Semi-Fragile Image Watermarking Using Quantization-Based DCT for Tamper Localization

1  Introduction

Semi-fragile image watermarking is a method to detect malicious attacks while still being tolerant of incidental attacks. In image transmission over the internet, incidental attacks such as JPEG compression have been widely used to compress data storage in the communication channel [1]. Unfortunately, the attackers may add, change, or delete the content of images during image transmission. Therefore, the image must be secured in the communication channel that allows incidental attacks such as JPEG compression, while still detecting malicious attacks.

Image watermarking can be divided into three categories: robust, fragile, and semi-fragile. Robust watermarking ensures the watermark image can resist various incidental and malicious attacks [2,3]. Researchers have performed different methods, such as a two-step process of de-colorization and colorization [4], and generative adversarial networks [5], to enhance the security in robust image watermarking. Fragile watermarking is designed to obtain high tamper detection accuracy under malicious attack [6]. Semi-fragile watermarking is designed to tolerate incidental attacks [7] while still detecting malicious tamper localization. However, fragile image watermarking cannot effectively secure an image under hybrid attack scenarios, where an image is subjected to both incidental attacks (e.g., JPEG compression) and malicious attacks (e.g., copy-move forgery). Fragile watermarking suffers from high false-positive rates due to its sensitivity to Least significant bit (LSB) changes. On the other hand, robust watermarking withstands image processing and geometric attacks, it is not designed to localize tampering. Semi-fragile watermarking provides more effective solutions for securing image transmission, as it permits incidental modifications from compression while preventing malicious tampering during transmission.

A key challenge in semi-fragile watermarking is balancing the imperceptibility of the watermarked images, accurately localizing tampering under malicious attacks, and maintaining tolerance under incidental attacks. To address this challenge, researchers have employed the Discrete Cosine Transform (DCT) to embed the authentication value. The DCT is widely used in JPEG compression [8] and multiple JPEG compression [9]. Prior studies have investigated the correlation of blocks [8], the impact of DCT coefficients under JPEG compression [10], and the use of multiple encryption and tamper localization based on DCT embedding strategies [11]. However, these studies primarily focused on robustness under JPEG compression.

To improve tamper localization, researchers have developed a two-step tamper detection in semi-fragile watermarking by [7,12,13]. In the first step, the embedded authentication data is extracted and verified to generate a tamper detection map. In the second step, the surrounding pixels of each non-tampered bit are examined to determine whether the corresponding bit has been tampered with or not. However, this approach still results in high false-positive rates.

In this study, we propose a semi-fragile image watermarking method based on DCT quantization by selecting the embedding amount and locations for the authentication data. The cover image is transformed using DCT, and the best embedding places are determined to achieve high detection accuracy and low false-positive rates under hybrid attacks. During the tamper detection, the surrounding bits of each block are checked to reduce the false positives, while the neighboring blocks of non-tampered regions are examined to improve the detection accuracy. The proposed technique can produce high tamper detection accuracy under malicious attacks, while remaining tolerant under incidental attacks.

2  Related Works

Yuan et al. [14] enhanced JPEG compression resilience by quantizing low-frequency DCT coefficients in image blocks. The method selected quantization steps to balance imperceptibility and robustness. Sivasubramanian and Konganathan [13] determined embedding threshold values based on the evaluation of diagonal zig-zag scanning. Li et al. [5] introduced a semi-fragile image watermarking method for effective tamper localization, achieving high accuracy in tamper detection. Yuan et al. [14] presented an embedding strategy in neighboring blocks that increased or decreased coefficient values in each block. These approaches highlight the resilience of DCT-based watermarking against incidental attacks while maintaining imperceptibility.

Lefèvre et al. [7] introduced a semi-fragile watermarking for tamper detection by using error control codes. The method improved tamper localization accuracy and reduced computational time. Tampered areas were identified by an error map, flagging pixels with at least three tampered neighbours. Results demonstrated effective error localization control, error detection, and error correction using these codes. However, limitations were observed with JPEG compression and Gaussian noise, indicating potential for further improvement.

Bolourian Haghighi et al. [15] presented a semi-fragile watermarking scheme using the Lifting Wavelet Transform (LWT) and a Feed-Forward Neural Network (FFNN). The method transformed the cover image into 2 × 2 blocks, applied the Integer Wavelet Transform (IWT) to extract HH coefficients, and then used the DCT on each HH coefficient to obtain the DC value, embedding authentication data into it. Tamper detection was performed using the FFNN, and image recovery was achieved by halftoning the original cover image to replace tampered areas. The method achieved an average PSNR of 43.89 and an average SSIM of 0.986. However, the tamper detection exhibited a high false-positive rate, suggesting opportunities for improvement.

Qi and Xin [16] introduced a semi-fragile watermarking technique based on Singular Value Decomposition (SVD). The scheme applied adaptive quantization based on the singular value to determine the scaling factor for embedding. The method localized tampered areas effectively against both incidental and malicious attacks and demonstrated resilience against JPEG compression and common image processing manipulations, including JPEG2000 compression. However, the tamper detection method exhibited a potential for a high false-positive rate, necessitating further research to reduce false positives and improve reliability.

Sivasubramanian and Konganathan [13] presented semi-fragile watermarking using Integer Wavelet Transform (IWT) and Discrete Cosine Transform (DCT) for tamper detection and recovery. The scheme generated an authentication watermark using IWT and recovery data using DCT. The recovery data, generated using a recovery tag, was sent with the watermarked image. At the receiver, tamper detection was performed to generate a tamper detection map. The scheme produced watermarked images with an average PSNR of 42 dB. However, a cryptanalysis and improvement of a semi-fragile watermarking technique is presented by Benrhouma [12] revealing vulnerabilities due to the static embedding position of the watermark data. A cryptanalysis was then performed, improving security by altering the embedded watermark’s position. The scheme performed more accurately and achieved significantly better SSIM and PSNR values for recovered images compared to the Sivasubramanian scheme.

Bolourian Haghighi et al. [17] proposed an optimized multipurpose blind watermarking method in the Shearlet domain using MLP and NSGA-II. The scheme embedded a semi-fragile random sequence authentication data using the Shearlet domain transform, Multilayer Perceptron (MLP), and the multi-objective optimization algorithm NSGA-II. The adaptive embedding process used texture analysis to dynamically adjust embedding strengths. NSGA-II was employed to find optimal embedding parameters that minimized both watermarking impact and the effect of various attacks. The scheme obtained an average PSNR of 38 dB and an average SSIM score of 0.95. However, the authors noted that despite strong performance against noise and compression, the scheme demonstrated tolerance, not resilience, against geometric attacks such as rotation and affine transformation. Therefore, tamper detection and tolerance against incidental attacks still offer potential for further optimization.

Chaotic-based image encryption is also conducted to secure the image during transmission. Wang et al. [18] presented a cryptosystem based on the logistic map with initial parameters. The given parameters in logistic maps play a crucial role in securing the image. Moreover, chaotic-based methods can improve the security of the image cryptosystem design [19]. The unpredictability and parameters of chaotic methods provide additional security in image watermarking.

This study presents a semi-fragile image watermarking method using DCT, which is sensitive to malicious image attacks, and still tolerant of incidental image attacks. The main contribution of this paper is as follows:

(1)   The authors investigate. 4200 pairs in the low frequency of DCT coefficients, especially in the diagonal order of 3, 4, and 5 of 8 × 8 pixels. The experiments identify the optimal embedding location, and they can produce high imperceptibility compared to [13,14,17].

(2)   The proposed scheme achieves high accuracy of tamper detection under malicious and hybrid attacks, and is tolerant of various incidental attacks. The tamper detection performance produced an improvement of 20.62% in terms of accuracy from the existing schemes under the malicious attacks. The proposed scheme also improved 36.62% over other schemes under the hybrid attacks.

(3)   The proposed scheme provides an effective tamper localization across various attacks by employing a two-step tamper detection. The proposed scheme produces an FNR value of 0% under various incidental attacks, which indicates its tolerance under incidental attacks.

3  Proposed Watermarking Technique

This study presents a semi-fragile watermarking using the quantization value of DCT to embed the authentication value in a selected location. The embedding location is determined by examining the combination of quantized coefficient values in diagonal order 3, 4, and 5 of the zig-zag scans. The proposed technique can localize the tampered pixel under malicious attack, while remaining tolerant under incidental attack, such as JPEG compression.

3.1 Proposed Embedding

To generate the watermarked image, the cover image is divided into blocks of size 8 × 8 pixels. Each block is transformed by using DCT to obtain a DC value and 63 AC coefficient values. The zig-zag scanning is applied to arrange low-frequency coefficients. The embedding location is determined by evaluating the 4200 pairs of non-overlapping combinations of the selected DCT coefficients. The proposed embedding process is illustrated in Fig. 1.

Figure 1: The proposed embedding technique

Fig. 1 illustrates the proposed embedding technique to generate the watermarked image. The DCT coefficients are arranged by zigzag order as shown in Fig. 2. There are 15 coefficients in the diagonals order of 3, 4, and 5 of the DCT coefficients will be examined by combination of 1 by 1 and 2 by 2. The combination of 1 by 1 can generates 105 pairs (15!/(2!×((15−2)!))) and the combination of 2 by 2 can generate. 4095 pairs ((15!/(2!×((15−2)!)))×13!)/((2!×((13−2)!))/2). The pair combinations are generated based on the possibility combinations in the diagonals order of 3, 4, and 5 of the DCT coefficients. The results of investigations show that the best embedding locations of K1 and K2 are in the index of 12 and 14 as shown in Fig. 3. The authentication data is determined by maximum quantization value of K1 and K2 times by difference between K1 and K2 as shown in Eq. (5). The proposed embedding steps are explained as follows:

Figure 2: (a) Zig-zag scan index, (b) JPEG Quantization value

Figure 3: The embedding location: (a) psychovisual threshold in DCT [21], (b) embedding location of K1 and K2

Step 1: Divide the cover image into non-overlapping blocks with the size of 8 × 8 pixels. Then, each block is transformed using DCT to obtain DC and AC values. The DC and AC value is obtained by Eq. (1).

[DC,AC]=DCT(BK)(1)

where BK represents corresponding block with the size of 8 × 8 pixels, DC represents the average AC coefficients of the BK.

Step 2: The embedding location of K1 and K2 are obtained by investigating. 4200 pairs in the diagonal order of 3, 4, and 5 of the DCT coefficients. The block coefficients of BK are re-arranged by using zig-zag scan as shown in Fig. 2. The fifteen (15) coefficients in the diagonal order of 3, 4, and 5 are then Quantized by selected JPEG quantization table. The JPEG quantization table is shown in Fig. 2.

Then, the quantization values in Fig. 2b are used to quantize the selected AC coefficients. This study examines the potential location for embedding authentication in the diagonal order of 3, 4, and 5 of the DCT coefficients. In the previous research, Ernawan and Kabir [20] have examined the best place to embed watermark for robust watermarking. The selected embedding locations of K1 and K2 are illustrated in Fig. 3b.

Fig. 3 illustrates the proposed embedding location of K1 and K2. The psychovisual threshold, as shown in Fig. 3a, showed that the diagonal order of 3, 4, and 5 of the DCT coefficients produced less error distortion to the imperceptibility. By adopting the psychovisual threshold, the author revealed that the embedding location of K1 and K2 in the index of 12 and 14 as shown in Fig. 3b, can achieve high imperceptibility of the watermarked image and tolerance under incidental attacks.

Step 3: Select the embedding location by using a chaotic map. The chaotic map is used to perform the randomized location for embedding authentication data. The chaotic map is defined in Eq. (2).

CMi+1=∝(|yi−1|)∗CMimod2(2)

yi+1=yi+CMi+1(3)

where CM represents chaotic map. In this study, ∝=2.30, CM1 = 0.1, and y1 = 0.2, the CM1 and y1 have interval value of [−0.5, 0.5]. The ∝ value is 2.30, it is fixed-point implementation of the chaotic map and gave (230)2 number in half-open interval of [0.1]. Based on the experimental results, when value of ∝ was changed by 0.00001, it will improve the FNR value of 0.57.

Step 4: Determine authentication value (AV) based on maximum quantization value in location of K1 and K2 with absolute difference between K1 and K2. The calculation of AV is defined in Eqs. (4) and (5).

sign(n)={n<0;−1otherwise;1(4)

AVi={sign(i)∗(Qmi∗⌊K1−K2⌋+1);CMi∼ =0.sign(i)∗(Qmi∗⌊K1−K2⌋);otherwise(5)

where AV represents authentication value, sign() represents function to return positive or negative value of 1, and Qm represents quantization matrix value.

Step 5: Embed the AV into selected chaotic map location CM. The embedding locations of AV are defined by:

BK′={K1+AVi; K1≤⌈K2/2⌉&& CMi==1K2+AVi; K2≤⌈K1/2⌉&& CMi==2K1+AVi||K2+AVi; otherwise.(6)

where BK′ represents watermarked block. The embedding locations are selected by using chaotic maps by following rules: if CMi equal to 1 and K1 less than or equal to ⌈K2/2⌉ then embeds AV in K1. If CMi equal to 2 and K2 less than or equal to ⌈K1/2⌉ then embeds AV in K2. Otherwise, embed authentication value in the locations of K1 or K2 by: if K1 less than or equal to ⌈K2/2⌉ then embed in K1, otherwise in K2.

Step 6: Generate recovery data by using two steps of scrambling the cover image. First, inverse scramble the pixel position of cover image using random permutation index. Second, inverse scramble eight binary bits of each pixel.

3.2 Tamper Detection and Recovery

In the communication channel over the internet, attackers may modify the content of the images, while simultaneously, application platforms compress the watermarked images to enhance the efficiency of data transmission to the receiver. Therefore, the proposed semi-fragile watermarking techniques need to effectively tolerate incidental attack, while accurately detecting malicious modifications during transmission. To address this challenge, it is crucial to ensure the integrity and authenticity of the image. The tamper detection and recovery process is shown in Fig. 4.

Figure 4: The proposed tamper detection and recovery

The proposed tamper detection and recovery are comprehensively described as follows:

Step 1: Divide watermarked image into non-overlapping blocks with the size of 8 × 8 pixels. Then, each block is transformed by DCT to obtain DC and AC values.

Step 2: Perform zigzag scanning to reorder the position of AC values. Then, quantize the block by using JPEG quantization table.

Step 3: Calculate the chaotic map location as described in Eq. (2) to compare the quantized value in the location of K1 and K2.

Step 4: Perform tamper detection by comparing K1 and K2 based on chaotic map. The tamper detection is defined in Eqs. (7)–(10).

CondAi=K1>⌈K22⌉&& CMi==1(7)

CondBi=K2>⌈K12⌉&& CMi==2(8)

CondCi=K1==K2 && CMi==0(9)

TBi={0; CondAi || CondBi || CondCi1; otherwise(10)

where TB is tampered block. The CondAi is fulfilled if the value of K1 is more than K2/2 and CMi equal to 1. The CondBi is fulfilled if the value of K2 is more than K1/2 and CMi equal to 2. The CondCi is fulfilled if the value of K1 equal to K2 and CMi equal to 0. The TB equal to 0 if CondAi or CondBi or CondCi are fulfilled. Otherwise, TB equal to 1. The proposed tamper detection is presented in Algorithm 1.

Algorithm 1 illustrates the identification of the tampered blocks. To check the tampered block, the experiment uses the same parameters for a chaotic map. The K1 and K2 are used to generate tampering maps. To evaluate the surrounding block, the TB is evaluated in two steps. First, check the non-tampered TB by: If the surrounding block consists of more than equal to three tampered, then labelled the TB as tampered, otherwise it is non-tampered. If TB is non tampered, the checking will not be proceeded to the second step. For each tampered TB will proceed to the second step. The tampered TB is evaluated by: if the neighbor TB consist of less than or equal four tampered block, then labelled TB as non-tampered, otherwise the block is tampered. To determine TB being tampered or not, the neighbor blocks in the first step and second step is shown in Table 1.

Table 1 presents the accuracy scores from tampered in neighbor of TB in the first and second step. The highest accuracy of 0.8959 was achieved when total tampered in neighbor is three for the first step and four tampered in the second step. The experiments reveal that the best threshold for first and second steps are 3 and 4. It can be noticed that these thresholds can achieve high accuracy of tamper detection.

3.3 Imperceptibility Measurement

In this experiment, a statistical analysis was performed to evaluate the perceptual quality of the watermarked image compared to the original cover image by Peak Signal-to-Noise Ratio (PSNR). The mathematical formulations employed for PSNR calculation are given in Eqs. (11) and (12) [2,21].

MSE=∑x=1M∑y=1M(Ox,y−Ox,y′)M×M(11)

PSNR=10log10⁡(2552MSE¯)(12)

where Ox,y represents the cover image, Ox,y′ represents the watermarked image, and the x,y represents the pixel of image matrix coordinates. The PSNR is indicative of image quality in the watermarked image, as determined through pixel-wise difference metrics. Concurrently, the Structural Similarity Index Measure (SSIM) was computed to assess the perceptual similarity between the original and watermarked images [12]. The calculation for SSIM is illustrated in Eqs. (13) and (14) [22,23].

l(o,w)=2μoμw+Cs1μo2+μw2+Cs1¯;c(o,w)=2σoσw+Cs2σo2+σw2+Cs2¯;s(o,w)=σow+Cs3σoσw+Cs3¯(13)

SSIM(o,w)=[l(o,w)]∝×[c(o,w)]β×[s(o,w)]γ](14)

where l represents comparison function of luminescence, c represents comparison function of contrast, s represents comparison function of the structure, o represents cover image, w represents the watermarked image, and positive constants to prevent division by zero is denoted by Cs1,Cs2, and Cs3.

The purpose of tamper detection in semi-fragile image watermarking is to achieve tolerance under incidental attack, while sensitive under malicious attack. To evaluate the sensitivity of malicious attack, the evaluation method such as accuracy is used to calculate the accurately the tampered areas. The accuracy is defined in Eq. (15) [24].

a⁢c⁢c⁢u⁢r⁢a⁢c⁢y=T⁢P+T⁢NT⁢P+F⁡P+F⁡N+T⁢N―(15)

where TP represents true-positive, TN represents true-negative, FP represents false-positive, FN represents false-negative.

4  Experimental Result and Discussion

To evaluate the efficacy of the proposed technique, this study employed various images with a size of 512 × 512 pixels from the USC-SIPI image database and two colour images from Kodak-PCD0992 with a size of 768 × 512, as depicted in Fig. 5. The experiments were conducted on a computing equipped with an Apple M2 chip processor and 8 GB of RAM, utilizing MATLAB version R2023b under the Ventura 13.5 operating system. The various images for the experimental test can be seen in Fig. 5.

Figure 5: A set of test images: (a) airplane (F-16), (b) barbara, (c) goldhill, (d) boat, (e) kodim01, (f) baboon, (g) splash, (h) pepper, (i) sailboat on lake, and (j) kodim11

4.1 Embedding Location Evaluation

In this study, the locations of K1 and K2 are determined by investigating fifty pairs from combination of 15 AC coefficients in diagonal order of 3, 4, and 5 of DCT coefficients. The diagonal order selection is limited to order 3, 4, and 5 due to it achieves high imperceptibility, less distortion, and balance between imperceptibility and robust performance. The fifty pairs as embedding locations for the authentication value is shown in Table 2.

Table 2 shows each of fifty pairs of embedding locations for the authentication value. Each pair was identified by analyzing coefficient pairs in the diagonal order of 3, 4, and 5 of DCT coefficients. The PSNR and SSIM values of the watermarked images from embedding authentication data for each of the fifty pairs are shown in Fig. 6. The author evaluates the accuracy of tamper localization under malicious attacks. The True-Positive Rate (TPR) and False-Negative Rate (FNR) are evaluated under JPEG compression with a quality factor of 50.

Figure 6: The embedding authentication value for each of the fifty pairs: (a) PSNR score values, (b) SSIM score value, (c) tamper detection accuracy under malicious attack with tampering rate of 50, and (d) TPR and FNR values under incidental attack with JPEG compression

Fig. 6 illustrates the results of imperceptibility as shown in Fig. 6a,b and tamper detection performance as shown in Fig. 6c,d. The experiments show the imperceptibility of the watermarked image when embedding authentication value for each of the fifty pairs in diagonal orders 3, 4, and 5 of the DCT coefficients. To evaluate tamper detection performance, the experiments tested the watermarked image under malicious attacks. Fig. 6c shows the tamper detection accuracy under malicious attacks with a 50% tampering rate. In this study, the authors selected the embedding locations that produced a high tamper detection accuracy of 0.99. Seventeen pairs from index 1 to 17, consistently achieved high malicious tamper detection accuracy while maintaining high imperceptibility of the watermarked images. Fig. 6d presents the TPR and FNR values under incidental attack such as JPEG compression. The same seventeen pairs provided tolerance under incidental attacks. Based on the results, pair index 11 (12;14) located in the diagonal order 4 of the DCT coefficients, achieved a TPR score of 1 and an FNR score of 0. This indicates that pairs offer tolerance to incidental attacks, while maintaining high accuracy under malicious tamper detection. To evaluate the imperceptibility, the PSNR and SSIM values are calculated after embedding the authentication value. The comparison of PSNR and SSIM values from the proposed scheme and the existing methods is shown in Table 3.

4.2 Semi-Fragile Tamper-Detection Performance Evaluation

To evaluate the effectiveness of the proposed scheme, a comparison with existing studies was conducted, as shown in Tables 3–5. Various malicious attacks were applied to the watermarked image and compared with existing studies. The experiments were also tested with various incidental attacks to evaluate the tolerance under various rates of incidental attacks. Moreover, the experiments were evaluated under hybrid attacks, which are a combination of incidental and malicious attacks. The experimental test was conducted to evaluate the semi-fragile property: tolerance of incidental attacks while still being sensitive to malicious attacks. The comparison results under malicious attacks are shown in Table 4.

Table 4 presents the tamper detection performance under various tampering ratios. The proposed scheme outperformed the existing methods in terms of accuracy, TPR, and FNR. The proposed technique produced an average TPR value of 96.03%, an average FNR value of 3.96%, and an average accuracy value of 97.58%. The scheme by [17] produced low tamper detection accuracy for a large tampering rate of 80%. The scheme by [17] produced an FNR value of 77.43%, indicating high false tamper detection. The schemes by [12,13] produced a tamper detection accuracy of 60%, and these schemes also produced a high false negative rate of 39%. The comparison of TPR and FNR under incidental attacks is shown in Table 5.

Table 5 presents the tolerant performance of the proposed scheme under incidental attack, compared to the existing methods. In semi-fragile image watermarking, the tamper detection is designed to tolerate an incidental attack. In this study, the author implements JPEG compression with various quality factors. The high TPR indicated the watermarking scheme tolerance under incidental attack, while the low TPR indicated the watermarking scheme was fragile under incidental attack. The proposed scheme outperforms schemes by [12,13,17] in terms of TPR and FNR values, which indicates tolerance under incidental attacks. The proposed scheme achieved high tolerance under incidental attack, with mostly a TPR value of 100% and an FNR of 0%. The schemes by [12,13] obtained the TPR and FNR values of 49 and 50, respectively. The proposed technique is indicated to tolerate under JPEG compression with a quality factor of 50 to 90. Table 6 shows the tamper detection evaluation of the proposed scheme and the existing methods under a hybrid attack of malicious and incidental attacks.

According to Table 6, the proposed scheme performed high tolerance against incidental attacks, while still being sensitive under various malicious attacks. The high TPR of the proposed technique indicated that the tamper detection can be tolerant under incidental attacks, with a TNR rate score of more than 93% indicating it can achieve high accuracy under malicious attacks. The scheme by [12,13] showed low tamper detection accuracy and the TPR and TNR values. Despite the scheme by [17] performing fair tolerance with high tamper detection accuracy, the scheme produced a low TPR value, with an average TPR value of 61.65%. The proposed scheme can produce efficient tamper detection in semi-fragile image watermarking with high accuracy, TPR, and TNR values.

4.3 Evaluation Performance of Hybrid Attack

In this section, the authors evaluate tamper detection performance by using various hybrid attacks. The experiments have tested various incidental and malicious attacks, such as JPEG compression with copy-paste attack, Gaussian noise, and Gaussian blur with object manipulation. The image information will be recovered based on the tamper recovery map. The result of tamper detection and recovery under various hybrid attacks can be seen in Table 7.

Table 7 illustrates the performance of tamper detection and recovery under various hybrid attacks. For proposed tamper detection, the tamper localization was detected with an accuracy above 90%. The high tamper detection accuracy of 98.15% was obtained under a hybrid attack of Gaussian noise attacks with density 0.005 and JPEG compression on kodim01 image. The lowest accuracy is achieved under multiple incidental and malicious attacks for kodim03 with an accuracy score of 88.25%. The proposed tamper detection scheme produces an improvement of 7.69% with an accurate score of 91.78%. The computational time for embedding and tamper detection can be seen in Table 8.

According to Table 8, the computational time for the proposed embedding and tamper detection was evaluated across various images. An average computational time for embedding authentication required 0.5042 and 0.3949 s for tamper detection. For grayscale images, the embedding and tamper detection required 0.3 s. The results of tamper detection perform faster than the existing scheme [13].

5  Conclusion

In this study, a semi-fragile image watermarking method based on DCT quantization for tamper localization has been proposed. This study investigates embedding locations for semi-fragile watermarking by evaluating 4200 pairs from non-overlapping combinations of 15 AC coefficients using 1 × 1 and 2 × 2 groupings. These selected coefficients in diagonal orders 3, 4, and 5 of DCT coefficients are examined to determine the optimal location for embedding authentication data. The proposed scheme was tested under various malicious, incidental, and hybrid attacks. The results show that the proposed technique achieves a balance between imperceptibility and tamper detection performance. In addition, the scheme remains tolerant under incidental attacks while maintaining sensitivity to malicious attacks. The experimental results under hybrid attacks demonstrate strong tamper detection performance under malicious attacks, while remaining tolerant to JPEG compression as incidental attacks. For future research, the proposed scheme can be extended semi-fragile watermarking by incorporating machine learning to develop a more adaptive embedding method and to further improve tamper detection accuracy.

Acknowledgement: The authors would like to thank the Ministry of Higher Education Malaysia for providing financial support under Universiti Malaysia Pahang Al-Sultan Abdullah for their support in facilitating this research.

Funding Statement: This work was funded by Ministry of Higher Education Malaysia through Universiti Malaysia Pahang Al-Sultan Abdullah under Internal Research Grant (RDU233003).

Author Contributions: The authors contributed to the study as follows: Conceptualization, investigation, analysis, interpretation of results, and writing manuscript: Agit Amrullah and Ferda Ernawan. All authors reviewed the results and approved the final version of the manuscript.

Availability of Data and Materials: Not applicable.

Ethics Approval: Not applicable.

Conflicts of Interest: The authors declare no conflicts of interest to report regarding the present study.

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