Reversible image authentication scheme based on prediction error expansion

Indonesian Journal of Electrical Engineering and Computer Science
Vol. 21, No. 1, January 2021, pp. 253~262
ISSN: 2502-4752, DOI: 10.11591/ijeecs.v21.i1.pp253-262  253
Journal homepage: http://ijeecs.iaescore.com
Reversible image authentication scheme based on prediction
error expansion
Thai-Son Nguyen, Phuoc-Hung Vo
School of Engineering and Technology, Tra Vinh University, Tra Vinh, Vietnam
Article Info ABSTRACT
Article history:
Received Mar 19, 2020
Revised Jul 21, 2020
Accepted Aug 21, 2020
Reversible image authentication scheme is a technique that detects tampered
areas in images and allows them to be reconstructed to their original version
without any distortion. In this article, a new, reversible, image authentication
scheme based on prediction error expansion is proposed for digital images.
The proposed scheme classifies the host image into smooth blocks and
complex blocks. Then, an authentication code that is created randomly with a
seed is embedded adaptively into each image block. Experimental results
showed that our proposed scheme achieves the high accuracy of tamper
detection and preserved high image quality. Moreover, the proposed scheme
achieved the reversibility, which is needed for some special applications,
such as fine artwork, military images, and medical images.
Keywords:
Fragile watermark
Image authentication
PEE
Reversibility
Tamper detection This is an open access article under the CC BY-SA license.
Corresponding Author:
Thai-Son Nguyen
School of Engineering and Technology
Tra Vinh University
126 Nguyen Thien Thanh Str., Ward 5, Tra Vinh city, Vietnam
E-mail: thaison@tvu.edu.vn
1. INTRODUCTION
With the rapid Advancement of network and digital image processing technologies, this leads that
copyright infringements can occur easily. For example, digital content can be copied illegally and modified
maliciously when it is stored or transmitted over the Internet. Therefore, the protection of digital content has
become an issue of increasing concern in both academia and industry [1, 2]. Recently, many authentication
techniques [3-13] have been proposed to identify the trustworthiness of digital content and to protect its
integrity. In principle, authentication techniques can be divided into two categories. The first category is
hashing-based schemes [3-5] in which the hashed result of the image is calculated. Different images provided
distinct hash results; therefore, hashing can be used for authentication. However, the hashed result must be
appended with the original image, and sent to the receiver. To detect received images to be maliciously
modified, the hashed result is re-calculated from the received image and compared with the appended hashed
result. The second category is fragile watermarking schemes [6-19] that can obtain image authentication by
embedding a watermark into the host image. Here, the watermark can be auxiliary information that can be
generated by a pseudo random number generator (PRNG) with the seed. If the received image is suspected to
have been tampered by malicious attackers, the watermark can be extracted to verify the tampered areas. In
this category, the accuracy of the tampered areas and the visual quality of the stego image are two criteria of
the fragile image watermarking techniques. The purpose of the earlier studies of fragile image watermarking
techniques was to verify the integrity of the image’s content in the spatial domain [7-9]. In 2011, Chan [7]
introduced a new image authentication algorithm that used the hamming code to rearrange the bits of pixels.

 ISSN: 2502-4752
Indonesian J Elec Eng & Comp Sci, Vol. 21, No. 1, January 2021 : 253 - 262
254
If a pixel has been tampered, the most-significant bits of the pixel can be determined. Zhang et al. [8]
proposed a novel watermarking scheme using the discrete cosine transform algorithm. If any modifications
are found in the part of the watermarked image, the corresponding data for recovering the image are extracted
from the area without any modification. In 2012, Qin et al. [9] proposed a new authentication technique to
obtain high-quality restoration. Their scheme used image hashing algorithm for generating
authenticationcode. Then, the adaptive bit allocation mechanism is used to encode the restoration bits. In
addition, recent studies on fragile image watermarking techniques [10-13] have been leaded to the image in
the compression domain, i.e., block truncation coding (BTC) and vector quantization (VQ).
From the literature, it is found that most of image authentication schemes are based on irreversible
data hiding algorithms [20-22]. However, the distortion offered by irreversible data hiding is permanent,
meaning that the embedded image cannot be reconstructed to its original version as reversible data hiding
[23, 24]. To meet the requirement of being able to restore the host image completely after detection, Lo and
Hu [25] proposed a reversible image authentication (RIA) scheme. Their scheme obtained the reversibility.
However, the accuracy of the detection is inadequate high while the image quality is unsatisfactory. In [14],
Yin et at. applied Hilbert curve for RIA scheme. Their scheme obtained higher detection rate and visual
quality than those of Lo and Hu’s scheme [25]. Later on, to maintain the integrity of digital images, Hong et
al. [15] proposed new RIA scheme based on IPVO. In this scheme, according to the information of the
unmodified pixels and the location, the hash code is is generated, and then embedded into modifiable pixels.
By doing so, their scheme obtains the greater detection rate while ensuring the satisfactory visual quality of
embedded images. Although the existing schemes effectively detect the tampered areas and can reconstruct
the host image completely if they are un-tampered. However, these schemes fail to protect the modification
in the complex blocks. To further improve the performance of existing schemes, in this article a new, RIA
scheme is proposed for digital images. The PRNG with the seed is used for creating authentication code. To
enhance the quality of the embedded image and to obtain more accurate detection, prediction error expansion
(PEE) [26] is used adaptively for concealing the authentication code with smooth distribution characteristic.
When there is reason to suspect that the image has been tampered by malicious attackers, the tampered areas
are detected. If none of the blocks are modified, the original cover image is reconstructed exactly.
The remain of the paper is organized as follows. The proposd scheme is described in Section 2.
Section 3 discusses the results and comparisons of the proposed scheme with the prior arts. Conclusions are
presented in Section 4.
2. PROPOSED SCHEME
The main purpose of our proposed scheme is to detect whether an image has been tampered or not.
If there are no modified or tampered areas in the image, the stego image is processed for reconstructing the
original version of the host image. If some areas in the image have been modified, they will be detected.
Figure 1(a) shows the framework of the proposed authentication scheme consisting of block classification,
generation of the authentication code, and embedding of the authentication code.
(a) (b)
Figure 1. (a) Framework of the proposed authentication scheme; (b) Example of an image block and its
satellite reference pixels

Indonesian J Elec Eng & Comp Sci ISSN: 2502-4752 
Reversible image authentication scheme based on prediction error expansion (Thai-Son Nguyen)
255
2.1. Block classification
Assume that a host image I of W × H pixels. Firstly, partition the host image into non-overlapping
blocks of size 3 × 3. Let the center pixel C of the current block that is being processed be the reference pixel,
and let L and R be the pixels that are located to the left and right of C, respectively. For non-border blocks,
the reference pixel C has four satellite reference pixels, i.e., SL, SR, SU, and SD, which are located to the left, to
the right, above, and below C, respectively, as shown in Figure 1(b).
𝐶𝑜𝑚𝑝𝑙𝑒𝑥𝑖𝑡𝑦 = max(|𝑆𝐿 − 𝐶|, |𝑆𝑅 − 𝐶|, |𝑆𝑈 − 𝐶|, |𝑆𝐷 − 𝐶|) (1)
Higher complexity values are associated with blocks that are in areas with more complex textures.
Note that according to (1), only the complexity of the non-border blocks can be calculated, thus, border
blocks will not be processed in the proposed scheme. After the complexity values are obtained, they are
compared with a classification threshold TH to determine whether the image block is in a smooth area or in a
complex area as follows. Note that, for different type of block, the different way is used for embedding.
Therefore, the threshold TH is also used to further improve the security of the proposed scheme.
a) Smooth area: AS = {Bi I: Complexity (Bi) < TH}.
b) Complex area: ACom = {Bi I: Complexity (Bi)  TH}.
2.2. Generation of the authentication code
With the host image sizes of W × H pixels, and block sizes of 3 × 3 pixels, a total of k × l image
blocks will be obtained, where k = W/3 and l = H/3. Let two bits be embedded into each image block. Thus,
to generate the authentication code sequence AC with size of k × l × 2 bits, the PRNG with a seed K is
utilized to create k × l random values. Then, the random value rvi is transformed to two bits, w1w2, of
authentication code by using (2), and they are concatenated into the authentication code sequence AC.
𝑤1𝑤2 = 𝑏𝑖𝑛(𝑟𝑣𝑖𝑚𝑜𝑑 22
) (2)
where bin( ) is the binary conversion function, w1w2 is two authentication bits that will be hidden into each
image block i, and w1w2 is in {00, 01, 10, 11}. As we know that the reversible data embedding schemes
provided much less embedding capacity than the irreversible data embedding schemes, thus, only two
authentication bits are embedded into each image block.
2.3. Embedding the authentication code
After block classification and generation of the authentication, two bits w1w2 of authentication code
sequence AC are embedded into each image block. The algorithm of the authentication code embedding is
listed below:
a) Step 1: For each image block Bi, read two bits w1w2 from authentication code sequence AC.
b) Step 2: Compute the prediction errors dL and dR of the left and right adjacent pixels L and R of the
center pixel C via dL = 𝐿 − 𝐶 and dR = 𝑅 − 𝐶, respectively.
c) Step 3: If Bi  AS, embed two bits w1w2 into the prediction errors dL and dR by using (3); here, bit w1 is
embedded into dL and bit w2 is embedded into dR.
𝑑′
= {
𝑑 × 2 + 𝑤 𝑖𝑓 – 𝑇∗
≤ 𝑑 ≤ 𝑇∗
𝑑 − 𝑇∗
𝑖𝑓 – 𝑇∗
> 𝑑
𝑑 + 𝑇∗
+ 1 𝑖𝑓 𝑇∗
< 𝑑
(3)
where d is the prediction error (dL or dR), and d 
is the embedded prediction error (dL

or dR

), w is the
authentication bit, i.e., w1 or w2, and T*
is the embedding threshold that is in the range 0 to 4.
d) Step 4: If Bi  ACom, compute the reference prediction error  using (4).  is used to normalize the
current prediction errors dL and dR as small as possible, based on the satellite reference pixels, which
guarantees that the proposed scheme can embed the authentication bits into the complex area without
distorting the image significantly.
𝜆 = 𝑚𝑖𝑛(|𝐿∗
− 𝐶|, |𝑅∗
− 𝐶|) (4)
where 𝐿∗
= ⌊
𝐶×2+𝑆𝐿
3
⌋ and 𝑅∗
= ⌊
𝐶×2+𝑆𝑅
3
⌋ are calculated from the center pixel C and its two satellite pixels, SL
and SR. Then, the current prediction errors dL and dR are normalized by:

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256
dL
∗
= dL − λ (5)
and 𝑑𝑅
∗
= 𝑑𝑅 − λ (6)
where dL
*
and dR
*
are two normalized prediction errors. Then, two bits w1w2 are embedded into dL
*
and dR
*
by
(3) to generate the embedded prediction errors dL and dR, respectively.
e) Step 5: Modify the pixel values of L and R to 𝐿′
= 𝑑𝐿
′
+ 𝐶 and 𝑅′
= 𝑑𝑅
′
+ 𝐶, respectively.
f) Step 6: Repeat Steps 1 through 5 until the image is processed completely.
In the proposed scheme, note that prediction error expansion (PEE) is used to embed the authentication bits.
To avoid overflow/underflow, only the pixels L and R of each block that satisfy the following
conditions can be used to carry an authentication bit as shown in Figure 2.
{
0 ≤ 𝐶 + 2𝑑 + 1 ≤ 255 𝑖𝑓 −𝑇∗
≤ 𝑑 ≤ 𝑇∗
𝐶 < 255 − 𝑇∗
𝑖𝑓 𝑑 > 𝑇∗
𝐶 ≥ 𝑇∗
𝑖𝑓 𝑑 < −𝑇∗
(7)
where C is the center pixel of the current block, T* is the embedding threshold, and d is the corresponding
prediction error of L or R. Otherwise, the pixels are skipped in the authentication code embedding process,
and their block locations are recorded in a location map, LM. Then, the location map is processed to obtain
reversibility. More discussion of the location map is presented in Subsection 2.5.
2.4. Tampered detection and restoration of the host image
Assume that the owner of the image suspects that a published image has been copied and modified
from her/his image. In this scenario, such image is authenticated to verify whether to be modified or not. If
the image has not been tampered, the original host image can be reconstructed completely after the
authentication sequence is extracted. To extract and verify the authentication code, some system parameters,
i.e., T*, TH, and K, are required. Figure 2 shows a main steps of the tamper detection phase.
Figure 2. Main processes of tamper detection
Two authentication code sequences are generated for tampered detection. The first sequence AC is
generated by using the PRNG with the seed K, as was done in Subsection 2.1. The second authentication
sequence AC is extracted from the embedded-image. After two authentication code sequences have been
obtained, each two bits of AC and AC are compared to determine whether the corresponding image block has
been tampered or not. The tamper detection algorithm is shown in detail as follows:
a) Step 1: Generate AC by using PRNG with the seed K.
b) Step 2: For each block Bi, compute embedded prediction errors 𝑑𝐿
′
= 𝐿′
− 𝐶 and 𝑑𝑅
′
= 𝑅′
− 𝐶 of the left
and right adjacent pixels L and R of the center pixel C, respectively.
c) Step 3: If Bi  AS, the original prediction errors dL and dR can be reconstructed as:
𝑑𝐿 = {
⌊
𝑑𝐿
′
2
⌋ −2𝑇∗
≤ 𝑑𝐿
′
≤ 2𝑇∗
+ 1
𝑑𝐿
′
+ 𝑇∗
𝑑𝐿
′
< −2𝑇∗
𝑑𝐿
′
− 𝑇∗
− 1 𝑑𝐿
′
> 2𝑇∗
+ 1
(8)

257
𝑑𝑅 = {
⌊
𝑑𝑅
′
2
⌋ −2𝑇∗
≤ 𝑑𝑅
′
≤ 2𝑇∗
+ 1
𝑑𝑅
′
+ 𝑇∗
𝑑𝑅
′
< −2𝑇∗
𝑑𝑅
′
− 𝑇∗
− 1 𝑑𝑅
′
> 2𝑇∗
+ 1
(9)
where . is the floor function. If 𝑑𝐿
′
and 𝑑𝑅
′
belong to [−2𝑇∗
, 2𝑇∗
+ 1], the authentication bits w1 and w2 can
be extracted as 𝑤1 = 𝑑𝐿
′
𝑚𝑜𝑑 2 and 𝑤2 = 𝑑𝑅
′
𝑚𝑜𝑑 2, respectively.
d) Step 4: If Bi  ACom, the normalized prediction errors, 𝑑𝐿
∗
and 𝑑𝑅
∗
, can be calculated by:
𝑑𝐿
∗
= {
⌊
𝑑𝐿
′
2
⌋ −2𝑇∗
≤ 𝑑𝐿
′
≤ 2𝑇∗
+ 1
𝑑𝐿
′
+ 𝑇∗
𝑑𝐿
′
< −2𝑇∗
𝑑𝐿
′
− 𝑇∗
− 1 𝑑𝐿
′
> 2𝑇∗
+ 1
(10)
𝑑𝑅
∗
= {
⌊
𝑑𝑅
′
2
⌋ −2𝑇∗
≤ 𝑑𝑅
′
≤ 2𝑇∗
+ 1
𝑑𝑅
′
+ 𝑇∗
𝑑𝑅
′
< −2𝑇∗
𝑑𝑅
′
− 𝑇∗
− 1 𝑑𝑅
′
> 2𝑇∗
+ 1
(11)
The authentication bits w1 and w2 also can be extracted as 𝑤1 = 𝑑𝐿
′
𝑚𝑜𝑑 2 and 𝑤2 = 𝑑𝑅
′
𝑚𝑜𝑑 2,
respectively. Then, the extracted authentication code bits w1w2 are concatenated to the authentication code
sequence AC. Compute the reference prediction error  using (4), as was done in authentication code
embedding phase, and, then, the original prediction errors can be recovered as 𝑑𝐿 = 𝑑𝐿
∗
+ λ and 𝑑𝑅 = 𝑑𝑅
∗
+ λ.
e) Step 5: Read two authentication bits w1w2 from the AC. If 𝑤1𝑤2 = 𝑤1′ 𝑤2′, the image block is marked
as a clear block; otherwise, the image block is marked as a tampered block.
f) Step 6: Restore the original values of pixels L and R via 𝐿 = 𝑑𝐿 + 𝐶 and 𝑅 = 𝑑𝑅 + 𝐶, respectively.
g) Step 7: Repeat Steps 2 through 6 until all image blocks have been processed completely; then combine
all the clear blocks and the tampered blocks to generate the raw detected image. If no tampered blocks
are found, the host image is restored without any distortion.
It is clear that the above raw detected image should be further processed because, in the proposed
scheme, some image blocks can not be used to contain authentication code bits because of the limited
embedding capacity. Therefore, one refinement process should be used for the raw detected image. Each
white block B is evaluated to be changed to a black block or not. To do so, the four test cases in Figure 3
were checked sequentially. For example, in the case 4 as shown in Figure 3(d), if the left and right adjacent
blocks of B are black, then block B is colored black. Each white block in the raw detected image should be
processed to construct the new refined detected image.
(a) (b) (c) (d)
Figure 3. Four test cases for refinement process. (a) Case 1, (b) Case 2, (c) Case 3, (d) Case 4
2.5. Discussion of the location map
Figure 4 shows that the host image is divided into two regions, i.e., A1 and A2. The first region A1
contains two first rows and two first columns of the image. This region is used to record the information of
location map LM. The region A2 consists of the rest of the pixels of the image which is embedded the
authentication code bits and the LSB bits of the region A1. Therefore, the LSBs of pixels in area A1 must be
extracted and merged into the authentication code sequence AC in advance. Let {a1, a2,…, an} be the set of
LSBs of the region A1 that are merged into the authentication code sequence AC = {w1, w2, …, w|AC|} as AC*
= w1||a1||w2||a2||…||w|AC|. Then, instead of using authentication code sequence AC during the embedding
phase, AC*
is used.
In the proposed scheme, avoiding the overflow/underflow problem is critical to the practical use of
the proposed scheme; therefore, the location map is used. Table 1 shows the size of the location map that was

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used during embedding authentication code with TH = 100 and various values of T* into six grayscale
images sized 512×512 [27], military images [28], and medical images [29]. In most cases, no location map is
required. It can be seen that the largest size of the location map is required that is 144 bits for the Peppers
image. However, more than 38,000 bits are embedded into this image as shown in Table 2, meaning that the
embedding capacity is large enough to accommodate the location map. In addition, the location map is still
compressed by using JBIG-kit in [30]. Then, the compressed location map LM, two thresholds, TH and T*,
and the seed K are also encrypted with the secret key PK and embedded into the image for reversibility. For
security reason, the secret key PK is shared between the sender and the receiver in advance.
Figure 4. Image partition and location map embedding
Table 1. Size of the location map (bits)
for various values of T*
T*
Image
0 1 2 3 4
Size of the location map (bits)
Tank 0 0 54 108 144
Car and APCs 0 0 0 0 18
APC 0 0 0 0 54
MRI1 0 0 0 72 117
CT1 0 0 0 18 63
MRA1 0 0 0 0 27
3. RESULTS AND DISCUSSION
The proposed scheme was tested on publicly–available, standard images, including “Lena,” “Boat,”
“Airplane,” “Girl,” “Goldhill,” and “Peppers” [27]. Our computations were implemented on a PC with an
Intel® Xeon® Processor E3-1230 v3 (8M Cache, 3.30 GHz), 8 GB of RAM. In the experiments, Windows 7
Ultimate 64-bit and by Python 2.7 are performed.
Table 2 shows the embedding capacity (EC) with various values of TH and T*. It is clear that the EC
of the proposed scheme increased when the thresholds TH and T* increased. Average EC of 6,866; 18,801;
27,812; 34,244; and 38,837 bits were obtained for TH = 100 when T* was set to 0, 1, 2, 3, and 4,
respectively. The EC was slightly increased when the threshold TH was increased from 100 to 150. Figure 5
shows the visual quality of the stego images with various values of T*, when TH = 100. The average visual
quality of the embedded image decreased when the value of the threshold T* increased. The PSNR of 51.72
dB and 49.90 dB was obtained with T* = 0 and T* = 1, respectively. Figures 6(a) and 6(d) show embedded
images “Lena” obtained by the proposed scheme with TH = 100 and various values of T*. In these four
embedded images, the value of T* was set from 0 to 3, respectively. In the tamper test, the tampered object in
Figure 7(a) was inserted on the wall of each stego image, and its binary version is presented in Figure 7(b).
Figure 8 shows that some white spots were found within the tampered object, meaning that some pixels in the
tampered object had the same value as the original pixels in the stego images.
Table 2. Embedding capacity with various values
of TH and T*
TH T* = 0 T* = 1 T* = 2 T* = 3 T* = 4
50 6,665 18,391 27,439 33,756 38,401
100 6,866 18,801 27,812 34,255 38,837
150 6,869 18,808 27,834 34,274 38,870
Figure 5. Image quality with difference values of T*

259
(a) PSNR = 51.41 dB,
T* = 0
(b) PSNR = 48.94 dB,
T* = 1
(c) PSNR = 46.27 dB,
T* = 2
(d) PSNR = 44.64 dB,
T* = 3
Figure 6. Embedded images (a-d) of the image “Lena” with various values of T*
(a) Tampered object 1 (b) Binary tampered
object
(c) Tampered object 2 (d) Tampered object 3
Figure 7. Tampered object used in the detection test
(a) Pixel difference
image with T* = 0
(b) Block difference
image with T* = 0
(c) Pixel difference
image with T* = 1
(d) Block difference
image with T* = 1
(e) Pixel difference
image with T* = 2
(f) Block difference
image with T* = 2
(g) Pixel difference
image with T* = 3
(h) Block difference
image with T* = 3
Figure 8. Difference images for tamper test
Figure 9 shows the detected results of the proposed schemes with various values of T*. The left
columns list the raw detected images, and the right columns list the refined detected images. No white spots
were found in the refined detected images. In comparison with the binary version of the tampered object in
Figure 7(b), the tampered region of each refined detected image is clearly determined, when the normalized
correlation coefficient (NC) was always larger than 0.918 for different values of T* as shown in Figure 9
while the average value of NC is 0.934 as shown in Table 3. NC can be calculated by (12).
𝑁𝐶 =
∑ ∑ [𝑇𝐼(𝑖,𝑗)−𝑇𝐼𝑚𝑒𝑎𝑛][𝐷𝐼(𝑖,𝑗)−𝐷𝐼𝑚𝑒𝑎𝑛]
𝑊
𝑗=1
𝐻
𝑖=1
√(∑ ∑ [𝑇𝐼(𝑖,𝑗)−𝑇𝐼𝑚𝑒𝑎𝑛]2
𝑊
𝑗=1
𝐻
𝑖=1 )(∑ ∑ [𝐷𝐼(𝑖,𝑗)−𝐷𝐼𝑚𝑒𝑎𝑛]2
𝑊
𝑗=1
𝐻
𝑖=1 )
(12)
where TI is the tampered binary image, DI is the detected image, and H and W are the height and the width of
the tamper binary image, respectively. The notations 𝑇𝐼𝑚𝑒𝑎𝑛 and 𝐷𝐼𝑚𝑒𝑎𝑛 are the average values of all pixels
in TI and DI, respectively. In addition, to further estimate the accuracy of detection, we used F_1 score that is
calculated using (13).
𝐹_1 =
2×𝑃𝑟𝑒𝑐𝑖𝑠𝑖𝑜𝑛×𝑅𝑒𝑐𝑎𝑙𝑙
𝑃𝑟𝑒𝑐𝑖𝑠𝑖𝑜𝑛+𝑅𝑒𝑐𝑎𝑙𝑙
(13)
where Precision is the proportion of true positives among the sum of true positives and false positives and
Recall is the proportion of true positives among the sum of true positives and false negatives, which are
defined in (14) and (15), respectively.

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𝑃𝑟𝑒𝑐𝑖𝑠𝑖𝑜𝑛 =
𝑇𝑟𝑢𝑒 𝑝𝑜𝑠𝑖𝑡𝑖𝑣𝑒
𝑇𝑟𝑢𝑒 𝑝𝑜𝑠𝑖𝑡𝑖𝑣𝑒+𝐹𝑎𝑙𝑠𝑒 𝑝𝑜𝑠𝑖𝑡𝑣𝑒
(14)
𝑅𝑒𝑐𝑎𝑙𝑙 =
𝑇𝑟𝑢𝑒 𝑝𝑜𝑠𝑖𝑡𝑖𝑣𝑒
𝑇𝑟𝑢𝑒 𝑝𝑜𝑠𝑖𝑡𝑖𝑣𝑒+𝐹𝑎𝑙𝑠𝑒 𝑛𝑒𝑔𝑎𝑡𝑖𝑣𝑒
(15)
As can be seen in Figure 9, the value of F_1 score obtained by the proposed scheme is greater than
0.915 for different values of T*, meaning that the proposed scheme provided highly accurate tamper
detection.
(a)Raw detected image
with T* = 0, NC = 0.606,
and F_1 = 0.547
(b) Refined detected
image with T* = 0, NC =
0.919, and F_1 = 0.917
(c) Raw detected image
with T* = 1,NC = 0.637,
and F_1 = 0.586
(d) Refined detected
0.922, and F_1 = 0.920
(e) Raw detected image
with T* = 2, NC = 0.673,
F_1 = 0.633
(f) Refined detected
0.924, and F_1 = 0.923
(g) Raw detected image
with T* = 3, NC = 0.695,
and F_1 = 0.663
(h) Refined detected
0.943, and F_1 = 0.942
Figure 9. Detected images of the proposed scheme
Figure 10 shows the test image “Lena” in the distribution of the embeddable (white color) and un-
embeddable (black color) locations in the proposed scheme with TH = 100. Obviously, when T* increases,
the number of un-embeddable blocks decreases, meaning that more authentication code bits are embedded.
(a) T* = 0 (b) T* = 1 (c) T* = 2 (d) T* = 3
Figure 10. Distributions of embeddable and un-embeddable blocks in the image “Lena”
To justify the performance of the proposed scheme, five existing schemes [12, 14, 15, 22, 25] are
compared with the proposed scheme in Table 3. In the tamper test, the tampered object in Figure 8(a) was
inserted on the wall of twelve embedded images, i.e., six common test images [27], three military images
[28], and three medical images [29]. Table 3 shows that the better PSNR value is obtained by our scheme
among six schemes. In this paper, the average NC and F_1 score are used to estimate the detection accuracy.
Moreover, to further evaluate the performance of the four schemes in detection accuracy, two tampered
objects in Figure 7(c) and (d) are inserted in the wall of each image. As can be seen in Table 3, the higher
detection accuracy is obtained by the proposed scheme, when the average NC and F_1 score both are greater
than 0.910 when double tampered objects are used, while the those of other five schemes [12, 14, 15, 22, 25]
are smaller than 0.905. In summary, the proposed scheme not only has several advantages over other five
existing schemes but also offers high detection accuracy and comparable embedded image quality.
Figure 11 provides the EC and image quality of the grayscale versions of the 24 test images in the
Kodak set (http://ww.r0k.us/graphics/kodak/), with TH = 50 and different values of T*. As can seen in this

261
figure, the larger value of T* is used, the higher EC is achieved and the more distortion is encountered.
However, the average PSNR is larger than 39 dB when more than 54,000 bits has been embedded with T* = 4.
Table 3. Comparison of the proposed scheme and the existing schemes [12, 14, 15, 22, 25]
Schemes
Block size
(pixels)
Average
PSNRs
(dB)
Detection accuracy
Embedding
technique
Reversibility
Single tampered
object
Double tampered
object
Average
NC
F_1
score
Average
NC
F_1
score
Hu et al.
[12]
4 × 4 39.27 0.915 0.896 0.832 0.811
AMBTC
modification
No
Nguyen et
al. [22]
3 × 3 41.92 0.920 0.894 0.827 0.809 Reference table No
Lo and Hu
[25]
4 × 4 51.73 0.918 0.902 0.875 0.862 HS Yes
Yin et al.
[14]
4 × 4 51.82 0.921 0.912 0.889 0.887 IPVO Yes
Hong et al.
[15]
4 × 4 50.40 0.926 0.921 0.903 0.889 IPVO Yes
Proposed 3 × 3 52.39 0.934 0.928 0.914 0.910 PEE Yes
Embedding capacity of 24 Kodak images
Image quality of 24 Kodak images
Figure 11. Performances of our scheme for 24 Kodak images with TH = 50 and different values of T*
4. CONCLUSION
In this article, a novel, RIA scheme is proposed by using PEE technique adaptively for embedding the
authentication code. On the receiver side, the authentication code is extracted to detect tampered areas. If none of
the blocks have been modified, the host image is reconstructed to its original version. Experimental results showed
that the good image quality obtained by proposed scheme when the average PSNR of 52.39 dB and 48.90 dB when
TH = 100 and T* = 0 and T* = 1, respectively. Moreover, the proposed scheme provided a clear tampered area and
achieved reversibility. In addition, the proposed scheme achieved better results than other five existing schemes, in
terms of the visual quality and the detection accuracy. Therefore, it should be suggested to be used for detecting
tampered regions for special applications, i.e., fine artwork, military images, and medical images.
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