International Journal of Pure and Applied Mathematics ... · the visual quality in terms of PSNR, by ignoring the low frequency of non zero coefficients. Keywords : DCT(Discrete Cosine

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POLYNOMIAL BASED NEAR REVERSIBLE DATA HIDING SCHEME USING

DCT

T. BHASKAR

Full-Time Research Scholar,

JNTUH, Hyderabad, Email: [email protected]

D. VASUMATHI

Professor, Dept of CSE,

JNTUH, Hyderabad

Abstract

Changing of original content up to some extent is acceptable in a scheme called Near Reversible. This scheme

is used in many applications. It is mostly used in remote sensing application, when the image is captured while

monitoring the damaged regions in the natural disasters such as tsunami, volcanic eruption, etc. The captured

image is not clearly visible so, changing the contents of original image is acceptable by using function.A

polynomial based function is proposedin this paper by considering non zero DCT coefficients values. A Zig-

Zag scan is used to select particular non zero AC coefficients values for embedding. Our focus is to improve

the visual quality in terms of PSNR, by ignoring the low frequency of non zero coefficients.

Keywords: DCT(Discrete Cosine Transform), PSNR(Peak Signal to Noise Ratio), Zig-Zag scan,

Reversible,Near Reversible..

1. Introduction

Data Hiding techniques can be carried out in 3 domains [15], Spatial Domain [26], [27],

Compressed Domain [23], [24], [25] and Frequency Domain [20],[33],[35]. Every

domain has its own advantages and disadvantages in hiding capacity, finishing time,

memory space, and other features. The data hiding schemes are classified into

Irreversible [28],[29], Reversible and Near Reversible. In Irreversible Data Hiding

scheme original content cannot be restored and in Reversible Data Hiding

Scheme[30],[31],[32],[33] not only embeds data into content, but also restores the

original content after extraction [2],[3],[4]. But, more modifications to the original

content and not emphasis on reversibility using scheme called Near Reversible data

hiding [9]. The essential features of any data hiding scheme are visual quality, hiding

capacity and robustness [6],[8],[21],[22]. Thus changes among three features vary from

application to application, depending on user’s requirements and applications domains.

Therefore, a class of data hiding scheme is needed (near reversible) for applications like

copyright protection of remote sensing images [10]. But in this we only focus on the

International Journal of Pure and Applied MathematicsVolume 119 No. 7 2018, 1311-1324ISSN: 1311-8080 (printed version); ISSN: 1314-3395 (on-line version)url: http://www.ijpam.euSpecial Issue ijpam.eu

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visual quality of the embedded image by proposing the polynomial based near reversible

scheme using DCT.

2. Existing Scheme

The visual quality, embedding capacity and robustness is partially achieved by the

sagar et al. scheme [1] which use logarithmic function. This scheme achieves reversibility

and high capacity, lags good visual quality which has to be addressed.

In sagar et al. scheme all the non zero AC coefficients are considered for embedding

[11], [12]. Because of this reason visual quality in terms of PSNR is low.

3. Proposed scheme

In the proposed scheme, our focus is to improve the visual quality in terms of

PSNR[5]. We are ignoring the low frequency i.e., non zero coefficients of DCT to

improve the PSNR values. As a result, the embedding capacity is reduced and NK is

almost same but achieving the good visual quality in the form of

PSNR[14],[16],[17],[19] is our motivation. When the multimedia content is not clear

instead of considering low frequency we go for middle and high frequency of the

multimedia content, because the multimedia content is not clear. This scheme is proposed

to embed the secret data or watermark instead of low frequency area.

Altering low frequency component results in poor visual quality. To increase the

visual quality we propose to use Zig-Zag scan process as in the Fig 1. The scan List of

Zig-Zag we are considering from the quantized DCT values from i=11.

Figure 3.1. Zig-Zag Scan Process

International Journal of Pure and Applied Mathematics Special Issue

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Zig-Zag scanning is move from low frequency component to high frequency

component and as most of the energy is stored in low frequency component that’s why

this scan is favoured and employed after non uniform quantization of N X N DCT [7]

coefficients and before run length coding of them.

The Zig-Zag scan instructions the DCT coefficients into an efficient manner for this

coding phase to take advantage of their structure. This ordering is quite optimal for

lossless compression algorithms. The DCT compression happens after zig-zag ordering.

A polynomial based mathematical equation (2) is used to achieve the above objective

i.e., visual quality of the images.

The input image [13] taken as input is portioned into blocks of intensity

values and 2- dimensional DCT is applied on each block. Then each block is divided by

quantization table of block. For each block Zig-Zag scan algorithm and in Zig-

Zag scanned list we have to consider the quantized DCT values from i=11. In embedding

process, the data is embedded in all non-zero DCT coefficients i.e. the block whose

number of non-zero DCT coefficients is greater than zero then the data is embedded in

that block is embedded as shown in Figure 2.

3.1 Data embedding procedure

Figure 3.2: Generic data embedding procedure

The data is embedded in all non-zero DCT Coefficients pixels in each block except

the blocks equal to zero. For better visual quality, the design is proposed to reduce the

modifications to the original coefficients i.e. the watermarked coefficients are retained to

nearer value of original coefficients. Polynomial equation (2) is used to transform the

generated DCT coefficients for hiding the secret data[9].


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Algorithm: Embedding

1. Take an input image I and

2. Partition I using DCT I

For each , where

(a) Quantize the DCT coefficients in as below.

for

for

end

end

3. Zig-Zag scan applied (b) Compute T as shown in equation (3.1) after converting the matrix to row

or column vectorization, If , then modify all the non-zero AC

coefficients and embed the data using equation (2). Let the resultant

block be .

4. Inverse Zig-Zag Scan is applied

5. Combine all the blocks into I .

6. For all the blocks repeat step 1 to step 5.

Where is the non-zero DCT Coefficient, S is the secret bit and Em be the

modified version of c.

3.2 Data Extraction Process

The extraction procedure extracts the image with rounded values of the real part of

the polynomial equations (3.4) are used to restore [18] the generated DCT coefficients

when the Secret bit S=0 or 1.


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Figure 3.3. Generic data extraction procedure

Data Extraction is an inverse process of Data Embedding.

Algorithm: Extraction 1. Take an watermarked input image ( )

2. Extract from I .

3. Zig-Zag is Applied

For each

(a) when

i. Extract the data bits using (3).

ii. Restore the modified coefficients using (4).

Let the resultant block be .

4. Inverse Zig-Zag is Applied

5. Dequantize the elements of as follows:

for

for

end

end

. Combine all the blocks to get I i.e.

6. For all embedded , repeat step 1 to step 5.


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Where is the restored version of original c.

Note that the data extraction and embedding is the near-reversible.

4. Results and discussions

We have implemented our proposed scheme using MATLAB. We used

GIF formatted grayscale images in the implementation.

Figure 4.1: Behaviour of existing function and proposed functions

Where equation 5 is y=AC coefficients of original image,

equation 6 is

equation 7 is

equation 8 is .

equation 9 is and

equation 10 is

Where be the non-zero DCT coefficient and y be the modified version of . From the

graph, we can observe that function 8 changes drastically with respect to their original

coefficients which cause the distortion or unclear. From equation 6 and equation 9 graphs


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it is observed that the incode because they retain maximum values to original values.

Here we have chosen equation 6 and 9 for hiding the data.

Figure 4.2: Comparison of Capacity

We can observe from the figure 4.2 that existing scheme and proposed scheme results are

not same because we are ignoring the low frequency non zero coefficients to improve the

visual quality as a result, embedding capacity is reduced.

Figure 4.3: Comparison of NK

As the Normalized Cross-Correlation checks the identity between images where

[0, 1] and more the value near to one the more they are highly correlated, we can

achieve them from figure 4.3 that the proposed scheme achieve values more nearer to

one than the existing scheme. Hence, proposed scheme is highly correlated and proposed

scheme achieves almost same NK than the existing scheme.


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Figure 4.4: Comparison of PSNR

We can observe from figure 4.4 that the proposed scheme achieves better results for

PSNR than the existing scheme

Therefore, proposed scheme performs better than the existing scheme, because ignoring

the low frequency non zero coefficients of DCT. We present different images of GIF

format of size in the following and their corresponding distorted images

can also be observed from all the observations, we can find that the existing scheme

distorts the images more where as the proposed scheme achieves better visual quality.

Figure 4.5: Embedded aerial image of existing and proposed scheme

a) Existing watermark imageb) Proposed watermark image

Figure 4.6: Embedded airplane image of existing and proposed scheme


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a) Existing watermark image b) Proposed watermark image

Figure 4.7: Embedded Barb image of existing and proposed scheme

a) Existing watermark image: b) Proposed watermark image:

Figure 4.8: Embedded Boat image of existing and proposed scheme

a) Existing watermark image: b) Proposed watermark image:

Figure 4.9: Embedded Couple image of existing and proposed scheme


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Figure 4.10: Embedded Elaine image of existing and proposed scheme


Figure 4.11: Embedded Lena image of existing and proposed scheme

a) Existing watermark imageb) Proposed watermark image:

Figure 4.12: Embedded Zelda image of existing and proposed scheme


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a) Existing watermark image b) Proposed watermark image:

5. Conclusion

The expansion of the new category near-reversible data embedding, there is a require for

more sophisticated scheme. The near reversible scheme addressed many applications of

remote sensing. The existing scheme degrades the visual quality and creates many

unclear images due to use of log function which transforms the coefficients with greater

difference. The proposed scheme achieves higher visual quality as it minimizes the

difference between original non-zero DCT coefficients to the embedded coefficients. The

same scheme can be extended to video sequences.

References

Sagar Gujjunoori, B. B. Amberker, “A DCT Based Near Reversible Data Embedding Scheme for

MPEG-4 Video,” Proceedings of the Fourth International Conference on Signal and Image

Processing 2012 (ICSIP 2012), pp 69-79, 2013.

Fridrich J, Du R, “Lossless authentication of MPEG-2 video,” In: ICIP’02, pp 893–896, 2002.

Sagar G, Amberker BB, “A DCT based reversible data hiding scheme for mpeg-4 video,” In:

Proceedings of international conference on signal, Image and Video Processing (ICSIVP)

2012, IIT Patna, pp 254–259, Jan 2012.

Zeng X, Chen Z, Zhang X, “Issues and solution on distortion drift in reversible video data

hiding,” Multimedia Tools Appl 52(2–3):465–484, 2011.

Barni M, Bartolini F, Cappellini V, Magli E, Olmo G, “ Near-lossless digital watermarking for

copyright protection of remote sensing images,” IGARSS ’02., vol 3, pp 1447–1449, 2002.


1321

12

Langelaar, G.C., Setyawan, I. and Lagendijk, R.L., Watermarking digital image and video data: a

state-of-the-art overview. IEEE Signal Processing Magazine. v17 i5. 20-46.

N. Ponomarenko, F. Silvestri, K.Egiazarian, M. Carli, V. Lukin, “On Between-Coefficient

ContrastMasking of DCT Basis Functions,” CD-ROM proceedings of Third International

Workshop on Video Processing and Quality Metrics for Consumer Electronics VPQM-07, 4p,

January 2007.

Podilchuk, C.I. and Delp, E.J., Digital watermarking: algorithms and applications. IEEE Signal

Processing Magazine. v18 i4. 33-46.

Hsu C-T, Wu J-L, “Hidden digital watermarks in images,” IEEE Trans Image Process 8(1):58–

68, 1999.

Ahmed F, Moskowitz, “A semi-reversible watermark for medical image authentication,” In: 1st

Transdisciplinary conference on distributed diagnosis and home healthcare. D2H2, pp 59–62,

2006.

Tang Y-L, Huang H-T, “Robust near-reversible data embedding using histogram projection,” In:

In IIH-MSP 2007, vol 02, pp 453–456, 2007.

Zhang B, Xin Y, Niu X-X, Yuan K-G, Jiang H-B, “A near reversible image watermarking

algorithm,” In: International conference on machine learning and cybernetics (ICMLC), vol 6,

pp 2824–2828, july 2010.

G. Wallace, “The JPEG still Picture Compression Standard,” Comm. of the AC, vol. 34, No. 4,

1991.

T. Movshon and L. Kiorpes, “Analysis of the development of spatial sensitivity in monkey and

human infants,” JOSA A. vol5, 1998.

P.G. J. Barten, “Contrast Sensitivity of the Human Eye and Its Effects on Image Quality,” SPIE,

Bellingham, WA, 1999.

S. Daly, “The Visible Differences Predictor: An algorithm for the assessment of image fidelity,”

Ch. 13 in Digital Images and Human Vision, A.B. Watson Ed., MIT Press, Cambridge, MA,

1993.

M. P. Eckert and A. P. Bradley, “Perceptual quality metrics applied to still image compression,”

Signal Processing, vol. 70, pp. 177–200, Nov. 1998.

E. P. Simoncelli,“ Statistical models for images: compression, restoration and synthesis,” in Proc

31st Asilomar Conf. Signals,Systems and Computers, Pacific Grove, CA, pp. 673–678, Nov.

1997.

B. Watson, “Visual detection of spatial contrast patterns: evaluation of five simple models,” Opt.

Exp., vol. 6, pp. 12–33, Jan. 2000.

J. Fridrich, M. Goljan and D. Rui., "Lossless Data Embedding-New Paradigm in Digital

Watermarking", In Special Issue onEmerging Applications of Multimedia Data Hiding, Vol. 2,

pp. 185-196, February 2002.

Petitcolas, F.A.P., Watermarking schemes evaluation. IEEE Signal Processing Magazine. v17 i5.

58-64.

F.A.P. Petitcolas, R.J. Anderson, M.G. Kuhn, Information hiding - a survey, in: Proceedings of

the IEEE 87(7) (1999) 1062-1078.


1322

13

Chin-Chen Chang , Wei-Liang Tai , Chia-Chen Lin, A Reversible Data Hiding Scheme Based

on Side Match Vector Quantization,IEEE Transactions on Circuits and Systems for Video

technology, v.16 n.10, p.1301-1308, October 2006

Ching-Chiuan Lin , Shih-Chieh Chen , Nien-Lin Hsueh, Adaptive embedding techniques for

VQ-compressed images,Information Sciences: an International Journal, v.179 n.1-2, p.140-

149, January, 2009

Jun-Xiang Wang , Zhe-Ming Lu, A path optional lossless data hiding scheme based on VQ joint

neighboring coding, Information Sciences: an International Journal, v.179 n.19, p.3332-3348,

September, 2009

Mielikainen, J., LSB matching revisited. IEEE Signal Processing Letters. v13 i5. 285-287.

Hang, X.P. and Wang, S.Z., Efficient steganographic embedding by exploiting modification

direction. IEEE Communications Letters. v10 i11. 1-3.

Tse-Hua Lan , A. H. Tewfik, A novel high-capacity data- embedding system, IEEE Transactions

on Image Processing,v.15 n.8, p.2431-2440, August 2006

Chiang-Lung Liu , Shiang-Rong Liao, High-performance JPEG steganography using

complementary embedding strategy, Pattern Recognition, v.41 n.9, p.2945-2955, September,

2008

Hyoung Joong Kim , V. Sachnev , Yun Qing Shi , Jeho Nam , Hyon-Gon Choo, A Novel

Difference Expansion Transform for Reversible Data Embedding, IEEE Transactions on

Information Forensics and Security, v.3 n.3, p.456-465, September 2008

Chih-Chiang Lee , Hsien-Chu Wu , Chwei-Shyong Tsai , Yen-Ping Chu, Adaptive lossless

steganographic scheme with centralized difference expansion, Pattern Recognition, v.41 n.6,

p.2097-2106, June, 2008.

Ching-Chiuan Lin , Nien-Lin Hsueh, A lossless data hiding scheme based on three-pixel block

differences, Pattern Recognition, v.41 n.4, p.1415-1425, April, 2008.

Hsien-Wen Tseng , Chi-Pin Hsieh, Prediction-based reversible data hiding, Information

Sciences: an International Journal, v.179 n.14, p.2460-2469, June, 2009


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International Journal of Pure and Applied Mathematics ... · the visual quality in terms of PSNR, by ignoring the low frequency of non zero coefficients. Keywords : DCT(Discrete Cosine

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