Anantha Rao Gottimukkala
| Anita Pradhan | Pramoda Patro | J. Hemalatha | Ranjan K. Senapati | Gandharba Swain*
© 2024 The authors. This article is published by IIETA and is licensed under the CC BY 4.0 license (http://creativecommons.org/licenses/by/4.0/).
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Tampering an image became more manageable due to the advent of photo editing software. So, it is essential to detect and correct the tampered locations. This article presents an image watermarking scheme that applies a modified version of 8 data bits and 4 redundant bits of Hamming code. It operates over a block of 3 pixels at a time. The 24 bits of the 3 pixels are rearranged and divided into 2 processing units, each comprising 12 bits. Out of 12 bits in a unit, 4 bits are used as redundant bits, and 8 bits are used as data bits. Watermark bits (WBs) are generated from data bits using a logistic map (LM) and stored in redundant bit positions. Experimental results reveal that this proposed technique maintains a fair balance for both capacity and distortion. The measured capacity is 2.67 bits per pixel (bpp) with a 39.21 decibels (dB) distortion. The estimated structural similarity (SSIM) is 0.9844, and the accuracy is 0.9999. Furthermore, it was also found that the proposed technique performs fairly well compared to existing techniques in capacity and distortion.
data hiding, watermarking, tamper detection, Hamming code, logistic map
Tampering a watermarked image (WI) is very easy by using photo editing tools. So, accurate tamper detection and correction mechanisms play a vital role in this field of study. Image watermarking can be done in the spatial domain and transform domain. In the spatial domain, the watermarking techniques use block-by-block or pixel-by-pixel for watermark hiding. To ensure the safety of the embedded watermark, we can use a chaotic map (CM) or logistic map (LM). Different kinds of error correction codes can be used in data hiding techniques for error detection and correction [1-3]. Hash functions can also be used to improve attack resistance [4].
Gul and Ozturk [5] proposed a triple data embedding approach for watermarking. Here, the recovery bits (RBs) are created based on the partner block concept with 4×4 size and embedded in the 2 least significant bits (LSBs). Sinhal et al. [6] arranged the color image pixels into 2×4 blocks of color components. A block has 8 bytes. From the most significant bits (MSBs) of the color components, watermark bits (WBs) are generated and stored in LSBs applying a base-9 numbering system. Authors claim they could detect 99% of tampering and correct 80% of it successfully. Qin et al. [7] brought a tamper detection and localization scheme using 3×3 blocks in an overlapped manner. In this technique, WBs and RBs are brought up from the 6 MSBs of the mean value. The WBs replace central pixel LSBs, and the RBs replace the remaining pixel LSBs. This technique effectively recovers the tampered locations.
To improve security, the WBs can be scrambled using CM and LM. Rawat and Raman [8] used Arnold’s map for this. In this approach, WBs and bits from the map are made exclusive-or (XORed) and then stored in LSBs. Botta et al. [9] argued that Rawat and Raman could not localize the tampered places. This issue is solved by using 7 MSBs to create the WBs. The LSBs are substituted by the WBs. Prasad and Pal [10] plied LM with shift and mod operators. Here, WBs are computed using 5 MSBs, which are camouflaged plying mod and shift operators. Tampered zones could be localized very effectively in this approach. Sahu [11] coupled LM and XOR functions to bury the WBs. The collage attack, text addition attack, cropping attack, and copy-paste attack cannot affect the watermark in Sahu’s technique. Nazari et al. [12] considered 2×2 pixels as a block and applied CM for watermarking. Here, WBs are generated from higher planes and buried in lower planes. The watermark is protected because of CM. Shehab et al. [13] devised a watermarking approach applying singular value factorization and LSB substitution with 4×4 blocks. Used Arnold transformation to decide the insertion of RBs. The authentication bits are plied to protect from vector quantization threats. This technique improves the peak signal-to-noise ratio (PSNR) and tamper localization accuracy.
Kosuru et al. [14] considered 2×2 pixel blocks and computed quotients and remainders from these 4 pixels of a block. The quotients are treated as leaf nodes of the Merkle tree and the root node is computed from the leaf nodes. The root node is converted to binary and treated as WBs. Gull et al. [15] also used the block concept for tamper localization. For a 4×4 pixel block, the WBs are generated from 4 MSBs of these 16 pixels. Furthermore, RBs are computed from the pixel value average in the block. Here, the payload is only 1 bpp with PSNR 51.94 dB. Laishram and Sing [16] proposed a multipurpose watermarking approach based on the zone of interest in frequency coefficients. It can achieve source authentication, confidentiality, integrity check, ownership identification, and tamper correction. It has built-in recovery against various attacks like scaling, translation, rotation, etc. This technique achieved a PSNR value of 53.17 dB, but the hiding capacity (HC) is very poor.
Rinki et al. [17] used a non-consecutive matrix of pixels and a matrix multiplication process to replace the 3 LSBs of the channels of a color image with the bits of a secret grey image. It achieves content integrity verification and copyright protection. Chen et al. [18] brought a data-hiding technique using Huffman code. Using this code, the MSB plane (4 MSBs) is compressed, and LSBs are buried in vacant MSBs. Thus, the room is created in LSBs to embed the data. The Huffman code performs compression by computing the difference among the higher nibbles. High embedding capacity is achieved. Jana et al. [19] performed watermarking over 4×4 blocks using a similarity matrix. A block may be categorized into one of 2 types: (i) smooth and (ii) complex. WBs are created from 8 MSBs. If the block is in the smooth category, then the block mean is used as RBs. If the block is a complex category, then fuzzy logic and imaging concept is utilized to generate RBs. WBs and RBs are buried in lower-bit planes. Pal et al. [20] applied interpolation to expand a 2×2 block into a 4×4 size. Used local binary pattern and Hamming code to embed the WBs. The error detection is possible at the receiver to some extent. It possesses high embedding capacity.
Patsariya and Dixit [21] proposed watermarking for copyright protection and authenticity using the CM for improved security. They achieved security in addition to robustness, but the resultant correlation values are not appreciable. Chennamma et al. [22] proposed authentication for medical images based on statistical correlations. This approach divides the image into 4 by 4 blocks and in each block estimates statistical correlations. The correlations serve as watermarks and are embedded in lower bit planes. The experimental readings like PSNR and SSIM are all right.
A majority of the articles detect the tamper locations effectively, but are not able to correct those locations accurately. This is a very crucial research issue in image authentication.
2.1 Review of related work
Figure 1 depicts the basic (7, 4) Hamming code [23]. The redundant bit r1 is derived by doing an XOR operation over bits f1, f2, and f4. Similarly, r2 is derived by doing an XOR operation over bits f1, f3, and f4. Furthermore, r3 is derived by doing XOR operation over bits f2, f3, and f4. Chang et al. [24] plied Hamming code along with LM to generate the WBs from 4 MSBs. The LSBs are replaced by these WBs. They claimed that the tampered pixels are correctly localized. The application of LM protects from different attacks. The security has been increased by the use of LM. The recorded value of PSNR is acceptable, and this value is 37 dB. Wang et al. [25] did watermarking using Hamming code for object verification. In this technique, the watermark has been created using Hamming code and embedded in LSBs. The integrity of the watermark is verified by Hamming code. The original model is not necessary for integrity verification and tamper correction. It is simple and achieves lower distortion. Medical images are very important objects. While transmitted over the internet, errors may occur due to various reasons. Islam et al. [26] did watermarking for medical images plying (8, 4) Hamming code. This method is implemented in an independent processor to be useful for real-life scenarios. Trivedy and Pal [27] used LM with Hamming weight to make the WBs, and these bits are concealed in pixels either by altering their value by ±1 or by keeping their value the same. If a bit of watermark is 1, then the pixel value is altered by ±1; otherwise, the pixel value is not altered. The tamper detection is possible. Hamming code has been used to identify the positions where the WBs can be hidden. This technique possesses very little HC.
Prasad and Pal [28] did watermarking using pixel value differencing (PVD) and Hamming code. In their scheme, a block (P1, P2) is considered. The 4 MSBs (2 from each pixel) are the data bits; 3 redundant bits are derived as WBs, which are then hidden in the lower bit plane by the PVD mechanism. It eradicates the pixel boundary problem and gives a higher PSNR value and higher SSIM. Prasad and Pal [29] also detected tampering at the pixel level plying LM and Hamming code. Using a generator matrix. Derived WBs from 4 MSBs. This matrix creates 7 bits, out of which the 3 rightmost bits are picked up as WBs and concealed at 3 LSBs. The PVD concept is applied to hide the 3 WBs in LSBs. Security is surely enhanced when LM is used. Jana et al. [30] also used basic Hamming code for watermarking and error correction using LSBs of 7 pixels. Nguyen and Le [31] performed data hiding over 5 pixels using (5,3) Hamming code. This code is used to detect possible places where the message bits can be buried. Although the HC is only 12.2 bpp, the security is high because the embedding positions are the key positions to secure the embedded data. Ramos et al. [1] used an error-correcting code to develop a fragile watermarking scheme, wherein the WBs are created from redundant bits and hidden in frequency bands. The primary objectives of data hiding techniques are higher HC, lower distortion, and higher security. Khadse and Swain [2] used quotient value differencing to hide data. They generated the authentication bits from MSBs using Merkle tree root and stored them in LSBs. The authentication bits can help detect errors. Kosuru et.al. [3] also used the principle of quotient value differencing for data hiding. They used the Hamming code to create the parity bits from MSBs and store them in LSBs. The error detection and correction happened accurately.
Figure 1. The (7, 4) Hamming code
2.2 Research contribution
There exists a good number of watermarking techniques for tamper detection, but very few of them provide perfect tamper correction. So, it is also essential and interesting work to detect the tampered pixels accurately and correct them perfectly. This article proposes a watermarking technique using a modified Hamming code version. The contribution is briefed below:
·The (12, 8) Hamming code is based on Hamming code (7, 4). Figure 2 can be referred to now. The 4 parity bits (P4, P3, P2, and P1) are computed from the 8 data bits. To use this in image watermarking, we have modified it by repositioning the redundant bit positions towards the LSB side and altering their computations appropriately.
·Three pixels are taken and divided into 2 units in such a way that the LSBs are used as redundant bits. The computation of redundant bits is modified as compared to the original way in Hamming code.
·The reorganization of redundant bits is performed so that the distortion will be minimal after storing the WBs in redundant bit positions. The modified Hamming code is described in Section 3.2.
Furthermore, we apply the LM sequence with the redundant bits to improve security and generate the WBs. The details of the computation are described in Section 3.1.
Figure 2. The (12, 8) Hamming code
Section 3.1 describes LM's generation of a random sequence of bits. Section 3.2 explains the generation of WBs and their hiding in the image. Section 3.3 explains the extraction of WBs, localization of tampered pixels, and correction of tampered pixels.
3.1 Used logistic map
The LM generates random values using 2 initial seeds α0 and γ. These seed values are constrained as follows: 0≤α0≤1 and 0<γ≤ 4. Our initial value α0 is 0.0396, and γ is 3.58. The subsequent values αi can be computed by Eq. (1).
$\alpha_i=\gamma \times\left(1-\alpha_{i-1}\right) \times \alpha_{i-1}$ (1)
The LM can generate perfect random values if we take 3.57 <γ≤ 4. After obtaining αi value, we multiply it by 255 to derive another value Xi. This Xivalue is rounded up to get Yi. Eq. (2) depicts this computation. The integer value Yi<255. Thereafter, representing Yi value in 8-bit binary, we get Si. The 4 MSBs of Si are termed as K and 4 LSBs of Si as T. So, K=k4 k3 k2 k1 and T=t4 t3 t2 t1.
$X_i=\alpha_i \times 255$ and $Y_i=$ Round $\left(X_i\right)$ (2)
3.2 Watermark embedding
The cover image is virtually split into 1×3 size disjoint blocks. Suppose (P1, P2, P3) is a sample block. The various bits of these 3 pixels are designated in Figure 3. The watermark hiding in this sample block is illustrated in the below steps.
Figure 3. Original 1×3 block
Step 1: Partition the 24 bits of the block into 2 units, U1 and U2, as shown in Figure 4.
Figure 4. Two data units, each 12-bit
Step 2: For U1 compute $\mathrm{r}_1^{\prime}, \mathrm{r}_2^{\prime}, \mathrm{r}_3^{\prime}$ and $\mathrm{r}_4^{\prime}$ using Eq. (3) and Eq. (4) respectively.
$\begin{aligned} & r_1^{\prime}=f_7 \oplus f_5 \oplus f_4 \oplus f_2 \oplus f_1, \\ & r_2^{\prime}=f_7 \oplus f_6 \oplus f_4 \oplus f_3 \oplus f_1\end{aligned}$ (3)
$\begin{aligned} & r_3^{\prime}=f_8 \oplus f_4 \oplus f_3 \oplus f_2, \\ & r_4^{\prime}=f_8 \oplus f_7 \oplus f_6 \oplus f_5\end{aligned}$ (4)
Step 3: For U2 compute $\mathrm{v}_1^{\prime}, \mathrm{v}_2^{\prime}, \mathrm{v}_3^{\prime}$ and $\mathrm{v}_4^{\prime}$ using Eq. (5) and Eq. (6) respectively.
$\begin{aligned} & v_1^{\prime}=q_7 \oplus q_5 \oplus q_4 \oplus q_2 \oplus q_1 \\ & v_2^{\prime}=q_7 \oplus q_6 \oplus q_4 \oplus q_3 \oplus q_1\end{aligned}$ (5)
$\begin{aligned} & v_3^{\prime}=q_8 \bigoplus q_4 \bigoplus q_3 \bigoplus q_2 \\ & v_4^{\prime}=q_8 \oplus q_7 \bigoplus q_6 \bigoplus q_5\end{aligned}$ (6)
Step 4: Accept the next 8 bits from the LM generator. Say it is Si, which is depicted in Eq. (7).
$S_i=K T$, where $K=k_4 k_3 k_2 k_1$ and $T=t_4 t_3 t_2 t_1$ (7)
Step 5: Compute the WBs $r_4^{\prime \prime}, r_3^{\prime \prime}, r_2^{\prime \prime}, r_1^{\prime \prime}$ for $U_1$ and $v_4^{\prime \prime}, v_3^{\prime \prime}$, $\mathrm{v}_2^{\prime \prime}, \mathrm{v}_1^{\prime \prime}$ for $U_2$ as in Eq. (8) and Eq. (9) respectively.
$r_i^{\prime \prime}=r_i^{\prime} \oplus k_i$, for $i=1,2,3$, and 4 (8)
$v_i^{\prime \prime}=v_i^{\prime} \oplus t_i$, for $i=1,2,3$, and 4 (9)
Figure 5. The watermarked block
Step 6: To form the watermarked block, replace each $r_i$ by $r_i^{\prime \prime}$ in Figure 4, for $i=1,2,3$ and 4. Similarly, replace each $v_i$ by $\mathrm{v}_{\mathrm{i}}^{\prime \prime}$ in Figure 4, for $\mathrm{i}$=1, 2, 3, and 4. The resultant block after watermarking is shown in Figure 5. It is denoted as $\left(\mathrm{P}_1^{\prime}, \mathrm{P}_2^{\prime}, \mathrm{P}_3^{\prime}\right)$. Diagrammatically, the embedding procedure is shown in Figure 6.
Figure 6. Watermark embedding
3.3 Retrieval of watermark with tamper correction
Divide the WI into 1×3 size blocks. Figure 5 represents a sample block. The extraction of WBs is narrated in the below steps.
Step 1: Partition the block ($\mathrm{P}_1^{\prime}, \mathrm{P}_2^{\prime}, \mathrm{P}_3^{\prime}$) into 2 units $\mathrm{U}_1^{\prime}$ and $\mathrm{U}_2^{\prime}$ as shown in Figure 7.
Step 2: Take the next 8 -bit LM sequence value, $S_i$ and represent it as $S_i=\mathrm{KT}$, where $K=k 4 k_3 k_2 k_1$ and $T=t 4 t_3 t_2 t_1$. Compute $r_4^{\prime}, r_3^{\prime}, r_2^{\prime}, r_1^{\prime}$ and $v_4^{\prime}, v_3^{\prime}, v_2^{\prime}$, $v_1^{\prime}$ using Eq. (10) and Eq. (11) respectively.
$r_i^{\prime}=r_i^{\prime \prime} \oplus k_i$, for $i=1,2,3$, and 4 (10)
$v_i^{\prime}=v_i^{\prime \prime} \oplus t_i$, for $i=1,2,3$, and 4 (11)
Step 3: Compute $r_1^*$, $r_2^*$ using Eq. (12) and $r_3^*, r_4^*$ using Eq. (13).
$\begin{aligned} & r_1^*=r_1^{\prime} \oplus f_7 \oplus f_5 \oplus f_4 \oplus f_2 \oplus f_1 \\ & r_2^*=r_2^{\prime} \oplus f_7 \oplus f_6 \oplus f_4 \oplus f_3 \oplus f_1\end{aligned}$ (12)
$\begin{aligned} & r_3^*=r_3^{\prime} \oplus f_8 \oplus f_4 \oplus f_3 \oplus f_2, \\ & r_4^*=r_4^{\prime} \oplus f_8 \oplus f_7 \oplus f_6 \oplus f_5\end{aligned}$ (13)
Step 4: Compute $\mathrm{v}_1^*, \mathrm{v}_2^*, \mathrm{v}_3^*, \mathrm{v}_4^*$ using Eq. (14) and Eq. (15).
$\begin{gathered}v_1^*=v_1^{\prime} \oplus q_7 \oplus q_5 \oplus q_4 \oplus q_2 \oplus q_1 \\ v_2^*=v_2^{\prime} \oplus q_7 \oplus q_6 \oplus q_4 \oplus q_3 \oplus q_1\end{gathered}$ (14)
$\begin{aligned} & v_3^*=v_3^{\prime} \oplus q_8 \oplus q_4 \oplus q_3 \oplus q_2 \\ & v_4^*=v_4^{\prime} \oplus q_8 \oplus q_7 \oplus q_6 \oplus q_5\end{aligned}$ (15)
Step 5: If $\mathrm{r}_4^* \mathrm{r}_3^* \mathrm{r}_2^* \mathrm{r}_1^* \neq 0000$, then there is tampering in $\mathrm{U}_1^{\prime}$. The correction is done as shown in Table 1. If $\mathrm{r}_4^* \mathrm{r}_3^* \mathrm{r}_2^* \mathrm{r}_1^*=$ 0000 . Then there has been no tampering in $U_1^{\prime}$. Extract the 4 watermarked bits from $U_1^{\prime}$, these are $r_4^{\prime \prime} r_3^{\prime \prime} r_2^{\prime \prime} r_1^{\prime \prime}$.
Figure 7. Two data units from the watermarked block
Step 6: If $v_4^* v_3^* v_2^* v_1^* \neq 0000$, then there is tampering in $U_2^{\prime}$. The correction is done as shown in Table 2. If $\mathrm{v}_4^* \mathrm{v}_3^* \mathrm{v}_2^* \mathrm{v}_1^*=$ 0000 . Then there has been no tampering in $\mathrm{U}_2^{\prime}$. Extract the 4 watermarked bits from $\mathrm{U}_2^{\prime}$, these are $\mathrm{v}_4^{\prime \prime} \mathrm{v}_3^{\prime \prime} \mathrm{v}_2^{\prime \prime} \mathrm{v}_1^{\prime \prime}$.
Diagrammatically, the extraction procedure is shown in Figure 8.
Table 1. Correction in $\mathrm{U}_1^{\prime}$
|
$\mathbf{r}_{\mathbf{4}}^* \mathbf{r}_3^* \mathbf{r}_2^* \mathbf{r}_1^*$ |
Tampered Location |
Correction |
|
0001 |
$\mathrm{r}_1^{\prime \prime}$ is tampered |
Correct $\mathrm{r}_1^{\prime \prime}$ by complementing it |
|
0010 |
$\mathrm{r}_2^{\prime \prime}$ is tampered |
Correct $\mathrm{r}_2^{\prime \prime}$ by complementing it |
|
0011 |
$\mathrm{f}_1$ is tampered |
Correct $\mathrm{f}_1$ by complementing it |
|
0100 |
$\mathrm{r}_3^{\prime \prime}$ is tampered |
Correct $\mathrm{r}_3^{\prime \prime}$ by complementing it |
|
0101 |
$\mathrm{f}_2$ is tampered |
Correct $\mathrm{f}_2$ by complementing it |
|
0110 |
$\mathrm{f}_3$ is tampered |
Correct $\mathrm{f}_3$ by complementing it |
|
0111 |
$\mathrm{f}_4$ is tampered |
Correct $\mathrm{f}_4$ by complementing it |
|
1000 |
$\mathrm{r}_4^{\prime \prime}$ is tampered |
Correct $\mathrm{r}_4^{\prime \prime}$ by complementing it |
|
1001 |
$\mathrm{f}_5$ is tampered |
Correct $\mathrm{f}_5$ by complementing it |
|
1010 |
$\mathrm{f}_6$ is tampered |
Correct $\mathrm{f}_6$ by complementing it |
|
1011 |
$\mathrm{f}_7$ is tampered |
Correct $\mathrm{f}_7$ by complementing it |
|
1100 |
$\mathrm{f}_8$ is tampered |
Correct $\mathrm{f}_8$ by complementing it |
Table 2. Correction in $\mathrm{U}_2^{\prime}$
|
$\mathbf{v}_{\mathbf{4}}^* \mathbf{v}_{\mathbf{3}}^* \mathbf{v}_{\mathbf{2}}^* \mathbf{v}_{\mathbf{1}}^*$ |
Tampered Location |
Correction |
|
0001 |
$\mathrm{v}_1^{\prime \prime}$ is tampered |
Correct $\mathrm{v}_1^{\prime \prime}$ by complementing it |
|
0010 |
$\mathrm{v}_2^{\prime \prime}$ is tampered |
Correct $\mathrm{v}_2^{\prime \prime}$ by complementing it |
|
0011 |
$\mathrm{q}_1$ is tampered |
Correct $\mathrm{q}_1$ by complementing it |
|
0100 |
$\mathrm{v}_3^{\prime \prime}$ is tampered |
Correct $\mathrm{v}_3^{\prime \prime}$ by complementing it |
|
0101 |
$\mathrm{q}_2$ is tampered |
Correct $\mathrm{q}_2$ by complementing it |
|
0110 |
$\mathrm{q}_3$ is tampered |
Correct $\mathrm{q}_3$ by complementing it |
|
0111 |
$\mathrm{q}_4$ is tampered |
Correct $\mathrm{q}_4$ by complementing it |
|
1000 |
$\mathrm{v}_4^{\prime \prime}$ is tampered |
Correct $\mathrm{v}_4^{\prime \prime}$ by complementing it |
|
1001 |
$\mathrm{q}_5$ is tampered |
Correct $\mathrm{q}_5$ by complementing it |
|
1010 |
$\mathrm{q}_6$ is tampered |
Correct $\mathrm{q}_6$ by complementing it |
|
1011 |
$\mathrm{q}_7$ is tampered |
Correct $\mathrm{q}_7$ by complementing it |
|
1100 |
$\mathrm{q}_8$ is tampered |
Correct $\mathrm{q}_8$ by complementing it |
Figure 8. The tamper detection, tamper correction, and watermark extraction procedure
3.4 Example of watermark embedding and watermark extraction
This sub-section presents 3 examples to help you better understand the proposed watermarking technique.
Figure 9 describes an example of watermark embedding in a step-by-step manner.
Figure 10 depicts an example of WB extraction where there is no error. This example presents the extraction procedure with pixel sample values at the bit level with no error case.
Figure 11 illustrates the extractions of WBs with error bits correction. This example presents the extraction procedure with pixel sample values at the bit level and an error correction case.
Figure 9. Example of watermark embedding
Figure 10. Example of watermark extraction
Figure 11. Example of watermark extraction with error correction
This MHCBW technique is coded in MATLAB on a computing device with an i5 processor. Figure 12 depicts the original images (OIs) from the SIPI database [32]. Although several images are used for testing, only a few samples are shown here. Figure 13 depicts some samples of WIs accordingly. Under each WI, the PSNR and SSIM are mentioned.
The effectiveness of the MHCBW scheme is measured by parameters like embedding time (ET), extraction time (ExT), SSIM, HC, PSNR, and accuracy (ACC). Eq. (16) computes the PSNR, a measure of distortion in WI.
PSNR $=10 \times \log _{10} \frac{\mathrm{~m} \times \mathrm{n} \times 255 \times 255}{\sum_{\mathrm{i}=1}^{\mathrm{m}} \sum_{\mathrm{j}=1}^{\mathrm{n}}\left(\mathrm{P}_{\mathrm{ij}}-\mathrm{Q}_{\mathrm{ij}}\right)^2}$ (16)
HC is the total hiding capacity in all the pixels of the image. Capacity of one pixel is represented as bpp i.e., bits per pixel. Eq. (17) represents structural similarity (SSIM) of WI with OI [26]. $P_{i j}$ is a pixel of OI and $Q_{i j}$ is a pixel of WI. $\overline{\mathrm{P}}$ is mean value of all $P_{i j}$ values of OI. $\overline{\mathrm{Q}}$ is mean value of all $Q_{i j}$ values of WI. Two constants $c_1$ and $c_2$ has been inserted in $(\left.\overline{\mathrm{P}}^2+\overline{\mathrm{Q}}^2+\mathrm{c}_1\right)$ and $\left(\sigma_{\mathrm{x}}^2+\sigma_{\mathrm{y}}^2+\mathrm{c}_2\right)$ to ensure the denominator to be non-zero. The constant $c_1=\left(\mathrm{K}_1 \mathrm{~L}\right)^2, \mathrm{~K}_1 \ll 1$ and L value is 255 for grey image. The constant $c_2=\left(K_2 L\right)^2$, and $K_2 \ll 1$. Here, variance of OI to WI is $\sigma_{\mathrm{pq}}$, variance of OI is $\sigma_{\mathrm{p}}^2$, and variance of WI is $\sigma_{\mathrm{q}}^2$. SSIM value will approach to 1 where the WI is very similar with OI. The ACC has been computed in Eq. (18) [26] using the counts of false negatives (FN), true negatives (TN), false positives (FP) and true positives (TP).
Figure 12. OIs
Figure 13. WIs
$\mathrm{SSIM}=\frac{\left(2 \overline{\mathrm{P}} \,\overline{\mathrm{Q}}+\mathrm{c}_1\right)\left(2 \sigma_{\mathrm{xy}}+\mathrm{c}_2\right)}{\left(\overline{\mathrm{P}}^2+\overline{\mathrm{Q}}^2+\mathrm{c}_1\right)\left(\sigma_{\mathrm{x}}^2+\sigma_{\mathrm{y}}^2+\mathrm{c}_2\right)}$ (17)
$\mathrm{ACC}=\frac{\mathrm{TP}+\mathrm{TN}}{\mathrm{TP}+\mathrm{TN}+\mathrm{FP}+\mathrm{FN}}$ (18)
Table 3 records the outcomes of this proposed MHCBW scheme. Table 3 records the PSNR value as 39.21 dB, so it is acceptable. The bpp is 2.67. The average value of SSIM is 0.9844, which indicates that OI and WI are more than 99% alike. ACC value is 0.99, which conveys that the number of tampered pixels is identified with 99% correctness. Furthermore, embedding and extraction of the watermark can be performed in 10.64 and 12.49 secs respectively.
Table 3. Performance measure of MHCBW scheme
|
512×512 Images |
SSIM |
PSNR (dB) |
ACC |
bpp |
E×T (secs) |
ET (secs) |
|
Lena |
0.9818 |
39.19 |
0.9999 |
2.67 |
11.43 |
10.35 |
|
Baboon |
0.9904 |
39.19 |
0.9999 |
2.67 |
11.29 |
10.09 |
|
Goldhill |
0.9883 |
39.16 |
0.9999 |
2.67 |
11.30 |
10.02 |
|
Crowd |
0.9869 |
39.30 |
0.9999 |
2.67 |
11.34 |
10.83 |
|
Camera-man |
0.9723 |
39.22 |
0.9999 |
2.67 |
11.27 |
10.96 |
|
Pepper |
0.9748 |
39.27 |
0.9999 |
2.67 |
14.77 |
10.87 |
|
Barbara |
0.9932 |
39.22 |
0.9999 |
2.67 |
14.17 |
10.80 |
|
Boat |
0.9877 |
39.18 |
0.9999 |
2.67 |
14.36 |
11.19 |
|
Average |
0.9844 |
39.21 |
0.9999 |
2.67 |
12.49 |
10.64 |
Figure 14 conveys the tampered Lena images with tampering % from 5% to 45%. A pixel is tampered with if one or more of its 8 bits are changed. The tampered pixels are localized and made white color for easy reference by the readers. It is shown for only one image. It is performed for all the test images. Table 4 depicts the mean value of bpp, PSNR, SSIM, and ACC over 8 images with tampering percentages starting from 0% to 45%.
Figure 14. Tampered Lena images (the tampered location pixels are made white color for reference)
(a)
(b)
(c)
Figure 15. (a) Tampering rate versus PSNR, (b) Tampering rate versus SSIM, and (c) Tampering rate versus ACC
Figure 15(a) depicts a graph for the PSNR at tampering rate. It can be observed from this graph that if we further raise the tampering rate after 45%, PSNR can be at least 30 dB. Figure 15(b) depicts a plot for SSIM at different tampering rates, and Figure 15(c) depicts a plot for ACC at different tampering rates. From Figure 15(b), we can achieve an SSIM value greater than 0.98 even after raising the tampering by more than 45%. From Figure 15(c), we can note that the ACC value is greater than 0.99 even after raising the tampering rate beyond 45%.
Table 5 represents a comparison of the average values of different parameters of this MHCBW technique with Nazari et al. [12], Chang et al. [24], Prasad and Pal [28], and Prasad and Pal [29]. Techniques of Chang et al. [24], Prasad and Pal [28], and Prasad and Pal [29] are based on Hamming code. Nazari et al.’s [12] scheme includes a chaotic map. Furthermore, Figure 16 shows a bar graph distinguishing the HC and PSNR of the MHCBW technique with the existing schemes; Figure 17 depicts a bar graph comparing the SSIM and ACC values of the MHCBW technique with existing schemes.
From Figure 16, it may be noted that there is a better trade-off between the HC and PSNR of the MHCBW scheme as compared to the 4 existing schemes. Prasad and Pal’s [28] technique possesses very low bpp but higher PSNR. Nazari et al.’s [12] technique possesses both low bpp and low PSNR.
From Figure 17, it may be observed that the SSIM value in MHCBW technique is lesser than the works of Nazari et al. [12], Chang et al. [24], Prasad and Pal [28], and Prasad and Pal [29], but the ACC values of the MHCBW scheme is higher than the works of Nazari et al. [12], Chang et al. [24], Prasad and Pal [28], and Prasad and Pal [29].
Figure 16. PSNR, bpp comparison
Figure 17. SSIM, ACC comparison
Table 4. Efficacy measurement at varied tampering rates
|
Efficacy Parameter |
Tampering Rate |
|||||||||
|
0% |
5% |
10% |
15% |
20% |
25% |
30% |
35% |
40% |
45% |
|
|
bpp |
2.67 |
2.67 |
2.67 |
2.67 |
2.67 |
2.67 |
2.67 |
2.67 |
2.67 |
2.67 |
|
PSNR |
39.21 |
38.68 |
38.22 |
37.79 |
37.41 |
37.07 |
36.76 |
36.48 |
36.23 |
36.01 |
|
ACC |
0.9999 |
0.9993 |
0.9986 |
0.9979 |
0.9973 |
0.9967 |
0.9961 |
0.9955 |
0.9948 |
0.9941 |
|
SSIM |
0.9844 |
0.9821 |
0.9899 |
0.9881 |
0.9864 |
0.9849 |
0.9836 |
0.9825 |
0.9816 |
0.9807 |
Table 5. Comparison of average efficacy parameter values
|
Technique |
bpp |
PSNR |
SSIM |
ACC |
|
Nazari et al.’s [12] |
1.66 |
36.50 |
0.9928 |
0.9845 |
|
Chang et al.’s [24] |
3.0 |
37.88 |
0.9844 |
0.9969 |
|
Prasad and Pal’s [28] |
1.5 |
42.09 |
0.9994 |
0.9995 |
|
Prasad and Pal’s [29] |
3.0 |
37.94 |
0.9861 |
0.9990 |
|
Proposed MHCBW scheme |
2.67 |
39.21 |
0.9844 |
0.9999 |
This article proposes MHCBW technique for image tamper detection and correction. It uses a modified version of Hamming code for error detection and correction. It uses an LM sequence to improve the security. The WBs are stored in redundant bit positions and can be extracted accurately. Experimental results reveal that this MHCBW technique maintains a fair compromise between HC and PSNR compared to existing techniques. Nazari et al.’s technique produces lesser PSNR and bpp than the proposed one. The other 3 existing techniques produce either higher bpp with lower PSNR or vice-versa compared to the MHCBW technique. The MHCBW scheme's estimated average PSNR is 39.21, and bpp is 2.67. The estimated SSIM value of the MHCBW technique is 0.9844, which indicates that the OIs are structurally similar to the corresponding WIs. The estimated ACC value of the MHCBW technique is 0.9999, which indicates that the WBs could be correctly extracted.
The error detection and correction are applied on 3 pixels, i.e., 24 bits, by spreading them in 2 evacuation units. In each unit, only 1 bit error is identified and corrected by applying the modified Hamming code. The error detection and correction ideas can be extended to 2 or more bits per unit by changing the modified Hamming code or introducing a new error-detecting and correcting code.
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