An improved capacity data hiding technique based

on image interpolation

Ahmad A. Mohammad1&Ali Al-Haj1&Mahmoud Farfoura2

Received: 23 September 2017 / Revised: 2 July 2018 / Accepted: 25 July 2018

#Springer Science+Business Media, LLC, part of Springer Nature 2018, corrected publication August/2018

Abstract

Data hiding in multimedia objects such as text, images, audio and video clips is a technique

that has been widely used to achieve security for applications requiring copyright protection,

covert communication, and tampering detection. Data hiding can be irreversible or reversible,

where the latter is used to ensure exact recovery of the media object after extracting the hidden

data. Different approaches to achieve reversible data hiding have been proposed. One of the

approaches is the interpolation-based data hiding which has been proposed to achieve high

data hiding capacity. This paper presents a new computationally simple interpolation-based

data hiding technique that increases data hiding capacity and limits the cover image distortion

that is caused by the two major steps of interpolation-based techniques; the downscaling/

expansion step and the data hiding step . Image distortion reduction in the downscaling/

expansion step is achieved by using a new image interpolation algorithm, whereas the image

distortion in the data hiding step is reduced utilizing a new adjustable data hiding algorithm,

which adaptively adjusts the level of tradeoff between data hiding capacity and image quality.

The performance of the proposed technique has been evaluated for data hiding capacity and

image quality using three metrics: peak signal to noise ratio (PSNR), weighted PSNR

(WPSNR), and structural similarity index (SSIM). The data hiding capacity achieved by the

proposed technique can be as high as 1.7bpp, which is higher by 8.5 to 72% as compared to

similar techniques. Moreover, for the data hiding step, the proposed algorithm achieved high

quality images as reflected by values up to 54 dB for PSNR, 78 dB for WPSNR, and 0.9998

for SSIM.

Keywords Data hiding .

Image interpolation .

High capacity data hiding .

Interpolation based data

hiding .

Reversible data hiding

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https://doi.org/10.1007/s11042-018-6465-8

* Ahmad A. Mohammad

[email protected]

1Princess Sumaya University for Technology, Amman, Jordan

2Royal Scientific Society, Amman, Jordan

1 Introduction

Information exchange over the Internet and the widespread use of computers have made access

to the transmitted data extremely simple. This has opened new venues for the exchange of

secret data, which in turn motivated the need for providing security for covert communication

of the confidential data. Thus, the development of protective measures for securing transmis-

sion of secret data has become deemed necessary. Over the last decades, researchers proposed

two fundamentally different methods to secure the transmitted data; cryptography and stega-

nography 1– 56 .

Different cryptographic data hiding algorithms have been proposed in literature 4, 11 ,15 ,

34 ,36 ,40 ,41 ,52 . In these algorithms, the plain messages are scrambled into meaningless

cypher data using secret keys shared by the sending and receiving ends of the transmission

channel. An obvious drawback of these algorithms is that the transmitted encrypted data will

draw the attention to the existence of a secret message. Moreover, sophisticated brute-force

attack may eventually disclose the shared secret keys, which in turn leads to the disclosure of

the transmitted secret data. On the other hand, Steganography conceals the secret message into

a meaningful cover image and hides the mere existence of the secret message 37. However,

embedding the secret message into the cover image results in a distorted stego image having a

low visual quality. Therefore, and in order to evade detection of the secret message, the

stenographic data hiding technique must maintain the visual quality of the stego image at a

minimal acceptable level 29.

Reducing the distortion of the stego image to a minimal or even to a zero level is of a

particular importance for applications such as diagnostic medical images, geographic maps,

official and legal archival documents and images, military applications and e-signatures 44,

54 . This has motivated the research community to explore the possibility of developing new

data hiding techniques by which the damage incurred to the cover image is not permanent.

Such techniques have been developed and became known as reversible data hiding techniques.

The following four categories of reversible data hiding techniques have been reported in the

literature 29: difference expansion 23,38 ,54 ,55 , histogram-shifting 7, 9, 13 ,17 ,44 ,45 ,

47 , prediction-based 6, 8, 12 ,14 ,24 ,26 ,39 ,46 and interpolation-based techniques 1, 16 ,

18 ,20 –22 ,29 –33 ,37 ,38 ,48 ,50 ,53 .

Different techniques have different performance

regarding data hiding capacity and image quality. Interpolation-based data techniques are

known to be simple, numerically efficient, can provide higher data hiding capacity and require

almost no side information to be transmitted to the receiving end in order to extract the

embedded secret data. As examples of interpolation-based data hiding techniques that possess these advantages,

we briefly describe the work of 21,29 . Jung and Yoo 21 proposed an interpolation-based

technique that consists of two main steps: the downscaling/interpolation expansion step and

the data hiding step. In the first step, the original cover image is downscaled, and then

expanded to the original size using an interpolation algorithm. In the second step, secret data

is inserted into the cover image using a data hiding algorithm. The proposed technique gives

relatively high data hiding capacity with acceptable PSNR values. However, Liu et al. 29

modified Jung ‘s technique by replacing the interpolation algorithm by an improved neighbor

mean interpolation algorithm to achieve higher data hiding capacity and higher stego image

quality.

Tmai main objectives of research in this area are the improvement of stego image quality

and the increase of data hiding capacity. Both of stego image quality and the data hiding

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capacity are highly dependent on both of the interpolation algorithm used in the expansion step

and on the data hiding algorithm used in the data hiding step. Our extensive analysis of the

performance of previous work revealed that secret data is hidden in a small portion of

interpolated cover image pixels. Thus, some of the pixels of the cover image will carry no

secret data reducing the data hiding capacity. On the other hand, other pixels may carry several

bits of secret data causing large distortions and reducing stego image quality.In this paper, we propose a simple interpolation-based data hiding technique that increases

the data hiding capacity and improves stego image quality without increasing numerical

calculations. This is achieved by a combination of a new simple interpolation algorithm and

a new data hiding algorithm. This combination increases the number of pixels that can carry

secret data and limit the maximum distortion in these pixels. It also allows for a tradeoff

between data hiding capacity and visual quality. The proposed technique leads to a noticeable

increase in the data hiding capacity, better visual quality of the stego image, while maintaining

the simplicity of numerical calculations. These improvement claims have been evaluated using

extensive simulation and comparisons with similar techniques. The rest of the paper proceeds as follows. Section 2gives a short survey on a number of

interpolation-based data hiding techniques reported in the literature. Section 3gives a detailed

description of the proposed algorithm, which includes in-depth description of the downscaling

/interpolation, data hiding and data extraction, and image recovery algorithms. Section 4gives

the experimental simulation results, and at the same time gives detailed performance compar-

ison with the performance of relevant techniques. Finally, the paper is concluded in section 5

with a discussion citing the main attributes of the proposed algorithm and outlining future

research work.

2 Related work

Reversible data hiding has been an active research area in information and data security for

more than a decade. Different schemes and techniques have been proposed to achieve

reversible data hiding using different methods such as least significant bit (LSB) compression

22 ,40 , histogram shifting 7, 9, 13 ,17 ,44 ,45 ,47 , difference expansion (DE) 23,24 ,38 ,

54 ,55 , interpolation 16,18 ,20 –22 ,29 –33 ,37 ,38 ,48 ,50 ,53 , among others. Interpolation

based data hiding techniques continues to receive researchers attention because they are

simple, numerically efficient, and can provide relatively higher data hiding capacity. In this

section, we will briefly describe a number of interpolation-based techniques. Jung and Yoo 21 proposed an interpolation-based technique, which starts by downscaling

an original NxNcover image Iinto an ( N/2xN/2) imageIdn. After that, they expand the

downscaled image Idnback to the original size ( NxN) using an interpolation algorithm which

they have proposed. The resulting expanded image Iexis used as a cover image to hide the

secret message resulting in the stego image Ist.The data extraction algorithm, which is a direct

reversal of the data embedding method, is used to extract the hidden data and recover the

original cover image. This technique gives relatively high data-hiding capacity with acceptable

PSNR values. Several attempts were made to improve the performance of the Jung and Yo

technique 21. Rudder et al. 37 used a modified algorithm for data embedding to achieve

higher data hiding capacity. However, the quality of the resulting stego image is relatively low.

Liu et al. 29 modified Jung et al. 21 technique by replacing the interpolation algorithm by

an improved neighbor mean interpolation algorithm to achieve higher data hiding capacity.

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This technique achieved higher data-hiding capacity and higher stego image quality. Jana et al.

18 proposed a weighted matrix interpolation technique; however, the technique suffers from

high computational requirements as compared to Jung and Yo 21. Luo et al. 33used

directional interpolation to improve capacity and image quality. Although, image quality was

improved, the data-hiding capacity was low and the computational complexity of the technique

was high. Liu et al. 30 used improved interpolation with block division and were able to

improve the data hiding capacity and image quality. However, numerical complexity was

increased. Sabeen 38 combined image interpolation with difference expansion achieving

higher data hiding capacity, lower image distortion. However, this improved performance

came at the cost of higher computational complexity. For comprehensive survey and perfor-

mance analysis of interpolation-based reversible data hiding techniques, the reader may refer to

Jung 20.

In summary, a great effort has been made to improve the performance of interpolation-

based data hiding; however, we believe that most improvements in capacity and image quality

have sacrificed numerical simplicity and low computational requirements. The objective of our

proposed interpolation-based technique is to increase data hiding capacity, improve image

quality, while maintaining computational simplicity. This has been achieved as will be

demonstrated in section four, where the performance of proposed technique has been evaluated

and extensively compared with the performance of 21,24 ,29 ,54 ,55 .

3 The proposed interpolation-based data hiding technique

In this section, we present a new image interpolation-based reversible data hiding technique.

We first describe the general structure of interpolation-based reversible data hiding techniques.

We proceed by proposing a new interpolation algorithm that leads to an increase the data

hiding capacity by increasing number of embeddable pixels. After that, we describe a new data

hiding algorithm that embeds the secret message while maintaining the visual quality of the

cover image. The data extraction and image recovery algorithm, which is a reversal of the data

hiding algorithm, is described next. Finally, a step-by-step numerical example is given to

illustrate the operational steps of the proposed algorithm.

3.1 General structure of interpolation-based reversible data hiding techniques

Interpolation-based reversible data hiding techniques share the general structure shown in

Fig. 1. The major sequence of operations involved are the downscaling, expansion / interpo-

lation, data hiding or embedding, and data extraction and image recovery. The general flow of Interpolation-based data hiding is described as follows:

To start with, we assume the original image Ito be a square image of size (2 N×2 N).

Original

2N×2N Image

downsize

Downsized

(N+1)×(N+1)

Original Image

Interpolation based

Scaling up

Scaled up

2N×2N Cover

ImageSecret

Data

Insertion

2N×2N Stego Image

Secret Data

Extraction ; Cover Image Recovery

2N×2N Cover Image

Secret Data

Fig. 1 Sequence of the Reversible Data hiding Techniques

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;Scale down the (2N×2 N) gray scale image Iinto an ( N+1)×( N+ 1)image Idnusing any

image interpolation technique such as cubic or bi-cubic interpolation.

;Expand the ( N+1)×( N+1) image Idninto a (2N+1)×(2 N+ 1)cover image Iex1using

interpolation. The last row and the last column of I

ex1are then discarded to obtain a (2N×

2 N )expandedimage I

exof the same size as the original image. This Downscale/Interpolate

Expand step is essential since it transfers the cover image into a form suitable for

‘ reversible ‘data hiding. However, this step results in a slightly lower visual quality of

the cover image with irreversible distortions.

;Hide the secret message in the interpolated distorted image.

;Data extraction and image recovery. This step performs exact recovery of the cover image

and the secret message.

3.2 Proposed interpolation/expansion algorithm

Given the ( N+1)×( N+ 1) downsized image Idn, which has been described earlier in this

section, our proposed interpolation/expansion algorithm is described as follows:

1. Proceed horizontally to form ( 2×2) overlapping blocks of each four adjacent cells as

illustrated in Fig. 2(a). Once the end of a row is reached, move down to the next row and

repeat until the last row. This step leads to forming ( N×N) overlapping blocks from the

( N +1)×( N+ 1) image I

dn.

2. Expand each ( 2×2)block into an ( 3×3)block by inserting an empty row and an empty

column and fill the empty pixels using the proposed interpolation algorithm. Figure 2(b)

illustrates in details how the expansion algorithm works. Given the ( 2×2)block with

entries p(0, 0), p(0, 1), p(1, 0) and p(1, 1). The expanded block entries are calculated as

given in Eq. ( 1). The operator ?.? in the equation denotes the rounding down to highest

integer (floor).

p

00;1

ðÞ¼p 0;0

ðÞþ p0;1

ðÞ

3 þp

0;1

ðÞþ p1;1

ðÞ

6

p

01 ;0

ðÞ¼p 0;0

ðÞþ p1;0

ðÞ

3 þp

0;1

ðÞþ p1;1

ðÞ

6

p

01 ;1

ðÞ¼p 0;0

ðÞþ p0;1

ðÞþ p0;1

ðÞþ p1;1

ðÞ

4

ð

1 Þ

Note that the four corner values are unchanged. The remaining two empty pixels in the

expanded block are calculated as parts of the neighboring horizontal and vertical blocks. This

proposed algorithm uses the four pixel values in the ( 2×2)block to find the value for each

interpolated pixel.

3.3 The proposed data hiding algorithm

This subsection outlines the proposed data hiding algorithm. The input to this algorithm is the

expanded interpolated ( 2N×2N)imageI

exobtained by applying the interpolation / expansion

algorithm which has been described earlier. The data hiding algorithm starts by dividing the

image I

exinto (2×2) non overlapping blocks Bijas shown in Fig.2(a). The division is carried

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out in a zigzag form, from left to right and top to down or any other sequence. After division,

the embedding procedure proceeds as follows:Step 1: Given the (2 × 2)blockB

ijshown in Fig. 3(b), the payload for each embeddable

pixel is represented by the differences between the shaded embeddable pixels and the

corner pixel p(0,0). The differences are calculated as given in Eq. ( 2), where the operator

|.| refers to the absolute value.

d

1¼Minimum p 0 ;1

ðÞ ?p 0;0

ðÞ

ðÞ

jj ;

255 ?p 0;1

ðÞ

ðÞ

½

d

2¼ Minimum p 1 ;0

ðÞ ?p 0;0

ðÞ

ðÞ

jj ;

255 ?p 1;0

ðÞ

ðÞ

½

d

3¼ Minimum p 1 ;1

ðÞ

?p 0;0

ðÞ

ðÞ

jj ;255 ?p 1;1

ðÞ

ðÞ

½ ð

2 Þ

Equation ( 2) prevents overflow by limiting the maximum value of embedded pixels by 255,

which is the maximum pixel value in gray level images. It is worthwhile mentioning here that

the overflow issue was not addressed in previously proposed interpolation-based techniques.

Step 2: Use Eq. ( 3) to compute the number of bits of the secret message that can be

embedded in each embeddable pixel.

The 2×2 block Expanded 3×3 block Interpolated

3×3 block

a

b

Fig. 2 aBlock division of Idn.b Expansion and interpolation sequence

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n1¼log2d1jj

bc

n

2¼ log2d2jj

bc

n

3¼ log2d3jj

bc ð

3 Þ

Step 3: Limit the number of the secret message bits that can be hidden in each

embeddable pixel. This is a necessary step in order to limit the maximum distortion in

a single pixel to an acceptable tolerated level. We limit the values of n

1,n2and n3to a

maximum number nas shown in Eq. ( 4).

n

1¼ Minimum log2d1jj

bc ;

n

ðÞ

n

2¼ Minimum log2d2jj

bc ;

n

ðÞ

n

3¼ Minimum log2d3jj

bc ;

n

ðÞ ð

4 Þ

Note that ncan take any value in the range 1 to 8. Selecting n=1 results in the highest image

quality but the lowest capacity, while setting n=8 results in lowest image quality and highest

capacity. Again, we point out that this feature, which allows adaptive setting of the tradeoff

level between the data hiding capacity and the stego image visual quality, was not studied in

the similar interpolation-based techniques.

Step 4: Extract a corresponding number of bits b

1,b2,and b3of lengths n1,n2and n3,

respectively, from the secret message and convert it to its equivalent decimal values b

c1,

b

c2and bc3.

Step 5: Insert the secret message bits into embeddable pixels as given by Eq. ( 5).

p

00 ;1

ðÞ¼ p0;1

ðÞþ bc1p01 ;0

ðÞ¼ p1;0

ðÞþ bc2p01 ;1

ðÞ¼ p1;1

ðÞþ bc3

ð5 Þ

Insertion of the secret message bits continues on each B

ijblock until the end of the message or

until all blocks have been covered. We point out here that one needs to send the size of the

secret message and the value of n, alongside with the stego image, in order to enable the

B00B01

B10B11

ij

B

bloc k 2×2

The ijB

bloc k 2×2

Embedded

ab

Fig. 3 aNon-overlapping 2 × 2 blocks Bij.b Data embedding of 2 × 2 block

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receiving end extract the embedded message. This can be done by adding 3 bytes concatenated

as a part of the secret message. These three bytes are embedded by following the steps of the

data hiding algorithm described above using a predetermined fixed value ofn=8.

3.4 Data extraction and image recovery algorithm

The data extraction and image recovery algorithm reverses the steps of the previous data

hiding algorithm. The extraction and recovery process is blind in the sense that it extracts the

secret message from the stego image I

swithout the need for the original cover image. This is in

addition to the fact that it allows for exact recovery of the original cover image. Given the

stego image I

s, which results from the embedding algorithm described earlier, the algorithm

starts by dividing I

sinto (3×3) overlapping blocks Bijin the same fashion and sequence as that

of the expansion step. Figure 4shows one of such blocks Bij.

We denote the corner pixels p(i,j)to emphasize that they remain intact during the entire

process of expansion, embedding, and extraction. We also denote pixels that carry the secret

data bits with p'( i,j ). The empty pixels go with the neighboring two blocks. With these

assumptions in mind, the data extraction algorithm proceeds as follows:

Step 1 : Calculate the original cover pixel values using Eq. ( 6).

p 0;1

ðÞ¼

p 0;0

ðÞþ p0;2

ðÞ

3 þp

2;0

ðÞþ p2;2

ðÞ

6

p 1;0

ðÞ¼

p 0;0

ðÞþ p2;0

ðÞ

3 þp

0;2

ðÞþ p2;2

ðÞ

6

p 1;1

ðÞ¼

p 0;0

ðÞþ p0;2

ðÞþ p2;0

ðÞþ p2;2

ðÞ

4

ð

6 Þ

Step 2 : Find the decimal values of the secret bits embedded in pixels p'( i,j )using Eq. ( 7).

b

1¼ p00;1

ðÞ ?p 0;1

ðÞ

b

2¼ p01;0

ðÞ ?p 1;0

ðÞ

b

3¼ p01;1

ðÞ ?p 1;1

ðÞ ð

7 Þ

Fig. 4 3×3stego image block Bij

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Step 3: Find the number of bits of secret message embedded in each pixel using Eq. ( 8).

d

1¼ Minimum p 0 ;1

ðÞ ?p 0;0

ðÞ

ðÞ

jj ;

255 ?p 0;1

ðÞ

ðÞ

½

d

2¼ Minimum p 1 ;0

ðÞ ?p 0;0

ðÞ

ðÞ

jj ;

255 ?p 1;0

ðÞ

ðÞ

½

d

3¼ Minimum p 1 ;1

ðÞ ?p 0;0

ðÞ

ðÞ

jj ;255 ?p 1;1

ðÞ

ðÞ

½ ð

8 Þ

Step 4 :Limitthelengths n

1,n2and n3to the maximum value nusing Eq. ( 9).

n

1¼ Minimum log2p0;1

ðÞ ?p 0;0

ðÞ

jj

bc ;

n

ðÞ

n

2¼ Minimum log2p1;0

ðÞ ?p 0;0

ðÞ

jj

bc ;

n

ðÞ

n

1¼ Minimum log2p1;1

ðÞ ?p 0;0

ðÞ

jj

bc ;

n

ðÞ ð

9 Þ

Step 5 : Find the binary equivalent for the extracted decimal values found in Step 2 above.

Assume these binary values to be b

1b, b2band b3bwith lengths n1,n2and n3respectively.

Step 6 : Concatenate the binary values b

1b, b2band b3bto get the secret message as w=

b

1 b:b2 b:b3 b.

Step 7 : Restore the original pixels of the cover image by replacing the pixels p'( 0,1 ),

p ‘( 1,0 )and p'( 1,1 )with the original pixel values obtained in Step 1: p(0,1 ), p( 1,0 )and

p( 1,1 )respectively.

Step 8 : Repeat Steps 1 through 7 until the whole secret message is extracted.

3.5 A numerical example

We conclude this section by giving a numerical example to illustrate the operational steps of

the proposed interpolation-based reversible data hiding technique. The three proposed algo-

rithms illustrated are the interpolation/expansion algorithm, data hiding algorithm, and data

extraction and image recovery algorithm.

The interpolation/expansion algorithmTo start with, Fig. 5shows the expansion of a 3×3

downscaled image I

dninto a5×5expanded interpolated image Iex1. After we insert empty

rows and columns, the empty pixels are filled using Eq. ( 1). The final expanded interpolated

image is simply the first 4×4block of I

ex1.

The data hiding algorithmThe data hiding algorithm follows as illustrated in Fig. 6.Weuse

the first 2 ×2 block of the output image I

exproduced in the expansion example above.

Assuming that the secret message is W= 101111101001101001, the message is hidden by

implementing the following steps:

&Calculate the differences using Eq. ( 4) which produces the following values: d1=80?

50 = 30, d

2=88?50 = 38, and d3=87?50 = 37

&Compute the number of bits that we can embed into each pixel using Eqs. 5as follows:

n

1= ?log2|30|? =4n2=?log2|38| ?=5 and n3=?log2|37|? =5.

&Divide the secret message into four smaller segments as follows: w1=1011,w2=11,101

and w

3= 00110.

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&Calculate the decimal values ofw1,w2,and w3producing bc1=11,bc2=29 and bc3=6.

&Compute the new pixel values using Eq. ( 6), giving p'(0, 1) = 80 + 11 = 91 p'(1, 0) = 88 +

29 = 117and p'(1, 1) = 87 + 6 = 93. Figure 6shows the original and embedded blocks.

;Insert remaining part of the message in subsequent blocks in the same fashion

The data extraction algorithmFinally, the data extraction and image recovery algorithm is

illustrated in Fig. 7.

;Starting with a ( 3×3)block of the stego image as found in the embedding example

above, we find the original block pixel values before embedding using Eq. ( 6)as

follows: p(0, 1) = ?(50 + 80)/3 + (130 + 90)/6 ?= 80, p(1, 0) = ?(50 + 130)/3 + (80 + 90)/6 ?=

80 and p(1, 1) = ?(50 + 80 + 130 + 90)/4 ?=87.

;The decimal values of the hidden message bits are as follows:

b

c1¼91?80 ¼11;bc2¼ 117 ?88 ¼29 and bc3¼93?87 ¼6:

;Using eq. ( 7), the lengths of bc1,bc2andbc3are as follows:

n

1¼ log280?50

jj

bc ¼

4;n2¼ log288?50

jj

bc ¼

5and n3¼ log287?50

jj

bc ¼

5:

;The binary values for bc1,bc2and bc3arew1= 1011, w2= 11,101 and w3= 00110. We treat

dark shaded pixels in neighboring blocks.

4 Experimental results

In this section we present, analyze, and evaluate the performance of the proposed technique.

This section starts with a description of the experimental setup used for performance evalu-

ations. Ensuing subsections present an in-depth performance analysis of the algorithm by

Th e 3×3 blo ck of IdnEx pan de d 5×5 blo ck of Iex1Interpolated 5×5 blo ck of Iex1

Fig. 5Expansion and Interpolation of a 3×3block

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describing the performance of the downscaling/expansion interpolation algorithm, perfor-

mance of the embedding/data hiding algorithm, performance of the data extraction/ image

recovery algorithm, and finally the overall performance. A comprehensive performance

comparison with two relevant algorithms 21,29 is given. In addition, we conclude this

section with a comparison between our algorithm and three difference-expansion based

algorithms that utilize a type of interpolation for prediction 24,54 ,55 .

4.1 Experimental setup

An extensive experimental evaluation was performed using twelve standard grayscale test

images having the size 512 ×512. The test images served as cover images for the proposed

reversible data hiding algorithm. These images, shown in Fig. 8, are commonly used to

evaluate and compare the performance of different data hiding techniques. Each image was

processed by the operational steps illustrated in Fig. 1. First, the cubic interpolation algorithm

was used to downscale each test image form its 512 × 512original size into a 257 × 257

image. Then, the proposed interpolation algorithm expanded the downscaled image into a

513 × 513 image. The final expanded 512 ×512 images were obtained by truncating the last

row and the last column of the 513 × 513expanded images.

For image quality assessment, we used the following performance metrics: PSNR, Weight-

ed WPSNR, and SSIM. These metrics are outlined in what follows:

;PSNR and WPSNR: The PSNR and WPSNR are used to measure the visual quality of

the stego image I

scompared to the original cover image I. Both images have the size M×

N . The standard PSNR and WPSNR formulas are given in Eq. ( 10) and Eq. (11),

respectively 16,31 .

PSNR I ;I

sðÞ¼ 10 log10NM 255

ðÞ2

?N

i

¼1?M

j ¼1Xi ;j

ðÞ ?Isi; j

ðÞ

ðÞ2dB ð10 Þ

2×2 block cover2×2 Embe dd ed b lock

Fig. 6 Embedding example

3×3cover block

3×3

stego block

Fig. 7 Data extraction example

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WPSNR I;IsðÞ¼ 10 log10N M 255

ðÞ2

NVF ?N

i¼1?M

j ¼1Xi ;j

ðÞ ?Isi; j

ðÞ

ðÞ2dB ð11 Þ

where NVF is a noise visibility measure given by Eq. ( 12).

NVF I ;I

sðÞ¼ Norm1

1 þ ?2

block

!

ð12 Þ

where ?

blockis the standard deviation of a block with some size such as 8 ×8 and the Normis a

normalization function so that NVFvalues range from 0 to 1.

;SSIM: The SSIM metric measures the similarity between the between an N×Moriginal

cover image Iandthestegoimage I

sas given by Eq. (13).

SSIM I ;I

sðÞ¼ lI;IsðÞ cI;IsðÞ sI;IsðÞ ð13 Þ

Original CoverImageInter po la ted e xp and ed Cover Image

Image

Le na

Pepper

Baboon

Boat

Plain

Barbara To we r

Or igin al Co ve r

Image

Interpolated expanded Cover ImageImage

Pumpkin

Swan

Couple

BW-Tree

Ow l

Fig. 8 Original and Interpolated expanded cover images

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wherelI;IsðÞ

¼2?I?Isþ C1

?2

Iþ?2

IsþC1

cI ;IsðÞ

¼2?I?Isþ C2

?2

Iþ?2

Isþ C2

sI ;IsðÞ¼?IIsþ C3

?Iþ ?IsþC3

ð14 Þ

where. l( I, I

s) measures the closeness of mean luminance ( ?I,?Is), c(I, Is)measures the closeness of

the contrast measured by standard deviation ( ?

I,?Is), ?IIsis the covariance, and s(I, Is)isa

measure of structural correlation and ?

IIsis the covariance.

4.2 Performance of the downscaling/interpolation expansion algorithm

The image quality due to the proposed interpolation algorithm is demonstrated by the test

cover images shown in Fig.8. In the figure, a comparison is made between the original cover

images before interpolation with the cover images after interpolation. In general, it can be seen

that proposed algorithm results in an acceptable image quality with almost no visible distor-

tions. Moreover, Table 1compares the PSNR, WPSNR and SSIM values due to the proposed

interpolation algorithm with the interpolation algorithms used in 21,29 . As can be seen from

the table, the performance of our interpolation algorithm is slightly better than that of 21,29 .

Other than causing little distortion, the proposed interpolation algorithm increases the data

hiding capacity by increasing the number of embeddable pixels, as will be shown later.

4.3 Performance of the data hiding algorithm

This subsection evaluates the data hiding step in terms of image quality and data hiding

capacity. The main objective of our data hiding algorithm is to increase the data hiding

capacity that has been achieved as demonstrated by the capacity results given in Table 2.

The achieved capacity results are compared with those obtained by 21,29 . It is clear from the

table that our proposed algorithm outperforms algorithm 21foralln ?2 and outperforms

algorithm 29foralln ?3. In terms of the percentage increase in the data hiding capacity, the

hiding capacity of the proposed algorithm is 32% –72% higher than the hiding capacity of 21

and 8.5% –17.5% higher than the hiding capacity of 29.

Image quality performance with respect to the data hiding step was also studied, and the

results are demonstrated in Tables 3,4 and 5. For different embedding steps, Table 3compares

the PSNR values, Table 4compares the WPSNR values, and Table 5compares the SSIM

values. Referring to Table 3, it can be seen that, the data hiding capacity achieved by our

algorithm for embedding step equals 2 ( n= 2) is almost equals to that of 21 with an average

increase of 7.5 dB in PSNR values over 21. For an embedding step equals to 3 ( n= 3), our

algorithm achieves a hiding capacity comparable to that achieved by 29 with an average

increase of 5 dB in PSNR values over 29. In applications where image quality is more

important, our algorithm with, embedding steps n=1 or n= 2, can provide PSNR values

between 41 and 54 dB. This is far higher than the PSNR values that are provided by 21,29 as

clearly shown in Table 3.

Table 4compares the WPSNR values obtained for different data hiding steps. It can be seen

from the table that for a hiding step equal to 2 (n = 2), our data hiding capacity is almost equals

to that of 21 with an average increase of 4.5 dB in PSNR values over that achieved by 21.

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Similar results are obtained when the hiding step is 3, where our data hiding capacity is almost

equals to that of 29 while our algorithm gives an average increase of 2.3 dB over that of 29.

In applications where image quality is more important than data hiding capacity, setting the

embedding step to 1 or 2 provides WPSNR values between 56 and 74 dB, which is way above

the WPSNR values achieved by 21,29 .

A final notice about performance of data hiding techniques is pointed out. Most perfor-

mance analysis regard the performance of the data hiding step as the overall performance.

They usually do not include the distortions of the downscaling step. This would be true when

starting with a low-resolution cover image and apply the interpolate/expand step without

downscaling. If that were the case, results presented in this subsection would be considered

as the overall performance. However, we provide complete performance analysis including the

downscaling step in subsection 4.5.

Table 1 Image quality, performance Comparisons of downscaling:expansion interpolation step

Image PSNR comparisons WPSNR comparisons SSIM comparisons

Proposed 2129 proposed 21 29proposed 21 29

Lena 30.24 26.82 30.15 50.36 50.86 49.01 0.9510 0.9287 0.9451

Owl 26.09 25.30 26.15 45.20 45.77 44.09 0.8929 0.8533 0.8824

Pepper 28.04 25.99 28.13 59.94 58.68 57.62 0.9516 0.9319 0.9468

BW-tree 22.93 21.95 22.92 47.39 47.62 46.16 0.8593 0.8057 0.8442

Baboon 21.22 20.09 21.29 40.73 40.36 39.38 0.8151 0.7726 0.7983

Couple 24.77 24.20 24.86 48.54 51.14 49.16 0.8921 0.8484 0.8806

Tower 30.63 29.54 30.66 53.51 51.04 50.55 0.9652 0.9516 0.9612

Pumpkin 31.84 30.31 31.89 59.12 58.65 58.05 0.9573 0.9344 0.9517

Swan 25 4 l 24.59 25.39 46.02 46.94 45.42 0.9025 0.86 79 0.8912

Boat 26.23 24.91 26.15 42.80 42.74 41.76 0.8845 0.8334 0.8714

Plane 27.37 24.66 27.43 53.86 52.69 54.68 0.9480 0.9226 0.9413

Barbara 23.84 23.41 22.92 38.95 38.98 38.64 0.8324 0.80 84 0.8244

Average 26.55 25.14 26.49 48.86 48.78 47.87 0.9043 0.8717 0.8949

Table 2 Embedding step Capacity Performance Comparison

Image Capacity

Proposed 2921

No Limit n=4 n=3 n=2 n=1

Lena 224,528 221,174 207,567 174,205 110,000 199,741 143,083

Owl 401,287 396,593 367,036 289,494 162,842 364,793 289,770

Peppers 223,295 218,935 204,636 174,110 113,027 199,340 145,037

BW-Tree 474,732 460,763 411,329 313,116 171,120 436,861 359,079

Baboon 459,737 448,464 400,798 306,337 168,666 420,301 345,884

Couple 299,203 295,711 277,856 228,960 137,598 259,993 183,410

Tower 107,198 104,703 100,053 89,459 61,877 91,905 62,405

Pumpkin 273,331 271,947 261,113 222,953 136,867 249,176 185,037

Swan 310,574 305,395 277,579 216,180 121,935 282,449 229,496

Boat 301,955 295,840 273,615 222,253 132,309 267,765 198,162

Plane 228,863 221,651 201,671 163,837 101,943 204,300 153,767

Barbara 290,234 286,920 266,801 217,799 131,985 267,928 207,059

Average 299,520 294,008 270,840 217,750 129,180 270,580 208,520

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Finally, the effect of the data hiding step on the visual quality of the cover image is

measured using the SSIM metric. The results are presented in Table 5given below. It can be

seen from the table for a data hiding step of 2 (n = 2), the data hiding capacity of our proposed

algorithmisalmostequalstothatof 21, however, our algorithm achieved an average SSIM

value of 0.997 whereas 21 achieved an average SSIM value equals to 0.8717. Similar results

are obtained when the data hiding step equals 3 (n = 3), where the data hiding capacity of our

proposed algorithm almost equals to that of 29, however, our algorithm achieves an average

SSIM value equals to 0.9927 compared to 0.8949 achieved by 29.

Table 3 Embedding step PSNR Performance Comparison

Image PSNR

Proposed 2921

n=1 n=2 n=3 n=4 No Limit

Lena 51.90 44.36 39.37 35.92 33.60 34.80 37.86

Owl 51.11 41.61 36.00 32.94 31.08 32.37 35.06

Peppers 50.19 44.52 39.70 35.94 33.18 34.30 37.19

BW-Tree 51.78 41.15 35.12 30.87 28.05 29.33 31.88

Baboon 49.98 41.26 35.28 31.03 28.77 30.13 32.49

Couple 50.04 42.92 37.80 34.55 32.20 33.20 35.87

Tower 50.93 47.80 43.82 40.48 35.23 36.19 38.66

Pumpkin 54.40 43.14 38.60 36.02 35.07 36.07 38.79

Swan 50.95 42.89 37.08 33.16 31.37 32.57 34.78

Boat 51.45 43.01 37.68 33.97 31.53 32.74 35.50

Plane 51.10 44.55 39.07 34.81 31.67 32.82 35.48

Barbara 52.23 43.18 37.87 34.30 32.88 34.03 36.79

Average 51.33 43.36 38.11 34.49 32.05 33.21 35.86

Table 4 Embedding step WPSNR Performance Comparison

Image WPSNR

Proposed 2921

n=1 n=2 n=3 n=4 No Limit

Lena 71.28 64.61 61.79 61.27 60.56 63.27 63.97

Owl 66.28 58.47 54.44 53.81 56.76 56.54 57.84

Peppers 70.72 64.74 60.45 57.45 56.05 56.13 59.44

BW-Tree 64.77 56.28 50.89 47.82 49.10 49.08 50.68

Baboon 67.75 59.75 54.53 51.77 51.66 51.20 51.58

Couple 71.05 64.87 59.53 56.10 53.44 54.07 56.61

Tower 78.28 73.84 71.49 68.04 62.19 65.29 69.20

Pumpkin 68.97 61.57 57.97 55.53 55.07 56.05 59.26

Swan 69.37 61.40 56.69 54.54 55.56 56.27 57.92

Boat 69.63 62.04 57.63 55.64 54.28 55.69 58.58

Plane 74.22 65.05 58.83 55.04 53.89 54.48 56.05

Barbara 68.56 61.08 56.40 54.01 54.16 54.80 57.94

Average 70.07 62.80 58.38 55.91 55.22 56.07 58.25

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4.4 Average and maximum absolute error performance

The objective of this subsection is to provide more insight into our reversible data hiding

technique. It is known that the data hiding capacity and the PSNR values depend on the

downscaling algorithm. The values presented in Tables1and 2are the results of our

implementation of the three data hiding algorithms using the same downscaling algorithm.

Therefore, the increase in hiding capacity in the proposed technique is not due to the

downscaling algorithm, since the other two algorithms use the same downscaling algorithm. Rather, the higher data hiding capacity results from the increase of the number of pixels that

can carry the secret data bits. Using the terminology of digital watermarking, we refer to these

pixels as embeddable pixels. The proposed algorithm increases the number of embeddable

pixels and, hence, increases the data hiding capacity. This is shown in Table 6, which also

compares the number of embeddable pixels of the proposed algorithm with those of 21,29 .

Table 5 Embedding step SSIM Performance Comparison

Image SSIM

Proposed 2921

n=1 n=2 n=3 n=4 No Limit

Lena 0.9994 0.9976 0.9943 0.9899 0.9865 0.9451 0.9287

Owl 0.9997 0.9973 0.9917 0.9817 0.9769 0.8824 0.8553

Peppers 0.9993 0.9975 0.9953 0.9922 0.9888 0.9468 0.9319

BW-Tree 0.9998 0.9980 0.9919 0.9805 0.9677 0.8442 0.8057

Baboon 0.9998 0.9981 0.9921 0.9791 0.9663 0.7983 0.7726

Couple 0.9994 0.9967 0.9910 0.9841 0.9815 0.8806 0.8484

Tower 0.9994 0.9977 0.9959 0.9947 0.9920 0.9612 0.9516

Pumpkin 0.9996 0.9975 0.9937 0.9900 0.9886 0.9517 0.9344

Swan 0.9997 0.9983 0.9942 0.9869 0.9821 0.8912 0.8679

Boat 0.9995 0.9973 0.9917 0.9846 0.9783 0.8714 0.8333

Plane 0.9994 0.9982 0.9958 0.9919 0.9869 0.9413 0.9226

Barbara 0.9995 0.9975 0.9847 0.9847

70.9813 0.8244 0.8084

Average 0.9995 0.9976 0.9927 0.9867 0.9814 0.8949 0.8717

Table 6 Number of embeddable pixels

Image Number of embeddable pixels

Ptoposed 29 21

Lena 109,988 101,304 78,471

Owl 162,839 156,830 141,384

Peppers 112,984 104,031 81,732

BW-Tree 171,094 166,374 154,334

Baboon 168,645 163,926 151,217

Couple 137,573 125,927 98,617

Tower 61,883 54,701 38,468

Pumpkin 136,859 130,428 107,930

Swan 121,936 116,786 105,169

Boat 132,251 123,406 101,382

Plane 101,897 93,769 75,516

Barbara 131,497 126,664 106,848

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In what follows we analyze error performance as a function of the of embedding step

variation. Our analysis is based on the calculation of two values: the maximum absolute error

between pixels before and after embedding, and the average absolute error. Assuming that the

original cover image is I,the marked image is Y, and the number of embeddable pixels is N

emb,

the two error values are calculated using Eq. ( 15)andEq.( 16), respectively.

Maximum Absolute Error ¼Maximum Ii;j

ðÞ ?Yi ;j

ðÞ

jj

ðÞ

;for all i ;j ð15 Þ

Average Absolute Error ¼?

N

i¼1?M

j ¼1Ii ;j

ðÞ ?Yi ;j

ðÞ

jj

=Nembð16 Þ

Table 7 Error Performance for embedding step

Image Maximum Absolute Error Average Absolute Error

Proposed Proposed

No limitn=4 n=3 n=2 29 21 No limit n=4 n=3 n=2 2921

Lena 63 15 7 3 63 63 4.89 4.37 3.38 2.16 4.49 3.69

Owl 63 15 7 3 63 63 6.38 5.91 4.46 2.55 5.59 4.27

Peppers 63 15 7 3 63 63 4.85 4.17 3.16 2.08 4.48 3.67

B W Tree 63 15 7 3 63 63 8.72 7.26 4.95 2.66 7.61 5.80

Baboon 63 15 7 3 63 63 8.25 7.13 4.87 2.63 7.12 5.53

Couple 127 15 7 3 119 63 5.32 4.78 3.73 2.32 4.80 3.88

Tower 63 15 7 3 63 63 4.12 3.17 2.57 1.89 3.85 3.51

Pumpkin 63 15 7 3 63 31 4.16 4.00 3.37 2.25 3.80 3.04

Swan 63 15 7 3 63 63 7.09 6.38 4.56 2.54 6.28 5.02

Boat 63 15 7 3 63 63 6.05 5.25 3.91 2.36 5.39 4.27

Plane 63 15 7 3 63 63 6.44 5.26 3.70 2.21 5.92 4.89

Barbara 63 15 7 3 63 31 5.40 5.00 3.78 2.30 4.87 3.92

Table 8 Overall PSNR Performance Comparison

Image PSNR

Proposed 2921

n=1 n=2 n=3 n=4 No Limit

Lena 30.22 30.10 29.76 29.17 28.35 28.62 27.89

Owl 26.08 25.97 25.65 25.14 24.79 25.12 24.77

Peppers 28.13 28.06 27.86 27.46 26.79 27.18 26.62

BW-Tree 21.74 22.87 22.69 22.30 21.47 22.00 21.48

Baboon 21.23 21.20 21.08 20.82 20.53 20.77 20.56

Couple 24.78 24.73 24.59 24.34 24.02 24.33 23.98

Tower 30.62 30.57 30.46 30.26 29.30 29.42 28.87

Pumpkin 31.77 31.48 30.93 30.37 30.16 30.54 29.77

Swan 25.40 25.34 25.13 24.73 24.41 24.62 24.13

Boat 26.23 26.16 25.97 25.63 25.26 25.43 24.63

Plane 27.45 27.40 27.21 26.76 25.97 26.32 25.63

Barbara 23.84 23.81 23.71 23.54 23.43 23.54 23.26

Average 26.45 26.47 26.25 25.87 25.37 25.65 25.13

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Table7compares the error performance between the proposed algorithm and algorithms 21,

29 . The results in the table reveal that the maximum absolute errors are high for the three

algorithms when no limit is imposed on the data hiding capacity ( n= 8). Although this gives a

higher hiding capacity, it causes high distortion to the cover image. To reduce the maximum

and average absolute errors, the data hiding algorithm described in the previous section was

developed to allow for the appropriate selection of the embedding step n. By choosing n,

which is the maximum number of bits that we embed in a single pixel, we are able to limit the

maximum absolute error due to the data hiding step to a maximum value of 2

n-1.Weusethe

value of nin the range of 1to 8to allow for an adjustable tradeoff between maximum

allowable image distortion and data hiding capacity. For example, if we chose n=3the

maximum absolute error due to the data hiding step is 7.Table 7demonstrates the effectiveness

Table 9 Overall WPSNR Performance Comparison

WPSNR

Image Proposed 2921

n=1 n=2 n=3 n=4 No Limit

Lena 49.66 48.86 48.61 48.96 51.47 49.01 49.60

Owl 44.50 42.67 42.75 43.57 43.59 42.48 44.00

Peppers 58.28 53.72 55.52 56.93 52.78 51.50 54.31

BWTree 46.32 41.67 43.02 44.79 42.31 41.58 43.10

Baboon 40.39 39.00 39.31 39.90 39.36 37.85 38.58

Couple 48.23 46.29 47.18 47.86 45.13 45.82 48.38

Tower 53.22 53.41 53.31 53.17 53.47 50.07 50.43

Pumpkin 57.07 51.72 52.80 54.76 51.46 51.57 54.02

Swan 45.53 43.58 44.04 44.83 43.58 44.03 45.10

Boat 42.48 41.95 41.81 42.12 42.85 41.38 42.03

Plane 54.12 52.78 53.92 54.21 51.33 51.79 51.71

Barbara 38.68 37.76 37.65 38.32 37.52 37.52 38.14

Average 48.20 46.11 46.66 47.45 46.23 45.38 46.61

Table 10 Overall SSIM Performance Comparison

Image SSIM

Proposed 2921

n=1 n=2 n=3 n=4 No Limit

Lena 0.9501 0.9486 0.9460 0.9423 0.9381 0.9361 0.9244

Owl 0.8926 0.8909 0.8853 0.8764 0.8717 0.8677 0.8475

Peppers 0.9509 0.9490 0.9468 0.9439 0.9402 0.9395 0.9280

BW-Tree 0.8592 0.8580 0.8536 0.8453 0.8347 0.8279 0.7989

Baboon 0.8149 0.8134 0.8087 0.8003 0.7933 0.7839 0.7660

Couple 0.8914 0.8892 0.8859 0.8817 0.8797 0.8719 0.8845

Tower 0.9639 0.9617 0.9600 0.9594 0.9575 0.9555 0.9483

Pumpkin 0.9665 0.9538 0.9500 0.9471 0.9463 0.9440 0.9311

Swan 0.9022 0.9008 0.8971 0.8911 0.8877 0.8813 0.8631

Boat 0.8838 0.8841 0.8763 0.8709 0.8674 0.8592 0.8279

Plane 0.9474 0.9464 0.9446 0.9414 0.9361 0.9326 0.9185

Barbara 0.8316 0.8298 0.8277 0.8250 0.8238 0.8189 0.8069

Average 0.9045 0.9021 0.8985 0.8937 0.8897 0.8849 0.8704

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Table 11Capacity and PSNR Comparisons with other algorithms

Proposed 24 One level 24TwoLevels 54 55

No limit n=4 n=3 n=2 n=1

Lena Capacity 224,528 221,174 207,567 174,205 110,000 130,560 261,120 184,652 53,045 PSNR 33.60 35.92 39.37 44.36 51.90 36.25 33.45 45.72 58.05

Baboon Capacity 459,737 448,464 400,798 306,337 168,666 130,560 261,120 134,614 53,045 PSNR 28.77 31.03 35.28 41.26 49.98 NA NA 47.37 57.14

Plane Capacity 228,863 221,651 201,671 163,837 101,943 130,560 261,120 186,922 53,045 PSNR 31.67 34.81 39.07 44.55 51.10 33.24 32.78 48.26 58.26

Peppers Capacity 223,295 218,935 204,636 174,110 113,027 130,560 261,120 169,704 53,045

PSNR 33.18 35.94 39.70 44.52 50.19 38.12 36.37 45.81 57.27

Average Capacity 284,110 277,556 253,668 204,620 123,409 130,560 261,120 168,973 53,045

PSNR 31.8 34.42 38.35 43.67 50.79 35.87 34.20 46.79 57.68

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of our embedding algorithm, compared to the other two algorithms, and shows high reduction

in the maximum and average absolute errors is achieved when n is chosen to be2, 3or4.

4.5 Overall performance

This subsection evaluates the overall performance of our proposed reversible data hiding

algorithm and compares its overall performance with those achieved by 21,29 . Comparisons

are made with respect to the data hiding capacity and the image visual quality.

;Data Hiding Capacity. As for capacity, comparisons are presented in Table 2. In summary,

our proposed algorithm gives a capacity increase in the range 32% -72% as compared with

the capacity achieved by 21 and in the range 8.5% -17.5% compared to the capacity

achieved by 29.

;Overall Image Quality. The visual quality of the stego image depends on the downscaling/

expansion and the data hiding steps. All comparisons were made between original cover

before downscaling and the resulting stego image after embedding with maximum hiding

capacity for each algorithm. Table 8compares the overall PSNR values for the three algorithms. It can be seen that

the PSNR values of all algorithms are close with an average of 1 dB advantage for our

proposed algorithm.

Table 9compares the of overall WPSNR values achieved by the three algorithms. The

given results show that our algorithm outperforms 21 by an average of 1 dB, and outperforms

29 by an average of 1.5 dB.

Table 10compares the overall SSIM values for the three algorithms. It shows that our data

hiding technique outperforms 21 by an average of 1 dB and outperforms 29 by an average

of 1.5 dB.

4.6 Comparison with recent difference expansion based algorithms

In this subsection, we compare the proposed algorithm with recent difference expansion

algorithms 24,54 ,55 . These algorithms have almost the same or higher numerical com-

plexity as the interpolation based techniques and utilize a type of interpolation for prediction.

The test images used for comparison are the same test images presented in 55. The

performance data for these three algorithms is taken as provided in 24,54 ,55 . Some data

is not available and is marked as NA in the table. Table 11compares the data hiding capacity

and PSNR values of the three algorithms and our algorithm. It shows that our data hiding

algorithm with embedding steps n = 1, 2, 3and4outperforms 24 in both capacity and PSNR.

Algorithm 54 gives comparable performance to our algorithm with embedding steps n=1

and 2 .Algorithm 55 gives the best PSNR values but its capacity is very low.

5Discussionandconclusion

The objective of any reversible data hiding technique is to increase the data hiding capacity

while at the same time maintain the visual quality of the stego image. Unfortunately, image

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quality and data hiding capacity are two conflicting requirements. That is, increasing the data

hiding capacity leads to image distortion and improving image quality allows less data to be

hidden in the cover image. In this paper, we proposed a new reversible data hiding technique

that increases data hiding capacity and the stego image visual quality while maintaining low

and simple numerical computations. To achieve an acceptable tradeoff between the data hiding

capacity and the stego image visual quality we proposed a new interpolation-expansion

algorithm that results in a larger number of embeddable pixels, which in turn increases the

data hiding capacity. We also proposed a new adaptive data hiding algorithm to reduce image

distortion and prevent overflow in the data hiding step.We carried out comprehensive error analysis of the proposed technique. This has been done

since interpolation-based techniques generate errors and image distortions in two major steps:

the downscaling/interpolation-expansion step and the data hiding step. We designed our

technique to reduce image distortion in both steps. Our proposed technique slightly reduces

distortions due to the expansion-interpolation step and largely reduces distortions due to the

data hiding step. In conclusion, our reversible data hiding technique gives a better visual quality of the stego

image and a higher data hiding capacity when compared with relevant interpolation based

techniques reported in the literature. It also allows for adjusting the level of trade-off between

the quality of the stego image and the data hiding capacity. This has been achieved without

increasing computational complexity. As it is generally the case with reversible data hiding

techniques, the proposed technique is meant to be fragile, and thus, no robustness experiments

against attacks were provided. Typical applications of the proposed technique are authenticated

transmission of medical images, military satellite images, and similar applications that require

exact recovery of the cover image. Finally, although our interpolation algorithm reduced distortion in the interpolation-

expansion step, we believe that distortions due to this step present a main drawback of

interpolation-based data hiding techniques. Hence, future work can be directed towards the

development of more efficient interpolation algorithms that can further reduce distortions.

Publisher’ sNote

Springer Nature remains neutral with regard to jurisdictional claims in published maps

andinstitutional affiliations.

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Dr. Ahmad Mohammadreceived his BSc in electrical engineering from Ein-Shams University, Egypt in 1981,

and the MSc and PhD degrees in electrical engineering, from Akron University, USA, in 1989, and 1992,

respectively. He has been an assistant professor at the Department of Computer Engineering, Princess Sumaya

University, Jordan, since 2000. His research interests include control systems, image processing, and information

security.

Ali Al-Haj received his first university degree in Electrical Engineering from Yarmouk University, Jordan, in

1985, the M.Sc degree in Electronics Engineering from Tottori University, Japan, in 1988 and the Ph.D degree in

Computer Engineering from Osaka University, Japan, in 1993. He then worked as a research associate at ATR

Advanced Telecommunications Research Laboratories in Kyoto, Japan, until 1995. He joined Princess Sumaya

University, Jordan, in October 1995, where he is now an associate professor. Al-Haj has published papers in

dataflow computing, information retrieval, VLSI digital signal processing, neural networks, and multimedia

watermarking.

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Dr. Mahmoud E. Farfourareceived his PhD. degree in computer science from National Taiwan University of

Science and Technology in 2013. He worked as a researcher in Royal Scientific Society for more than 10 years.

Currently, he is a faculty member in King Talal Faculty of Business and Technology, Princess Sumaya University

for Technology, Jordan-Amman. His research interests include digital watermarking, image processing and

multimedia security.

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