Efficient Reversible Data Hiding Algorithms Based on Dual Prediction

Signal & Image Processing : An International Journal (SIPIJ) Vol.7, No.2, April 2016
DOI : 10.5121/sipij.2016.7201 1
EFFICIENT REVERSIBLE DATA HIDING
ALGORITHMS BASED ON DUAL PREDICTION
Enas N. Jaara and Iyad F. Jafar
Computer Engineering Department, The University of Jordan, Amman, Jordan
ABSTRACT
In this paper, a new reversible data hiding (RDH) algorithm that is based on the concept of shifting of
prediction error histograms is proposed. The algorithm extends the efficient modification of prediction
errors (MPE) algorithm by incorporating two predictors and using one prediction error value for data
embedding. The motivation behind using two predictors is driven by the fact that predictors have different
prediction accuracy which is directly related to the embedding capacity and quality of the stego image. The
key feature of the proposed algorithm lies in using two predictors without the need to communicate
additional overhead with the stego image. Basically, the identification of the predictor that is used during
embedding is done through a set of rules. The proposed algorithm is further extended to use two and three
bins in the prediction errors histogram in order to increase the embedding capacity. Performance
evaluation of the proposed algorithm and its extensions showed the advantage of using two predictors in
boosting the embedding capacity while providing competitive quality for the stego image.
KEYWORDS
Prediction, Prediction Error, Histogram Shifting, Reversible Data Hiding, Watermarking.
1. INTRODUCTION
Data hiding is an important technology in the areas of information security and multimedia
copyright protections as it allows the concealment of data within the digital media for copyright
protection and data protection. Many schemes of data hiding have been proposed to address the
issues and challenges related to hiding the data, such as embedding capacity, imperceptibility and
reversibility.
In this technique, the data is supposed to be seamlessly hidden or embedded into a carrier or
cover signal (audio, images, video) in way that makes it hard for unauthorized people to access it
[1]. In the digital imaging domain, several data hiding techniques have been proposed [2-4].
Despite the efficiency of these techniques in protecting the data, most of them are not capable of
restoring the original cover image upon the extraction of embedded data. This poses a challenge
to applications that require the preservation of the cover image after the hidden data is extracted.
Accordingly, a great interest has grown in the past few years in the development of reversible
data hiding (RDH) techniques that are capable of restoring the original image.
Several RDH techniques have been proposed in the literature and they compete in different
aspects which include the embedding capacity, the quality of the stego image, size of overhead
information and computational complexity [2]. Generally, they can be grouped into three
different classes based on the concept of operation: difference expansion, histogram shifting, and

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prediction-based techniques. Difference expansion (DE) algorithms are one popular class of
reversible data hiding that are characterized with low distortion and relatively high embedding
c b
a x
Figure 1 Context for predicting pixel x
capacity. The first difference expansion technique was proposed by Tian in [5]. In this technique,
the cover image is partitioned into a series of non-overlapping pixel pairs. A secret bit is then
embedded using the difference expansion of each pixel pair. Several DE-based algorithms were
developed based on Tian’s technique [6-9]. Alattar [6] used DE with vectors instead of pixel pairs
to extend and improve the performance of Tian’s algorithm. Hu, et al. proposed a DE-based
technique that improved the compressibility of the location map [8]. Compared to traditional DE-
based algorithm, their technique increased the embedding capacity and performed well with
different images.
Another important category of RDH algorithms are those that are based on the idea of histogram
shifting (HS) [10-13]. Actually, the basis of these algorithms is the work presented by Ni, et al.
[13]. In this algorithm, the histogram of the intensities in the original image is computed. Then,
the histogram bins that lie between the peak bin and a zero (or minimum) bin is shifted by one
toward the zero bin to open space to embedded data. Afterwards, the secret data bits are
embedded by modifying the intensity value that corresponds to the peak only. This technique
provided reasonable embedding capacity with minimum peak-signal-to-noise ratio (PSNR) of
48.1 dB. However, the main drawback of this technique is the limited hiding capacity due to the
fact that it is dependent on the pixel count of the peak value, which is relatively low in natural
images. Additionally, the embedded secret data cannot be recovered without knowing the values
of peak and zero point of histogram. So the peak and zero points must be recorded as overhead or
side information. Many algorithms were proposed to enhance the embedding capacity of Ni’s
algorithm while taking its advantage of producing high quality stego images. Hwang, et al. [10]
extended Ni’s algorithm by using two zero points and one peak point of the histogram to embed
the data. Lin, et al. [12] employed multilevel hiding strategy to obtain high capacity and low
distortion.
In order to take advantage of the HS techniques in terms of reversibility, several techniques
attempted to overcome the issue of limited embedding capacity by extending the approach to
histogram of prediction errors. Basically, these techniques modify the values of the prediction
errors, which are computed using some predictor, instead of the actual intensities. The use of
prediction errors is motivated by the fact that these errors are sharply centred near zero. This
implies higher embedding capacities and avoids the need to save the peaks and zeros when
compared to the original HS algorithm. Hong, et al. proposed extending Ni’s algorithm by using
the median edge detector (MED) [15]. The MED predicator computes the prediction p of pixel x
using three neighbouring pixels a, b and c using
p = ൝
minሺa, bሻ , if c ≥ maxሺa, bሻ
maxሺa, bሻ , if c ≤ minሺa, bሻ
a + b − c, othrwise
(1)

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where a, b and c pixels are defined with respect to pixel x as shown in Figure 1. Afterwards, the
prediction error (PE) which is the difference between pixel value and its prediction is computed.
These prediction errors are changed based on their values and the bits of the secret message.
Basically, the error values of 0 and -1 are used for embedding only. On other hand, prediction
errors greater than 1 and less than -1 are incremented and decremented by 1, respectively. This is
done to free the histogram bins at 1 and -2 to allow embedding of secret bits with value of 1,
while zero bits are embedded in the 0 and -1 bins. The modified prediction errors are added to the
prediction to produce the new values of the pixels in the stego image, the cover image after
embedding the data. The algorithm showed remarkable results in terms of embedding capacity
when compared to the original HS algorithm and it guaranteed a 48.1 dB as a lower bound for the
quality of the stego image.
Several algorithms utilized the concept in prediction in data hiding [16-19]. Hong, et al. [16]
proposed a reversible data hiding technique that is based on image interpolation and the detection
of smooth and complex regions in the host images. Li, et al. [17] and Lin, et al. [18] introduced
an information hiding scheme, with reversibility, based on pixel-value-ordering (PVO) and
prediction-error expansion.
One of the main issues of prediction-based reversible data hiding algorithms is related to the type
of the predictor that is used to compute the prediction errors. The accuracy of the predictor affects
the embedding capacity and the quality of the stego image. So many predictors were used in
different data hiding algorithms in the literature. However, most proposed algorithms rely on
using a single predictor. The objective of this paper is to improve the efficiency of prediction-
based reversible data hiding algorithms by designing an algorithm that employs two predictors to
improve the prediction accuracy, thus the embedding capacity.
The proposed algorithm is based on the efficient modification of prediction errors (MPE)
algorithm; however, it incorporates two predictors and uses only one bin of the prediction errors
histogram for embedding the data, and it is referred to as 1-Bin MPE2. The1-Bin MPE2 algorithm
is further extended to use more prediction errors in the embedding phase in order to increase the
embedding capacity. These extensions are referred to by 2-Bin MPE2 and 3-Bin MPE2
algorithms. The performance evaluation of the proposed algorithm showed its ability to increase
the embedding capacity with competitive image quality. Additionally, no overhead information is
added to cope with the increase in the number of predictors. The rest of this paper is organized as
follows. In Section 2, the proposed algorithm and its extensions are presented, followed by the
experimental results in Section 3. Finally, the paper is concluded in Section 4.
2. THE PROPOSED ALGORITHM
As we mentioned earlier, most prediction-based RDH rely on the use of a single predictor to
compute predictions that are used for data embedding. This may put a limitation on the prediction
accuracy, since different predictors behave differently at the same pixel in the image [20,21]
which consequently affects the embedding capacity and possibly the visual quality of the stego
image.
In this paper, we propose a new histogram-shifting RDH algorithm that is based on the idea of
employing two predictors to compute the predictions in order to take advantage of the different
capabilities of different predictors. This is expected to increase the prediction accuracy, hence,
increasing the embedding capacity. Additionally, and unlike the MPE algorithm [15], the
proposed algorithm uses one bin of the prediction errors histogram for embedding the data. This
algorithm, referred as the 1-Bin dual predictor MPE (MPE2), is further extended to use more

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prediction errors in the embedding phase in order to increase the embedding capacity. These
extensions are referred to by 2-Bin MPE2 and 3-Bin MPE2.
2.1. Design Considerations
The proposed algorithm is essentially based on the modification of prediction errors (MPE)
algorithm [15]. In other words, it is a histogram shifting technique that is applied to prediction
errors. However, the proposed 1-Bin MPE2 algorithm uses two predictors instead of a single one
and uses one bin from the prediction errors histogram for embedding. Specifically, the algorithm
uses the error value of 0 for embedding as it is usually the most occurring value in the prediction
errors histogram of natural images. Accordingly, when the cover image is scanned during the
embedding phase, two predictors are used to compute the prediction at each pixel. When the
prediction error of any of these predictors is 0, this predictor is selected for embedding. However,
identifying the selected predictor at each pixel and guaranteeing reversibility during the extraction
pose a challenge on the design of the proposed algorithm.
Consider the case for embedding a secret bit of value 1 in a pixel with intensity value of 105
using two predictors. If the predictions of these predictors are P1 = 106 and P2 = 105, then the
prediction errors between the original pixel value and these predictions are PE1 = -1 and PE2 = 0,
respectively. Next, the predictor with prediction error of 0 is used for embedding, and in this
example it is the second predictor. Since the bit to be embedded is 1 and the prediction error is 0,
the modified pixel value in the stego image is computed by shifting the prediction error PE2 to
the right by 1, i.e. the modified prediction error PE2 becomes 1 and the pixel value in the stego
image is 106 which is computed by adding the modified prediction error to prediction.
Now, in the extraction step, the same two predictors are used to compute the predictions in the
stego image and they have the same prediction values P1 = 106 and P2 = 105. However, the
prediction errors have been increased by 1 and become PE1 = 0 and PE2 = 1 due to embedding
since the pixel value in the stego image was incremented by 1. Based on these prediction errors,
the extraction procedure cannot identify the predictor that was originally used for embedding
since we have prediction errors of 0 and 1 which according to MPE algorithm [15] correspond to
embedding of a secret bit of 0 in prediction error 0 or embedding of a secret bit of 1 in prediction
error 0, respectively. This implies that this approach for identifying the predictor might not be
reversible in some cases.
A straight forward approach to overcome the issue of determining the used predictor during the
extraction phase is to store the identity of the predictor at each pixel as an overhead that is
communicated with the stego image to ensure reversibility. However, for an image of size M×N
pixels, the size of the overhead will be (M-1)×(N-1) bits given that one bit is used to store the
identities of the two predictors.
Based on the previous discussion, extending the original MPE algorithm to use two predictors
without the need to increase the overhead size and to guarantee reversibility requires adopting a
strategy for the selection of the predictor that is independent of the change in the prediction error
values after embedding. As a general observation, the prediction errors produced by the two
predictors should not be shifted or modified in all cases. Thus, we investigated all possible cases
and put several rules for modifying the errors based on the relation between the values of the
prediction errors from the two predictors.
The first rule considers the case when one prediction error is 0. In this case, the prediction error of
the other predictor is checked. If it is positive and the bit to be embedded is 1, then both
prediction errors are incremented by 1, i.e. PE1 and PE2 become PE1+1 and PE2+1. On the other

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hand, if the prediction error of the second predictor is negative and the bit to embed is 1, then
both errors are decremented by 1. In both cases, no changes are made to the prediction errors
when the bit to embed is 0 as this will preserve the values of the prediction errors.
However, a careful look at this first rule reveals that this approach is not reversible for some
cases. Specifically, this happens when none of the predictors have zero prediction error. The
following example shows one out of many cases that may make this approach irreversible.
Consider the embedding of a secret bit in a pixel with intensity value of 107 using two predictors.
If the predictions of these predictors are P1 = 106 and P2 = 108, then the prediction errors
between the original pixel value and these predictions are PE1 = 1 and PE2 = -1, respectively.
Thus, none of the predictors produces a prediction error of 0. So, the pixel value should be only
shifted without any embedding. The question now is where to shift the pixel? Suppose that we
shift the data to the right, the modified pixel value in the stego image is computed by shifting the
prediction error to right PE1 = PE1+1=2, and adding it to the predicted value of the first
predictor, i.e. the value of the pixel in the stego image is 108. Now, in the extraction step, the
same two predictors are used to compute the predictions in the stego image and they have the
prediction values P1 = 106 and P2 = 108. However, the prediction errors were increased by 1 and
become PE1 = 2 and PE2 = 0, since the pixel value in the stego image was incremented by 1.
These values indicate that there was embedding a bit of 0 at the pixel since one of the prediction
errors is 0, which completely wrong.
Now suppose that we shift the data to the left, the modified pixel value in the stego image is
computed by shifting the prediction error to left is PE2 =PE2-1= -2, and adding it to the predicted
value of the second predictor, i.e. the value of the pixel in the stego image is 106. Now, in the
extraction step, the same two predictors are used to compute the predictions in the stego image
and they have the same prediction values P1 = 106 and P2 = 108. However, the prediction errors
decrease by 1 and become PE1 = 0 and PE2 = -2, since the pixel value in the stego image was
decremented by 1. Again, these values indicate that there was embedding a bit of 0 at the pixel
since one of the prediction errors is 0, which completely wrong.
Accordingly, we added a second rule that is applied to consider modifying the pixel value
according to the sign of the prediction errors. The two prediction errors must be either positive or
negative in order to modify the corresponding pixel value, i.e. the prediction errors should be
unipolar. If the two prediction errors are positive, then both prediction errors are incremented by
1, i.e. PE1 and PE2 become PE1+1 and PE2+1. On the other hand, if the two prediction errors are
negative, then both errors are decremented by 1 to make this approach reversible.
Going back to the previous example, if the predictions of a pixel with intensity value of 107 are
P1 = 106 and P2 = 108, then the prediction errors between the original pixel value and these
predictions are PE1 = 1 and PE2 = -1, respectively. Thus, none of the predictors produces a
prediction error of 0 and as stated in the second rule, for any bipolar prediction error values, the
value of the corresponding pixel will remain unchanged.
In the extraction step, the same two predictors are used to compute the predictions in the stego
image and they have the same prediction values P1 = 106 and P2 = 108. Then the prediction
errors unchanged PE1 = 1 and PE2 = -1. These values indicate that there was no embedding or
shifting at the pixel since the two prediction errors must be either positive or negative in order to
modify the corresponding pixel value, which is completely right and makes this approach
reversible.
Let’s consider a case when the two prediction errors are positive, consider the embedding of a
secret bit in a pixel with intensity value of 27 using two predictors. If the predictions of these
predictors are P1 = 26 and P2 = 22, then the prediction errors between the original pixel value and

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these predictions are PE1 = 1 and PE2 = 5, respectively. Thus, none of the predictors produces a
prediction error of 0. So, the pixel value should be incremented by 1, i.e. the value of the pixel in
the stego image is 28.
Now, in the extraction step, the same two predictors are used to compute the predictions in the
stego image and they have the same prediction values P1 = 26 and P2 = 22. Then the prediction
errors become PE1 = 2 and PE2 = 6. These values indicate that there was no embedding and there
is shifting at this pixel since the two prediction errors are positives. To recover the original pixel
value, the pixel value should be decremented by 1, i.e. the value of the pixel in the recovered
image is 27 which is the same as in the original image.
In summary, adopting these two rules in the 1-Bin MPE2 algorithm adds no overhead to the
embedding process for the purpose of predictor identification and it works whether the secret bit
is 0 or 1, and whether there is embedding or not since in all cases the prediction errors from all
predictors are adjusted with the same value. It is expected that the proposed algorithm will be
capable of increasing the embedding capacity due to the use of two predictors which increases the
possibility of obtaining a 0 prediction error. Additionally, the quality of the stego images in the
proposed algorithm is expected to be higher than the original MPE algorithm since pixels with
bipolar errors are not modified. In the following two subsections, we present the steps of the
embedding and extractions procedures in the proposed algorithm.
2.2. The Embedding Procedure for the 1-Bin MPE2 Algorithm
To embed secret messages S, let CI be an 8-bit grayscale image with size M × N and (i, j) be the
pixel located on row i and column j in image CI, 1 ≤ i ≤ M, 1 ≤ j ≤ N. SI is the stego image and
the size is the same as CI. Note how the cover image is only used to initialize the first row and
first column of the stego image. The embedding procedure of our algorithm involves calculating
the prediction errors from the neighbourhood of a given pixel, and then embedding the message
bits in the modified prediction errors. The detailed embedding steps are as follows:
Input: An n-bit secret message S and 8-bits M×N grayscale cover image CI.
Output: A M×N stego image SI, end of embedding position L, and a data structure O
containing the overhead information.
Step 1. Prepare an empty 8-bit M×N matrix SI to store the stego image and initialize the
first row and first column with the values of the first row and first column of CI.
Step 2. For the pixels in the range 1 < i ≤ M and 1 < j ≤ N, scan the image in a raster
scan order. If the CI(i,j) is 0 or 255, then record the location of the pixel in O and
go to Step 11.
Step 3. Compute the predictions P1(i, j) and P2(i, j). Where P1(i,j) and P2(i,j) are the
predicted values calculated using two predictors.
Step 4. Calculate the prediction errors PE1(i,j) and PE2(i,j) which are the
difference between the original value CI(i,j) and the predicted values
P1(i,j) and P2(i,j), i.e., PE1(i,j) = CI(i,j) – P1(i,j) and PE2(i,j) = CI(i,j) –
P2(i,j).

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Step 5. In case PE1(i,j) is 0 and PE2(i,j) is greater or equal to 0, then keep PE1(i,j)
unchanged if the secret bit B is 0, or modify PE1(i,j) to PE1(i,j)+1 if the secret
bit B is 1. Compute the pixel value in the stego image by SI(i,j) = P1(i,j) +
PE1(i,j). Go to Step 11.
Step 6. In case PE2(i,j) is 0 and PE1(i,j) is greater than 0, then keep PE2(i,j) unchanged
if the secret bit B is 0, or modify PE2(i,j) to PE2(i,j)+1 if the secret bit B is 1.
Compute the pixel value in the stego image by SI(i,j) = P2(i,j) + PE2(i,j). Go to
Step 11.
Step 7. In case PE1(i,j) is 0 and PE2(i,j) is less than 0, then keep PE1(i,j) unchanged if
the secret bit is 0, or modify PE1(i,j) to PE1(i,j)-1 if the secret bit is 1. Compute
the pixel value in the stego image by SI(i,j) = P1(i,j) + PE1(i,j). Go to Step 11.
Step 8. In case PE2(i,j) is 0 and PE1(i,j) is less than 0, then keep PE2(i,j) unchanged if
the secret bit is 0, or modify PE2(i,j) to PE2(i,j)-1 if the secret bit is 1. Compute
the pixel value in the stego image by SI(i,j) = P2(i,j) + PE2(i,j). Go to Step 11.
Step 9. If both prediction errors PE1(i,j) and PE2(i,j) are greater than 0 or less than 0,
modify PE1(i,j) to PE1(i,j)+1 or PE1(i,j)-1, respectively. Compute the pixel
value in the stego image by SI(i,j) = P1(i,j) + PE1(i,j). Go to Step 11.
Step 10. In case the prediction errors PE1(i,j) and PE2(i,j) are bipolar, then keep SI(i,j)
unchanged.
Step 11. If all bits in the secret message S have been embedded, then record the location
of the pixel L as the last embedding location. Go to Step 13.
Step 12. Update i and j. If pixel location (M-1, N-1) is not processed, then go to
Step 2.
Step 13. Embedding is complete.
The assumption in this algorithm is that the used predictors are 3x3 and causal. Thus, the
scanning in the embedding procedure excludes the first column and first row in the image, so,
these pixels are not used for embedding. The algorithm can be easily modified to accommodate
for larger and/or non causal predictors. Note that the overhead data structure O is used to save the
locations of the pixels at which embedding may cause overflow or underflow. Because no
changes are allowed to the prediction errors if the pixel value after modified is overflow or
underflow case in order make this approach reversible. Fortunately, the size of overhead data
structure O is often zero or negligibly small for most natural images since the overflow/underflow
problem rarely occurs [15]. Also, the last embedding location in the embedding level is saved in
the overhead data structure O. The flowchart of the embedding procedure is shown in Figure 2.

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Figure 2. Flowchart of the embedding procedure of the 1-bin proposed algorithm
2.3. The Extraction Procedure of the 1-Bin MPE2 Algorithm
Using the same scan order sequence in the embedding procedure, we predict the pixel values
again using the same predictors, and calculate the prediction errors PE1 and PE2 at each pixel in
the stego image SI. Then we can restore the original image and the hidden data. The details of the
extraction procedure are shown in Figure 3. The detailed steps for extracting hidden data and
recovering the original image are as follows:

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Input: A M×N stego image SI and a data structure O containing the overhead
information.
Output: An n-bit secret message S and 8-bit M×N grayscale recovered image OI.
Step 1. Prepare an empty 8-bit M×N matrix OI to store the output image and initialize the
first row and first column with the values of the first row and first column of SI.
Prepare an empty array to store the extracted secret message S.
Step 2. For the pixels in the range 1 < i ≤ M and 1 < j ≤ N, scan the image in a raster scan
order. If the location of the pixel is found in O, then set OI(i,j)= SI(i,j). Go to Step
15.
Step 3. Compute the predictions P1(i,j) and P2(i,j). Where P1(i,j) and P2(i, j) are the
predicted values calculated using two predictors.
Step 4. Calculate the prediction errors PE1(i,j) and PE2(i,j) which are the difference
between the original value SI(i,j) and the predicted values P1(i,j) and P2(i,j), i.e.,
PE1(i,j) = SI(i,j) – P1(i,j) and PE2(i,j) = SI(i,j) – P2(i,j).
Step 5. If PE1(i,j) is 0 and PE2(i,j) is greater or equal to 0, append a bit of 0 to S and keep
PE1(i,j) unchanged. Compute the pixel value in the original image by OI(i,j) =
P1(i,j) + PE1(i,j). Go to Step 15.
Step 6. If PE1(i,j) is 1 and PE2(i,j) is greater or equal to 1, append a bit of 1 to S and
modify PE1(i,j) to PE1-1. Compute the pixel value in the original image by OI(i,j)
= P1(i,j) + PE1(i,j). Go to Step 15.
Step 7. If PE2(i,j) is 0 and PE1(i,j) is greater than 0, append a bit of 0 to S and keep
PE2(i,j) unchanged. Compute the pixel value in the original image by OI(i,j) =
Step 8. If PE2(i,j) is 1 and PE1(i,j) is greater than 1, append a bit of 1 to S and modify
PE2(i,j) to PE2-1. Compute the pixel value in the original image by OI(i,j) =
Step 9. If PE1(i,j) is 0 and PE2(i,j) is less than 0, append a bit of 0 to S and keep PE1(i,j)
unchanged. Compute the pixel value in the original image by OI(i,j) = P1(i,j) +
Step 10. If PE1(i,j) is -1 and PE2(i,j) is less -1, append a bit of 1 to S and modify PE1(i,j) to
PE1+1. Compute the pixel value in the original image by OI(i,j) = P1(i,j) +
Step 11. If PE2(i,j) is 0 and PE1(i,j) is less than 0, append a bit of 0 to S and keep PE2(i,j)
unchanged. Compute the pixel value in the original image by OI(i,j) = P2(i,j) +
Step 12. If PE2(i,j) is -1 and PE1(i,j) is less -1, append a bit of 1 to S and modify PE2(i,j) to
PE2+1. Compute the pixel value in the original image by OI(i,j) = P2(i,j) +

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Step 13. If both prediction errors, i.e. PE1(i,j) and PE2(i,j) are greater than 1 or less than -1,
modify PE1(i,j) to PE1(i,j)-1 or PE1(i,j)+1, respectively. Compute the pixel value
in the original image by OI(i,j) = P1(i,j) + PE1(i,j). Go to Step 15.
Step 14. In case the prediction errors, i.e. PE1(i,j) and PE2(i,j) are bipolar, then keep OI(i,j)
unchanged.
Step 15. If the location of the pixel is L, extraction is complete. Otherwise, update i and j
and go to Step 2.
Step 16. Extraction is complete.
In order to demonstrate the idea of the proposed algorithm, we discuss here a detailed numerical
example which considers all possible cases that might be encountered. Suppose that we have a
4x5 image that is shown in Figure 4(a) and assuming the secret message S to be embedded is
(011101)2. Here, we assume the predictions at each pixel are computed using the MED and mean
predictors. The MED predictor is the predictor that is used in MPE algorithm [15]. The mean or
average of three neighboring pixels [22, 23] computes the prediction value P using
P = ‫ہ‬ሺa + b + cሻ/3 ‫ۂ‬ (2)
where •   is the floor operator. As presented in the embedding procedure, the first step is to find
the prediction values P1 and P2 using the MED and Mean predictors, respectively. The algorithm
starts at location (2,2) and computes the predictions P1and P2 to be 6 and 3, respectively.
Accordingly, the prediction errors will be 2 and 5. Since none of the prediction errors is 0 and
both values are positive, no embedding is performed. However, PE1, which is the minimum, is
incremented by 1 and added to P1to compute the pixel value in the stego image SI(2,2) to be 9 as
shown in Figure 4(b).
The algorithm proceed to location (2,3) and computes the predictions P1 and P2 to be 9 and 4,
respectively. Accordingly, the prediction errors will be 0 and 5. Since one of the prediction errors
is 0 and other value is positive, embedding can be performed. However, the first bit in the secret
data is zero, so PE1 is unchanged and added to P1 to compute the pixel value in the stego image
SI(2,3) to be 9 as shown in Figure 4(c).
For location (2,4), the predictions are 9 and 5, respectively. Accordingly, the prediction errors
will be -5 and -1. Since none of the prediction errors is 0 and both are negative, no embedding is
performed. However, PE1, which is the minimum, is decremented by 1 and added to P1 to
compute the pixel value in the stego image SI(2,4) to be 3 as shown in Figure 4(d).
At location (2,5), the computed predictions P1 and P2 are 3 and 4, respectively. Accordingly, the
prediction errors will be 0 and -1. Since one of the prediction errors is 0 and other value is
negative, embedding can be performed. Since the second bit in the secret data is one, PE1, is
decremented by 1 and added to P1 to computed the pixel value in the stego image SI(2,5) to be 2
as shown in Figure 4(e). After hiding the secret data 011101 in the original image, the stego
image is shown in Figure 4(f).
In the extraction process, we use the same scan order as in the embedding process to predict pixel
values again, and calculate the prediction errors PE1 and PE2 using the same two predictors. We
realize that, when the value PE1 or PE2 is 0, then the embedded secret bit is 0. However, when
the value PE1 or PE2 is 1 or -1, then a secret bit of value 1 is embedded in this

11
Figure 3. Flowchart of the extraction procedure of the 1-bin algorithm
pixel. Lastly, if the value PE1 or PE2 is not one of the three numbers -1, 0 and 1, then there is no
bit embedded. Since we have changed the prediction errors during embedding, the original image
can be recovered by modifying the prediction errors back to their original. Figure 5(a) shows the
stego image. As shown in the extracting procedures, the first step is to find the predictive pixel
values P1 and P2 for location (2,2). To compute the predictions P1and P2, we

12
Figure 4. Embedding Example (a) Original image (b) – (e) embedding in consecutive pixels (f) stego image
Figure 5. Extraction Example. Stego image is (a) while Images (b) through (e) show the extraction in
consecutive pixels (f) the original image after extraction.
used the same MED and Mean predictors. P1 and P2 will have the same values obtained in the
embedding procedure as shown in Figure 4(a). After extraction process ends, we obtain the secret
data and the covered image again shown in Figure 5(f).
2.4. Extensions of the 1-Bin MPE2 Algorithm
The performance of the 1-Bin MPE2 algorithm can be further improved in terms of embedding
capacity by using more prediction error values for embedding. In this section, we discuss the
extension of the proposed algorithm to use two and three bins. We refer to these extensions as the
2-Bin MPE2 and 3-Bin MPE2 proposed algorithms. Also, we discuss extending the algorithm to
incorporate more than two predictors.
A straight forward approach to increase the embedding capacity of the proposed 1-Bin MPE2
algorithm is to use more prediction error values for embedding. Here, we propose the 2-Bin
MPE2 algorithm that uses error values of 0 and -1, which are the error values used by the 2-Bin

13
MPE algorithm. The steps in embedding procedures for the 2-Bin MPE2 algorithm are the
essentially same as presented in the embedding procedure of the 1-Bin MPE2 algorithm.
However, a third rule is added and used during the embedding and extraction phases. The new
rule considers the case when one prediction error is -1, which is the new value that is considered
for embedding. In this case, the prediction error of the other predictor is checked. If it is
Figure 6. Benchmark test images.
negative and the bit to embed is 0, then both prediction errors are decremented by 1, i.e. PE1 and
PE2 become PE1-1 and PE2-1. And if the bit to embed is 1, then both prediction errors are
decremented by 2, i.e. PE1 and PE2 become PE1-2 and PE2-2. On the other hand, if the
prediction error of the second predictor is positive, no data will be embedded. Additionally,
when the prediction errors of the two predictors are both negative and less than -1, they are
shifted to the left by 2 instead of 1 to guarantee reversibility. However, this excessive shifting will
result with images quality below 48.1 dB.
A second simple extension to the 1-Bin MPE2 considers using error values of -1, 0 and 1 for
embedding. Here, we propose the 3-Bin MPE2 algorithm that uses error values of 0, -1 and 1.
The steps in embedding procedures for the 3-Bin MPE2 algorithm are the essentially same as
presented in the embedding procedure of the 2-Bin MPE2 algorithm. However, a forth rule is
now added and used during the embedding and extraction phases. The new rule considers the case
when one prediction error is 1, which is the new value that is considered for embedding. In this
case, the prediction error of the other predictor is checked. If it is positive and the bit to embed is
0, then both prediction errors are incremented by 1, i.e. PE1 and PE2 become PE1+1 and PE2+1.
In case the bit to embed is 1, then both prediction errors are incremented by 2, i.e. PE1 and PE2
become PE1+2 and PE2+2. On the other hand, if the prediction error of the second predictor is
negative, no data will be embedded. Additionally, when the prediction errors of the two
predictors are both positive and greater than 1, they are shifted to the right by 2 instead of 1 to
guarantee reversibility of this version. However, this excessive shifting will result with images
quality below 48.1 dB.

14
3. EXPERIMENTAL RESULTS
In this section, we evaluate the performance of the proposed algorithm and its extensions and
compare it with other RDH algorithms. The evaluation was performed on a large set of
benchmark images that are usually used for this purpose. In this paper, we present sample results
obtained for a set of commonly used benchmark images are obtained from (USC-SIPI Image
Database) [24]. The test images are shown in Figure 6. In all experiments, a random secret
message is generated an embedded in the images using different algorithms.
In the proposed algorithm and its extensions, the mean [23] and the MED [15] predictors are used
due to their simplicity and efficiency. These predictors compute the predictions as given in (1)
and (2). Nonetheless, this does not imply that the proposed algorithms work only with these
predictors.
The proposed algorithm and its extensions are compared with the original version of the MPE
algorithm [15], Hong, et al. algorithm [16], Li et al. [17] and Lin, et al. algorithm [18]. These
algorithms are selected as they are prediction-based algorithms and they are proposed to produce
high image quality at reasonable payloads. In addition, the comparison includes an extended
version of the MPE algorithm. Specifically, this extension, 3-Bin MPE, uses three prediction
errors (-1, 0, and 1) instead of two and is used to provide a fair comparison with the 2-Bin MPE2
algorithm.
The evaluation considered using two performance metrics; the peak signal-to-noise ratio (PSNR)
and the pure embedded capacity (EC). The PSNR [25-27] of a stego image SI when compared
with original cover image CI is given by
ܴܲܵܰ = 10 logଵ଴
ଶହହమ
ቀ
భ
ಾಿ
ቁ ∑ ∑ [ௌூሺ௜,௝ሻି஼ூሺ௜,௝ሻ]మಿషభ
ೕసబ
ಾషభ
೔సబ
(3)
where M and N are the number of rows and columns in the images, respectively. Higher values
for the PSNR are preferable as they indicate better correspondence between the original image CI
and the stego image SI. The pure embedded capacity is basically the total number of bits
embedded in the stego image.
Many experiments were performed to evaluate the performance of the proposed algorithm and its
extensions. The experiments include the performance evaluation of different algorithms at
maximum embedding capacity and variable payload. Additionally, the experiments investigated
the effect of using more than two predictors in the proposed algorithms. The details of these
experiments are presented in the following subsections.
3.1. Evaluation under Maximum Embedding Capacity
The experiment here tests the performance of the proposed algorithm and its extensions and
compares to other algorithms in terms of the maximum embedding capacity and the associated
image quality. Table 1 and Table 2 list the pure embedding capacity and PSNR values for
different algorithms, respectively.
For the 1-Bin MPE2 algorithm, it is clear from the numbers that it outperforms the original MPE
[15], Hong, et al. [16], Li, et al. [17] and Lin, et al. [18] algorithms in terms of the maximum
embedding capacity (EC). As a matter of fact, the 1-Bin proposed algorithm achieved a
remarkable increase in the embedding capacity despite the fact that it uses one bin only for
embedding. This is related to the fact that the proposed algorithm uses two predictors instead of

15
one as in the 2-Bin MPE, which increases the possibility of obtaining more zero values for the
prediction errors that are used for embedding.
Table 2 lists the PSNR values of different algorithms. It is obvious how the PSNR values of the 1-
Bin MPE2 are slightly higher than those of the 2-Bin MPE. This related to the fact that some of
the pixels in our algorithm are not modified when the prediction errors are bipolar. When the
PSNR values of Hong, et al. [16], Li, et al. [17] and Lin, et al. [18] are compared with those of
the 1-Bin MPE2, it is clear that the1-Bin MPE has relatively lower values. However, this little
difference is hardly noticeable when the stego images from different algorithms are compared
visually as shown in Figure 7. This makes the proposed algorithm highly competitive as it has
higher embedding capacity with comparable visual quality for the stego images. The following
simple theoretical analysis verifies the PSNR values obtained in the 1-Bin proposed algorithm. In
the worst case, assume that the probability of obtaining one out of the three cases for prediction
errors (all positive, all negative and bipolar) encountered during embedding is 1/3 and all of the
bits in the secret message are ones. Since all bits to embed are 1, prediction errors are
incremented by 1 or decremented by 1 when all errors are positive and negative, respectively.
However, no the errors are not modified in case of bipolar error. Accordingly, the PSNR value
will be 10 × log10(255/ (
ଵమାଵమ
ଷ
)) or 49.89 dB. However, the quality of stego image will be around
Table 1. Comparison between different algorithms in terms of pure maximum embedding capacity
(bits)
Image
2-Bin
MPE
[15]
3-Bin
MPE
Hong et
al. [16]
Li, et
al.
[17]
Lin, et
al. [18]
The proposed algorithm (MPE2)
1-Bin 2-Bin 3-Bin
Lena 46,667 63,489 45,416 27,006 33,111 57,406 77,746 101,121
Baboon 39,863 56,263 13,024 15,665 18,224 40,957 48,250 64,019
Airplane 66,153 82,522 62,813 36,193 46,367 69,213 89,184 116,517
Peppers 60,160 79,803 35,603 35,688 44,922 62,796 82,419 106,634
Boat 45,705 62,174 28,739 30,711 37,367 46,760 64,211 83,615
Barbara 35,727 49,268 34,423 21,361 25,669 37,685 50,445 65,619
Average 49,046 65,587 36,670 27,771 34,277 52,470 68,709 89,588
Table 2. Comparison between different algorithms in terms of PSNR (dB) at maximum capacity
Image
2-Bin
MPE
[15]
3-Bin
MPE
Hong
et al.
[16]
Li, et
al.
[17]
Lin, et
al. [18]
The proposed algorithm (MPE2)
1-Bin 2-Bin 3-Bin
Lena 48.56 44.95 49.98 52.31 50.91 49.64 46.84 44.79
Baboon 48.49 44.91 49.69 51.77 50.42 49.67 46.36 44.44
Airplane 48.73 45.20 50.15 53.08 51.61 49.78 47.16 45.14
Peppers 48.69 45.21 50.05 52.85 51.45 49.74 47.03 45.01
Boat 48.55 44.96 49.90 52.53 51.07 49.65 46.60 44.60
Barbara 48.45 44.79 49.79 52.03 50.65 49.52 46.26 44.24
Average 48.58 45.00 49.93 52.43 51.02 49.67 46.71 44.70

16
this value since probability of obtaining bipolar errors is not always equal to 1/3 in addition to the
fact that the secret message is usually a mix of zeros and ones.
Considering the 2-Bin MPE2 algorithm, Table 1 shows the significant increase in the embedding
capacity due to incorporating one more bin in the embedding process. Comparing with the 2-Bin
MPE shows the advantage of using two predictors in increasing the embedding capacity, despite
the fact that these two algorithms use two bins for embedding. Nonetheless, this increase in
Figure 7. Results for different algorithms at maximum embedding capacity for the original image Lena
(a) 2-Bin MPE [15] (b) 3-Bin MPE (c) Hong et al. [16] (d) Li et al.[17] (e) Lin et al. [18]
(f) 1-Bin MPE2 (g) 2-Bin MPE2 (h) 3-Bin MPE2.
embedding capacity comes at the cost of decreasing the PSNR values in the 2- Bin MPE2
algorithm. However, this decrease is hardly noticeable by the human eye since the PSNR values
are higher than 40 dB [28] and as shown in Figure 7. Similar observations in terms of increasing
the embedding capacity and the associated decrease in the PSNR values can be drawn when the
3-Bin MPE2 is considered and compared with other algorithms, especially the 3-Bin MPE
algorithm. In this case, the increase in the embedding capacity and the comparable PSNR values
for the 3-Bin MPE2 are related to using two predictors.
The theoretical analysis for 2-Bin version on the lower PSNR bound is similar to the discussion
presented for the 1-Bin MPE2 algorithm except that negative prediction errors are decremented
by 2 instead of 1 when the bit to be embedded is 1. Thus, the PSNR will be 10 ×
log10(255/(
ଵమାଶమ
ଷ
)) or 45.91 dB. Similarly, the lower PSNR bound for the 3-Bin MPE2 algorithm
will be 10 × log10(255/(
ଶమାଶమ
ଷ
)) or 43.87 dB.
In addition to the results presented for the images shown in Figure 6, the proposed algorithm and
its extensions were tested on 1000 images of size 512×512 selected from a large image database
(Image Database Website) [29]. The maximum EC and PSNR values are listed in Table 3. The
results shown in Table 3 reveal that the 3-Bin MPE2 algorithm performs better than all others
algorithms in terms of embedding capacity However, and as discussed earlier, the increase in
embedding capacity comes at the cost of lowering the PSNR values. Additionally, the maximum

17
payload of the 2-Bin version of the proposed algorithm is also higher than all others algorithms.
Comparing the 2-Bin version to the 2-Bin MPE shows the power of the proposed algorithm.
When higher PSNR values are considered, the 1-Bin version of the proposed algorithm achieves
competitive values when compared with the original MPE [15], Hong, et al. [16], Li, et al. [17]
and Lin, et al. [18] algorithms, but with higher EC.
3.2. Evaluation under Variable Payload
The proposed algorithm and its variants were also investigated when the payload is less than the
maximum embedding capacity. Specifically, image quality in terms of PSNR values is assessed
when small payloads are embedded in the images. Figure 8 shows examples for the PSNR
Table 3. Comparison of average maximum embedding capacity (bits) and
PSNR (dB) on images selected from a large image database [29]
Algorithm Maximum EC PSNR
2-Bin MPE (Hong, et al., 2009) 61,983 48.74
3-Bin MPE 73,765 45.23
Hong, et al., (2011) 64,777 50.19
Li, et al., (2013) 31,585 53,28
Lin, et al., (2014) 39,460 51,43
1-Bin MPE2 67,266 49.84
2-Bin MPE2 85,238 47.00
3-Bin MPE2 106,842 45.12
Figure 8. PSNR values for different algorithms under variable embedding capacity for images
(a) Lena (b) Cameraman (c) Toys (d) Baboon.
values of the different algorithms with variable payload size when applied to Lena, Cameraman,
Baboon and Toys images. The figure clearly illustrates that 1-Bin MPE2 algorithm outperforms

18
the original MPE algorithm [15] and its extensions. This is mainly due to the fact that some
pixels in the cover image are not modified when the prediction errors are bipolar in the proposed
1-Bin MPE2 algorithm. Additionally, the use of two predictors improves the prediction accuracy.
This implies that fewer pixels need to be modified to embed a specific payload, which improves
the PSNR values. Comparing the proposed algorithm with Hong, et al. [16], Li, et al. [17] and
Lin, et al. [18] algorithms, it is evident, for some images, how these algorithms outperform the
proposed algorithm and its extensions. For example, in the Cameraman image, these algorithms
have better PSNR values when the payload is lower than 40000 bits. However, the proposed 1-
Bin algorithm performs better when the payload is increased.
Going back to Figure 8, it is obvious how the 2-Bin version and the 3-Bin version of the proposed
algorithm outperform the 3-Bin version of the MPE algorithm in terms of PSNR at the same
payload. The 2-Bin version of the proposed algorithm can do better than the original MPE
algorithm, e.g. for images Toys and Baboon, even that 2-Bin version pixels may be shifted by 2
and in original MPE algorithm, the shift only by one. This shows the power of the proposed
algorithm by utilizing the bins of two histograms of prediction error for embedding and when
more accurate predictions is provided, it will result with modifying less pixels to embed the same
payload as the image is scanned.
On overall, these results prove the efficiency of the proposed algorithms for embedding small and
large payloads with competitive image quality. The 2-Bin version and 3-Bin version of the
proposed algorithm have a lower PSNR values when compared to Li, et al. [17] and Lin, et al.
[18] algorithms. This can be explained by the fact that the 2-Bin version and 3-Bin version of the
proposed algorithms shift some pixels by more than 1 depending on the outcome of the prediction
errors, while the algorithms in Li, et al. [17] and Lin, et al. [18] are designed to shift pixels by 1
at maximum. However, the maximum embedding capacity of 2-Bin version and 3-Bin version of
the proposed algorithms are much higher than that of Li, et al. [17] and Lin, et al. [18].
Additionally, this small difference in PSNR is hardly noticeable by the human eye as we
discussed earlier.
3.3. Evaluation with More than Two Predictors
It is known that the embedding capacity in prediction-based RDH algorithms depends on the
prediction accuracy. Accordingly, if the number of predictors increases, the chance of obtaining
prediction errors values that are used for embedding will increase. This would in turn result in
increasing the embedding capacity, so; we considered the evaluation of the proposed algorithms
when the number of predictors is increased. Specifically, we considered using three and four
predictors. This evaluation requires no modification to the steps outlined in the embedding and
extraction procedures. The only difference lies in the fact that more predictions are computed at
each pixel in the image. The two additional predictors that we used in this evaluation are the
median and minimum predictors. The Median and minimum of three neighbouring pixels
computes the prediction value P using equation (4) and (5). The median of a set of data is the
middle value of a sorted list [21]. The average of two middles is calculated if the number of list n
is even. However, the median will be the value of number 1/ 2n + if the number of list n is odd.
P = Medianሺ[a b c]ሻ (4)
P = Minimumሺ[a b c]ሻ (5)
Table 4 shows the embedding capacity and the PSNR values for the 1-Bin MPE2 algorithm and
its extensions when two, three and four predictors are used. The numbers show a slight difference
in the performance of the three algorithms when the number of predictors is increased. Although
this contradicts with the general understanding that increasing the number of predictors should

19
increase the prediction accuracy, the behaviour of the three algorithms can be simply explained
by considering Figure 9 which shows the distribution of prediction errors in terms of polarity for
four different images as the number of predictors is increased. The figure clearly shows how
increasing the predictors reduce the possibility of obtaining unipolar errors which are used for
embedding in the proposed algorithms. It is worth to mention that the increase in the PSNR
values in some cases is related to the fact that using more predictors results in having more
bipolar errors. This implies that the corresponding pixels are not modified according to the
proposed algorithms.
Table 4. Comparison between different algorithms using different number of predictors in
terms of pure maximum embedding capacity (bits) and PSNR
Image
1-Bin MPE2
Algorithm Using
Two Predictors
1-Bin MPE3
Algorithm Using
Three Predictors
1-Bin MPE4
Algorithm Using
Four Predictors
Capacity PSNR Capacity PSNR Capacity PSNR
Lena 57,406 49.64 57,232 49.99 53,580 50.70
Baboon 38,957 49.67 31,151 49.99 27,199 50.65
Airplane 69,213 49.78 70,501 50.19 64,922 50.85
Peppers 60,796 49.74 60,553 50.11 55,702 50.84
Boat 46,760 49.65 46,764 49.97 44,025 50.66
Barbara 35,685 49.52 35,403 49.85 33,221 50.53
Figure 9. Distribution of prediction errors using variable number of predictors for images
(a) Lena (b) Airplane.
4. CONCLUSIONS
The goal of this paper is to improve the efficiency of prediction-based reversible data hiding
algorithms by designing an algorithm that employs two predictors to improve the prediction
accuracy, thus the embedding capacity. The proposed algorithm is based on the efficient
modification of prediction errors (MPE) algorithm; however, it incorporates two predictors and
uses only one bin of the prediction errors histogram for embedding the data, and it is referred to
as 1-Bin MPE2. Performance evaluation of the proposed algorithm showed its ability to increase
the embedding capacity with competitive image quality. Additionally, no overhead information is
added to cope with the increase in the number of predictors. These results motivated us to
propose two simple extensions extend the proposed algorithm. Basically, these extensions
consider the use of more bins of the prediction errors histogram. Specifically, the original

20
algorithm is modified to use two and three bins. These extensions are referred to by 2-Bin MPE2
and 3-Bin MPE2. These extensions provide significant increase in the embedding capacity with
reasonable and acceptable image quality.
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AUTHORS
Enas N. Jaara received her B.Sc. and M.Sc. degrees in computer engineering from the University of
Jordan in 2007 and 2015, respectively. She is currently working as a teaching assistant and lab supervisor in
the Computer Engineering Department at the University of Jordan. Her research interests are in embedded
systems and image processing.
Iyad F. Jafar received his Ph.D. degree in Computer Engineering from Wayne State University, Michigan,
in 2008. He is currently working as an associate professor in the Department of Computer Engineering at
the University of Jordan. His research interests are in signal and image processing, pattern recognition,
multimedia and computer networks.

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