior 2.3 | 27.9184 | 33.1113 | 33.0334 | 0.9317 | 0.9792 | 0.9785 |

Bior 2.4 | 27.9021 | 32.8812 | 32.9961 | 0.9319 | 0.9784 | 0.9785 |

Bior 2.5 | 27.9108 | 31.9343 | 32.5639 | 0.9310 | 0.9744 | 0.9770 |

Bior 2.6 | 27.9108 | 32.9812 | 33.0178 | 0.9318 | 0.9787 | 0.9785 |

Bior 2.7 | 27.9177 | 33.0944 | 33.0323 | 0.9317 | 0.9792 | 0.9785 |

Bior 3.2 | 28.5637 | 31.5690 | 33.7217 | 0.9409 | 0.9713 | 0.9817 |

Bior 3.3 | 28.3537 | 31.4638 | 33.6922 | 0.9409 | 0.9708 | 0.9817 |

Bior 3.4 | 28.4990 | 31.0926 | 33.5275 | 0.9407 | 0.9689 | 0.9813 |

Bior 4.1 | 28.2647 | 32.8723 | 33.3862 | 0.9366 | 0.9780 | 0.9801 |

Bior 4.2 | 29.2301 | 30.0958 | 34.4807 | 0.9487 | 0.9594 | 0.9844 |

Bior 5.3 | 27.9252 | 27.1127 | 33.1375 | 0.9317 | 0.9238 | 0.9790 |

Bior 5.4 | 27.9938 | 27.9990 | 31.5637 | 0.9328 | 0.9366 | 0.9699 |

Bior 5.5 | 28.0853 | 27.9101 | 33.2794 | 0.9340 | 0.9354 | 0.9796 |

DB2 | 27.7940 | 33.1176 | 32.9531 | 0.9290 | 0.9792 | 0.9780 |

DMEY | 27.8467 | 33.1273 | 32.9959 | 0.9300 | 0.9793 | 0.9782 |

Haar | 28.0611 | 33.1331 | 33.1714 | 0.9337 | 0.9793 | 0.9791 |

The findings in

As mentioned in the previous section, the performance of the three selected beta wavelet filters bior1.2, bior2.3, and bior4.2 is investigated further as the experiments progress. The quality measures of the four images when inserting the watermark using the safeguard procedure with beta wavelets under block size of 256 × 256 is shown in

The plots in

In this experiment, the images are extracted using the verification process with the Beta wavelet for block sizes 256 × 256, 128 × 128, and 64 × 64 without any attack. This method aims to ensure that the images are obtained from its watermarked version with minimal degradation. Again, the quality of the extracted images is measured by three metrics: PSNR, and Cr. Also, the extracted images are shown in each of the following

The block correlation plots shown in the

Beta wavelet filter | Block size | _{r} |
|||||||
---|---|---|---|---|---|---|---|---|---|

Brabra | Male | baboon | Cameraman | Brabra | Male | baboon | Cameraman | ||

Bior1.3 | 256 × 256 | 31.397 | 33.95 | 33.492 | 32.244 | 0.9701 | 0.984 | 0.9684 | 0.9801 |

128 × 128 | 33.133 | 34.76 | 32.219 | 32.191 | 0.9793 | 0.987 | 0.9587 | 0.9802 | |

64 × 64 | 28.061 | 28.67 | 28.834 | 27.141 | 0.9337 | 0.948 | 0.9131 | 0.9370 | |

Bio2.3 | 256 × 256 | 31.653 | 33.85 | 33.389 | 32.146 | 0.9695 | 0.984 | 0.9678 | 0.9797 |

128 × 128 | 33.111 | 34.74 | 32.192 | 32.165 | 0.9792 | 0.987 | 0.9586 | 0.9801 | |

64 × 64 | 27.919 | 28.52 | 28.688 | 26.999 | 0.9317 | 0.946 | 0.9105 | 0.9350 | |

Bior4.2 | 256 × 256 | 32.177 | 33.66 | 33.956 | 32.7301 | 0.9736 | 0.983 | 0.9711 | 0.9822 |

128 × 128 | 30.097 | 31.71 | 29.177 | 29.1922 | 0.9594 | 0.975 | 0.9211 | 0.9616 | |

64 × 64 | 29.232 | 29.67 | 30.139 | 28.4806 | 0.9487 | 0.958 | 0.9337 | 0.9532 |

The paper presented an efficient ABW-based image watermarking protection and verification framework. The proposed ABW-based image integrity verification framework applied a certain ABW orthogonal filter for embedding internal segment-based watermarks into other segments of the transmitted image. Three different ABW orthogonal filters are examined in the proposed ABW-based image integrity verification framework. Simulation tests demonstrated that the possibility of watermark protection and verification using the suggested ABW-based image watermarking framework. Additionally, the proposed method provided a high robustness against multimedia attacks. Also, tampering and forgery detection simulations indicate superior results. The test results also indicated the high sensitivity of the suggested ABW-based image watermarking framework to detect different types of image tampering, although the received tampered image appeared to be visually not manipulated. Finally, we showed that the proposed method can be applied to provide a confidential image communication and detect any forensic operations.

The authors would like to thank the Deanship of Scientific research, Taif University Researches Supporting Project number (TURSP-2020/216), Taif University, Taif, Saudi Arabia for supporting this scientific research work.