R. Benlamri (Ed.): NDT 2012, Part II, CCIS 294, pp. 243–252, 2012. © Springer-Verlag Berlin Heidelberg 2012

High-Capacity Image Steganography Based on Overlapped Pixel Differences and Modulus Function

El-Sayed M. El-Alfy and Azzat A. Al-Sadi

College of Computer Sciences and Engineering King Fahd University of Petroleum and Minerals

31261 Dhahran, Saudi Arabia alfy@kfupm.edu.sa, azzat.sadi@gmail.com

Abstract. Several steganographic methods have been proposed based on pixel value differencing (PVD) attempting to increase the embedding capacity with-out great loss in the perceived image quality. Among these methods is the over-lapping pixel-value differencing (OPVD) which can hide more data than the original PVD. However, it still skips huge number of image pixels during the embedding process due to the out-range condition. In addition, it has some se-curity flaws which can be visualized through histogram analysis. In this paper, a high capacity steganographic method is proposed based on the overlapping concept. Unlike OPVD, the proposed method involves a modulus function and a correction procedure to mitigate the out-range condition. The proposed me-thod is evaluated on a number of test images and it is found to yield better re-sults as compared to PVD and OPVD.

Keywords: Digital Image Steganography, Pixel-Value Differencing, Overlap-ping PVD, Modulus Function, Histogram Analysis.

1 Introduction

Nowadays the Internet is playing a major role in the developed and developing socie-ties. Hence, its use in transferring confidential information is growing in several ap-plications. Securing this information can be very critical to government, business, industry and even individuals. Steganography is one of the extremely important areas of information security. Unlike cryptography which changes the message to make it unreadable by an adversary (a third party), steganography hides the very presence of secret information [1], [2]. It uses a cover (carrier) medium to conceal the secret mes-sage in it before transmission over a public communication channel. Thus, it protects the message confidentiality against unauthorized access. Data can be encrypted and/or compressed before applying steganography to increase the security level and reduce the amount of data to be embedded which consequently can reduce the perceived artifacts in the carrier image.

In the literature, several steganographic methods have been proposed for embed-ding data in digital images as cover media, whether in spatial or frequency domains. One of the relatively recent methods, pixel-value differencing (PVD), was proposed

244 E.-S.M. El-Alfy and A.A. Al-Sadi

[4] aiming to increase the embedding capacity without creating perceptible artifacts. This method utilizes the characteristic that human eyes cannot observe large changes around edges as they can do in smooth areas. Hence, the number of embedded bits at each pixel pair is varied based on the pixel pair value difference. PVD uses non-overlapping blocks and divides the value to be embedded among the pixels in each pixel pair. Another method proposed by Chang et al. [3] is known as overlapping PVD (OPVD). Unlike the original PVD, OPVD utilizes the overlapping blocks and hide the secret bits in the second pixel only of each pixel pair using a simple least-significant bit (LSB) replacement method [5][6][7]. Although this method has higher capacity than the original PVD, it skips many pixels with no embedding.

In this paper, we propose an image steganography based on the concept of over-lapping blocks similar to OPVD but with a correction procedure to reduce the number of unused pixels. Unlike OPVD, the proposed method also uses a modulus function for embedding instead of the LSB replacement. With these modifications to the OPVD method, the proposed method has higher embedding capacity without visible artifacts in the image histogram.

The rest of this paper is organized as follows. In the next Section, we briefly re-view the related steganographic methods. In Section 3, the proposed method is de-scribed. Experimental results are discussed in Section 4. Finally, Section 5 concludes the paper.

2 Background

In this section, we provide a brief review of two related methods: The pixel-value differencing (PVD) method and the overlapping PVD (OPVD).

2.1 Pixel Value Differencing (PVD)

The pixel-value differencing (PVD) method was originally proposed to hide secret messages into 256 gray-valued images [4]. It can embed larger amount of data with-out much degradation in the image quality and thus are hardly noticeable by human eyes (i.e. more resistant to visual attacks than the traditional LSB). It is based on the fact that human eyes can observe small changes in the gray values of smooth areas in the image much easier than they can observe at the edge areas. PVD uses the differ-ence of each pair of pixels to determine the number of message bits that can be em-bedded into that pixel pair. It starts at the upper-left corner of the cover image and scans the image in a zigzag manner. Then, it partitions the resulting sequence into blocks where each block consists of two consecutive non-overlapping pixels. The differences of the two-pixel blocks are used to categorize the smoothness properties of the cover image. Pixels around an edge area will have larger differences whereas pixels at smooth areas will have smaller differences. The larger the difference is, the more bits can be embedded into that pixel-pair.

Thus, instead of inserting a fixed number of bits into each pixel, as the least signif-icant bit (LSB) replacement method does, PVD adapts the number of embedded bits

High-Capacity Image Steganography Based on Overlapped Pixel Differences 245

to the characteristics of each pixel pair. In order to accomplish that, the range of gray values (0, 255) is divided into smaller ranges and each range ri is demarcated by low and upper boundary, li and ui, respectively. Then, the absolute value of the difference of each pixel pair is located into one range and the number of bits to be embedded into this pixel pair is determined by the width of this particular range. The width of range ri is wi = ui ‒ li + 1 and hence the number of bits to be embedded is given by ni

= log2(wi). Ranges close to the 0 bound represent smoother areas and thus have small-er widths. Although widths of ranges can take any values, it is common to use values that are powers of 2 and monotonically increase as they move away from the 0 bound. The authors of PVD have used two different sets for ranges: {(0-7), (8-15), (16-31), (32-63), (64-127), (128-255)} and {(0-1), (2-3), (4-7), (8-11), (12-15), (16-23), (24-31), (32-47), (48-63), (64-95), (96-127), (128-191), (192-255)}. Note that each set covers the whole gray scale range of 256 values.

Although PVD has some advantages in terms of embedding capacity and peak-signal-to-noise ratio (PSNR), it has some defects. To enhance the quality of the stego-image of the PVD method, Wang et al. [10] proposed PVD with modulus function approach. Unlike the original PVD which uses the difference between a pixel-pair, PVD with modulus function approach adjusts the remainder of two consecutive pixels to embed a certain number of secret bits. But similar to the PVD, the number of em-bedded bits in each pixel-pair is defined by the width of the range within which the difference of the two pixels falls.

2.2 Overlapping PVD

The goal of the Overlapping PVD (OPVD) approach is to increase the embedding capacity of the original PVD while keeping acceptable image quality [3]. Comparing to the original Wu and Tasi’s PVD method [4], OPVD achieved higher embedding capacity with an average gain around 84.16%. OPVD method hides the secret data using in individual pixels instead of hiding it in a pixel pair using LSB replacement. Fig. 1 demonstrates the concept of overlapping pixel-value differencing (OPVD) and contrasts it to PVD.

Fig. 1. Demonstration of the difference between PVD and OPVD approaches

If the pixel-pair's difference before and after hiding the secret data belongs to the same range, the embedding process is executed. Otherwise, the secret bits cannot be embedded and the second pixel is adjusted to indicate this situation. This adjustment sets the pixel-pair difference to the upper or lower boundary of its range. Regardless of embedding or not, the second pixel will be the first pixel in the next pixel pair.

PVD

di di+1 di+2

P0

di di+1

P1 P2 P3 P0 P1 P2 P3

OPVD

246 E.-S.M. El-Alfy and A.A. Al-Sadi

Although this approach embeds more secret bits than PVD, it still has a large num-ber of unused pixels which in turn limits its embedding capacity. Furthermore, using simple LSB method and the adjustment procedure deforms the stego-image histo-gram. Thus, this approach can be easily detected by the steganalyzer using the image histogram. Our proposed method, as explained in the next section, mitigates these problems by forcing the difference of the pixel-pair to fall in the same range and by using modulus PVD instead of the LSB method.

3 The Proposed Method

We aim at increasing the hiding capacity and enhancing the security of the overlap-ping pixel-value differencing (OPVD) method while preserving the image quality. To achieve these goals, we propose a novel steganographic method based on the pixel overlapping concept. Similar to OPVD, the proposed method utilizes the difference of a two-pixel block to identify the smoothness and contrast in that block. Then, it em-beds a number of secret bits in the second pixel based on the calculated difference. After that, the second pixel is used as a first pixel in the next block and the process is repeated. This leads to increasing the embedding capacity.

Unlike the overlapping PVD (OPVD) approach which skips too many pixels while embedding because of the out-range condition, the proposed method overcomes this problem by a correction procedure. By adjusting the range of the new difference d’ between the two pixels after embedding to fall in the same range as the pixel differ-ence d before embedding, our proposed method can utilize more unused pixels. Al-though this adjustment affects the value of the pixel, it does not change the value of the embedded data. In addition, instead of using LSB replacement which is used in OPVD, our proposed method embeds the secret message into the cover-image pixels by modifying the remainder of the pixel pair using some modulus function. Thus, the proposed method mitigates the LSB security limitation and its embedding noise on the stego-image histogram [11] [12].

3.1 Embedding

The embedding procedure is shown in Fig. 2 and it can be described by the following steps:

• Consider a pixel-pair block Fi that has pixels Pix and Piy, calculate the absolute pixel value difference:

i iy ixd P P= − (1)

Find the corresponding range such that li ≤ di ≤ ui and calculate the range width wi = ui – li + 1,

the number of secret bits to be embedded ni = log2(wi) and its decimal

value is bi. Then calculate the block remainder Firem from:

( ) 2 inirem ix iyF P P mod= + (2)

High-Capacity Image Steganography Based on Overlapped Pixel Differences 247

• Embed ni bits of the secret data into the second pixel Piy such that 'irem iF b= as

follows:

1

11 1

2 1

1 1

2 1

1

1

, and 2

, and 2'

, and 2

, and 2

i

i

i

i

niy irem i

niy irem i

iy niy irem i

niy irem i

P m F b m

P m F b mP

P m F b m

P m F b m

−

−

−

−

=

− > ≤ + > > + ≤ ≤ − ≤ >

(3)

where 1 irem im F b= − ,

2 12 inm m= − and 'iyP is the value for the second pixel of

the pixel-pair after embedding.

Fig. 2. The embedding procedure of the proposed method

• Check the new difference of the pixel-pair after the embedding to ensure that the new difference ' '

iy ixd P P= − is in the same range as the old difference d. If they

are in different ranges, 'iyP is adjusted by adding or subtracting 2 in . This adjust-

ment will return the value of d’ to the same range as d without affecting the em-bedded secret bits.

• After this modification to preserve the same range, only few pixel values may fall out of the range (0, 255) which is not a proper gray level. These pixels are not used for embedding and they will be marked as unused by moving them to the upper limit 255.

Take a 2-pixel

block {Pix ,Piy} Calculate di , Firem , ni Embed ni bits from the

secret message M such

that F’rem= bi

End

Adjust Piy by

±2ni

M

Yes

No

Piy ∈ (0,255)

Mark as

unused

YesNo

Pix+1 =P’iy

Cover

Stego

d and d’

same range?

No

Yes

248 E.-S.M. El-Alfy and A.A. Al-Sadi

3.2 Extraction

The extraction of the secret bits from the block 'iF is straightforward by calculating

the binary bits from the pixel block remainder of the stego-image, which is 'irem iF b= .

Similar to other steganographic methods applied in spatial domain, we assume that if compression is used after embedding, it is lossless compression. In the latter case, the stego-image is decompressed first before extraction is applied.

4 Experimental Work

We implemented the proposed method in Matlab R2010b and evaluated it using ten 512×512 gray-level test images as cover images. These test images were commonly used in other publications on image processing, image compression and steganogra-phy. In our experiments, a very long secret message of 9Mbits was randomly generat-ed and used for all evaluations. The absolute difference ranges were set to {(0-7), (8-15), (16-31), (32-63), (64-127), (128-255)}; similar to what has been used in the original PVD. We calculated the embedding capacity, the number of unutilized pixels and the peak signal to noise ratio (PSNR) as performance measures. The PSNR is calculated from:

[ ]2

10

( )10

max xPSNR log dB

MSE= × (4)

where MSE is the mean-square error and is calculated as follows:

1 1

2

0 0

1( ) ( )

m n

ij iji j

MSE x ym n

− −

= =

= −× (5)

where m×n represents the size of the cover image, x refers to the pixels of the cover image and y refers to the pixels of the stego-image.

For the sake of comparison, we implemented two other methods (the pixel-value differencing (PVD) [4] and the overlapping pixel-value differencing (OPVD) [3]) and applied them on the same test images. The results of our experiments are summarized in Table 1 for the ten test images and the three embedding methods. Although the original PVD made use of all the image pixels, its embedding capacity is low com-pared to OPVD. But the number of unused pixels in OPVD is still high and our pro-posed method reduces it significantly. Moreover, the proposed method has increased the embedding capacity drastically by very small degradation in the image quality, as assessed by PSNR. Fig. 3 shows the embedding capacities for the proposed method as compared to PVD and OPVD. It is obvious that our proposed method succeeded to increase the capacity by 1.14 up to 1.94 times more than the OPVD method and by about 2 times more than the original PVD. The average PSNR for our method is re-duced by only 5.3 dB than the original PVD and by 3 dB than the OPVD method. However, the average PSNR of the proposed method is still above 30 dB; this makes the stego-image indifferentiable from the cover image by the human eyes.

High-Capacity Image

Table 1. Comparing th

Image

PVD Capacity

(bits) PSNR

(dB)

Tank 403990 41.20

Plane 397904 42.00

Elaine 408582 41.44

Car 400504 42.72

Bridge 442290 37.64

Aerial 430783 38.48

Boat 419317 39.55

Lena 409804 40.77

Peppers 402552 40.62

Baboon 456867 36.05

Avg. 417259.3 40.047

Fig. 3. Capacity c

Fig. 4 illustrates sampleafter embedding the secret one). The corresponding imFig. 5. We can notice fromcaused by the OPVD methohistogram when our propos

0

100000

200000

300000

400000

500000

600000

700000

800000

900000

1000000

Tank Plane

Cap

acit

y (b

its)

e Steganography Based on Overlapped Pixel Differences

he proposed method to PVD and OPVD on ten test images

OPVD

Proposed Capacity

(bits) PSNR

(dB)

Unused

pixels

Capacity

(bits) PSNR

(dB)

Unuse

pixe

570013 37.99 74118

810426 36.41 1

691542 38.10 32129 794906 38.09 1

540343 38.98 84636 820296 36.42 7

597815 38.94 64109 802006 38.36 0

507384 37.24 103171 889368 32.04 398

559041 37.10 83617 863783 32.71 730

549873 37.91 84217 845209 33.34 169

590573 38.04 68557 820150 35.56 13

587458 37.63 68822 815337 35.05 14

478723 35.50 115772 921399 29.90 9

567276.5 37.743 77914.8 838288 34.788 134

comparison for different methods for ten test images

s of the test images (Boat, Aerial and Peppers) before data by different methods (PVD, OPVD and the propo

mage histograms for the same sample images are shownm this figure the clear distortion in the image histogrod. On the other hand, no artifacts are clear from the imsed method is applied.

Elaine Car Bridge Aerial Boat Lena Peppers Baboon

Image

PVD OPVD Proposed

249

ed

els

4.2

and osed n in ram

mage

250 E.-S.M. El-Alfy and

(a)

(d) Ste

Fig. 4. Image compa

A.A. Al-Sadi

Original images (Boat, Aerial and Peppers)

(b) Stego-images resulted from PVD

(c) Stego-images resulted from OPVD

ego-images resulted from the proposed method

arison before and after embedding by different methods

High-Capacity Image Steganography Based on Overlapped Pixel Differences 251

(a) Histograms of original images (Boat, Aerial and Peppers)

(b) Histograms of stego images resulted from PVD

(c) Histograms of stego images resulted from OPVD

(d) Histograms of stego images resulted from the proposed method

Fig. 5. Histogram comparison for different methods on three sample test images

5 Conclusion

Invisibility, capacity and security are three aspects of a good steganographic method. In this paper, we proposed a new steganographic method using the concept of overlap-ping with pixel difference and modulus function. Our method aims at increasing the capacity of hidden data by utilizing the unused pixels in the OPVD method without much degradation in the image quality. In addition, no visible artifacts are noticed in the images or in their histograms after the embedding process of the proposed method.

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252 E.-S.M. El-Alfy and A.A. Al-Sadi

Acknowledgments. The authors would like to thank King Fahd University of Petro-leum & Minerals (KFUPM), Saudi Arabia, and the Hadhramout Establishment for Human Development, Yemen, for their support during this work.

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