1
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
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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
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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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a) Existing watermark image b) Proposed watermark image
Figure 4.10: Embedded Elaine image of existing and proposed scheme
a) Existing watermark image b) Proposed watermark image
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.
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