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A Semi-Fragile Watermarking Method Using Slant
Transform and LU Decomposition for Image
Authentication
Imran Sikder1, Pranab Kumar Dhar*1, and Tetsuya Shimamura2
1

Department of Computer Science and Engineering, Chittagong University of Engineering and Technology (CUET),
Chittagong-4349, Bangladesh
2
Department of Information and Computer Sciences, Saitama University, Saitama 338-8570, Japan
Email: sikder.5.imran@gmail.com, pranabdhar81@gmail.com, shima@sie.ics.saitama-u.ac.jp

Abstract— Semi-fragile watermarking has been widely used for content
authentication. In this paper, we propose a semi-fragile watermarking
method using slant transform (ST) and LU decomposition (LUD) for
image authentication. Initially, the watermark image is scrambled using
an algorithm to enhance the confidentiality of the image. The host image
is separated into red, green, and blue channels. The red channel is divided
into 8×8 non-overlapping blocks. ST is applied to each block to get the ST
coefficients. LU decomposition is then applied to these coefficients to
obtain the lower and upper triangular matrix. Watermark data is
embedded into the upper triangular matrix of ST coefficients using an
embedding equation. Simulation results indicate that proposed method
produces high quality watermarked image, provides secure embedding,
extraction and authentication. Moreover, it effectively detects malicious
tempering on image while being resistant to various content preserving
manipulations. Furthermore, it shows superior performance than the
state-of-the-art methods in terms of imperceptibility.
Keywords—Semi-fragile watermarking;
decomposition; content authentication.

slant

transform;

LU

I. INTRODUCTION
Due to the ease of tampering, now-a-days authentication of
digital image has become an important issue. Authentication
technique needs to differentiate between content preserving
and malicious manipulation. Digital watermarking is an
effective way to solve this problem. Fragile and semi-fragile
schemes have been used so far for image authentication.
Fragile schemes are very sensitive to even slightest
modification in the test image while semi-fragile schemes can
withstand against some content preserving manipulation.
Many image watermarking method were proposed in last
few decades. A comprehensive survey on image watermarking
can be found in [1]. Most image watermarking methods utilize
the spatial domain [2] or the transform domain [3]-[5]. Qin et
al. [6] proposed a fragile scheme based on non-subsampled
contourlet transform. In this scheme, watermark sequence was
generated using hashing technique. Watermark bit was
embedded using LSB embedding technique. Apart from
authentication, it can also localize the tampering. It provides
good quality image, however, data embedding capacity is
quite low. Al-Otum [7] introduced a semi-fragile
watermarking scheme based on an adjusted expanded-bit multi
*

Corresponding author

978-1-5090-5627-9/17/$31.00 ©2017 IEEE

scale quantization for grayscale image authentication and
tamper detection. But this method can not applicable for color
image. A semi-fragile watermarking method for authentication
and restoration of images using irregular sampling was
proposed by Zhu et al. [8]. Liu [9] proposed a color image
watermarking method for tamper proofing and pattern-based
recovery. But the peak signal-to-noise-ratio (PSNR) result of
these methods is little low. The authors of [10] introduced a
semi-fragile image watermarking method based on index
constrained vector quantization. Roldan et al. [11] presented a
watermarking-based image authentication method with
recovery capability using halftoning technique.. The authors of
[12] presented a novel wavelet-based QIM data hiding
technique for tamper detection and correction of digital
images. Maeno et al. [13] introduced a new semi-fragile image
authentication watermarking technique using random bias and
nonuniform quantization. However, these methods can not
applicable for color image. Preda and Vizireanu [14] presented
an authentication scheme in DCT domain. Watermark
sequence has been generated using hash function,
pseudorandom sequence, and block feature. Watermark bit
was embedded using a modified QIM approach. It produced
high quality image and robustness against lossy compression,
but provided false positive and false negative results in
detecting malicious attacks. Chamlawi et al. [15] proposed a
wavelet based image authentication and recovery system.
Here, DCT is performed on LL1 band of integer wavelet
coefficients of host image. Then coefficients are quantized
using JPEG quantization matrix. This method provides
robustness against lossy compression but produced image
quality is poor and scheme only works for grayscale image. To
overcome these limitations, this paper proposes a semi-fragile
authentication method based on slant transform (ST) and LU
decomposition (LUD) which provides good quality images
and efficiently detect malicious manipulations and alterations.
The rest of the paper is organized as follows. Section II
provides background information including ST and LUD.
Section III introduces the proposed watermarking method.
Section IV discusses the experimental results of the proposed
method. Finally, Section V concludes this paper.

II. BACKGROUND INFORMATION
A. Slant Transform
ST has been widely used in signal processing. It converts
the original signal from spatial domain to frequency domain. It
is an orthogonal transform which has fast computing capacity.
It also has good recovery characteristic and is sub-optimum
for energy compaction. If I, S, J represents original matrix,
slant matrix, and transformed matrix, respectively, then ST
can be given as:
(1)
J = S × I × ST
The inverse ST is given by:
T

I = S ×J × S

(2)

B. LU Decomposition
LUD decomposes a matrix into lower triangular matrix and
an upper triangular matrix. If [A] is the original matrix, [L]
and [U] are lower and upper triangular matrix, respectively,
then LU decomposition can be given as:
(3)
A=L×U

blue channels.
Step 2: The red channel is then divided into 8×8 nonoverlapping block.
Step 3: ST is performed on each block of the red channel.
Step 4: LUD is applied to each transformed matrix to get
the lower and upper triangular matrices.
Step 5: Watermark is embedded into selected coefficients of
the first row of upper triangular matrix using a new
embedding equation with a secret key K which is given as
follows:
(7)
U' (i, j) =floor(U(i ,j)/2q+1)×2q+(1-w(i, j))
Here, U(i, j) and U'(i, j) are original and watermarked upper
triangular matrices, respectively, q is the quantization step
size.
Step 6: Inverse LUD is applied to obtain the watermarked
upper triangular matrix.
Step 7: Inverse ST is applied to obtain the watermarked red
channel.
Step 8: Finally, all channels are combined to get the
watermarked image.

Upper matrix contains the better energy distribution.
Therefore, this matrix is suitable for embedding watermark.

Separate the image into
Red, green and blue channel

III. PROPOSED WATERMARKING ALGORITHM

Host image

Let A={ a(i, j), 1 ≤ i ≤ M, 1 ≤ j ≤ M } be the host image
and W={w(k, l), 1 ≤ k ≤ N, 1 ≤ l ≤ N } be a binary watermark
image that embeds into the original image.
A. Watermark Preprocessing
Watermark image is preprocessed first to enhance its
confidentiality. The watermark image is encrypted using a
scrambling method. In this process, new position for each
pixel is found randomly and pixel pair is exchanged. After
exchanging the position, pixel pair is marked to avoid
repetition. The randomness is controlled by using a key K
which is a real number, indicating the random number
generation process. For a specific value of K specific random
sequence is generated. Two random numbers R1 and R2 are
generated using the following equation:
(4)
[R1, R2]=rand()
where, rand() is a random number generating function.
Let (a1, a2) and (b1, b2) be the two arbitrary points in
watermark image, then these two points can be found by the
following equations:
(5)
(a1, a2)=floor([R1, R2] × [N N]+[1 1])
(b1, b2)=floor([R1, R2] × [N N]+[1 1])
(6)
Here, different [R1, R2] will be generated for the two points
[a1, a2] and [b1, b2]. These two points are replaced by each
other. This process continues until all pixel positions have
been exchanged at least once. For decryption, same procedure
is followed and value of K will be same as used in encryption.
B. Watermark Embedding Process
Step 1: The host color image is divided into red, green and

Watermark image
Secret key K

encryption

Red channel is divided
into 8×8 block
ST is applied to each
block of red channel
LUD is applied to
ST coefficients
Select upper triangular
matrix

Watermark
formation

Insert watermark into
selected coefficients
Apply inverse LUD
and inverse ST
Combine all channels

Watermarked image

Fig. 1 Watermark embedding process

C. Watermark Extraction Process
Step 1: The attacked image is divided into red, green and
blue channels.
Step 2: The red channel is then divided into 8×8 nonoverlapping block.
Step 3: ST is performed on each block of the red channel.
Step 4: LUD is applied to each transformed matrix to get
the lower and upper triangular matrices.

the proposed method. From this table, we observed that the
PSNR values range from 44 dB to 46 dB. Fig. 5 shows the
qualitative evaluation of the watermarked images using the
proposed method. Table II shows the PSNR comparison
between the proposed and several recent methods for same
images. From this comparison, we observed that the proposed
method provides better result than all other methods in terms
of PSNR.

Separate the watermarked
image into different channel
Attacked
watermarked image

Red channel is divided
into 8×8 block
ST is applied to each
block of red channel
LUD is applied to
ST coefficients

TABLE I.

PSNR OF THE HOST IMAGES USING THE PROPOSED METHOD

Select upper triangular
matrix

Test Image
Baboon
Lenna
Pepper
Airplane
House
Average

Extract watermark

Secret key K

Decryption

PSNR
46.44
45.65
45.84
45.58
44.94
45.69

B. Robustness
To test the similarity between the original watermark W
and the extracted watermark W*, the normalized correlation
coefficient (NC) is calculated which is represented as follows:

Extracted watermarked image

Fig. 2 Watermark extraction process

Step 5: Watermark is extracted from the selected
coefficients of the first row of upper triangular matrix using
the following equation:
(8)
w(i,j )* = 1 if mod(round(A (i,j)/q),2)=0
(9)
w(i,j )* = 0 if mod(round(A (i,j)/q),2)=1
Step 6: The encrypted watermark image is constructed
using the extracted bits.
Step 7: Using the same scrambling procedure using the
same key K, the binary watermark image W* is formed.



*

NC (W ,W ) =

I

i =1



I

i =1

w(i) ⋅ w* (i)

w(i) ⋅ w(i)



I

i =1

w* (i) ⋅ w* (i)

(11)

In order to test the robustness of the proposed
watermarking method, different attacks such as white
Gaussian noise, JPEG compression, cropping, and mean
filtering were performed on the watermarked images.

IV. SIMULATION RESULTS AND DISCUSSION
In this section, several experiments were carried out to
evaluate the performance of the proposed method. Fig. 3
shows the watermark image and encrypted watermark image.
In our experiment, five different images (Lena, Baboon,
Pepper, Airplane, and House) of size 512×512 were used as
host image shown in Fig. 4. In this study, the selected value
for q is 5.

(a) watermark image (b) Encrypted image
Fig. 3. Watermark preprocessing

(b) Lenna

(d) Airplane

(e) House

(c) Pepper

Fig. 4 Different host images used in this study

A. Imperceptibility
The visual quality of the watermarked image is done by
calculating the peak signal-to-noise ratio (PSNR) which is
represented as:


M ×M
M ×M 

P SN R = 10 log 10 
10
log
=
10

M
M
 1
' 2
 M SE 
 MM   ( A − A )
k =1 l =1


(a) Baboon








(10)

Table 1 shows the PSNR results of different images using

The proposed method successfully detected various
malicious attacks on image which includes salt and pepper
noise, cropping, deletion and insertion of image components,
rotation, JPEG compression, brightness adjustment etc. Fig 6
shows watermarked ‘Lena’ image and extracted watermark
image after applying various attacks. We observed that
extracted images are distorted after applying various attacks.
Table 3 shows NC values of the proposed method for different
images against various attacks. The NC values range from

0.32 to 1, indicating that the proposed method is sensitive
against attacks especially salt and pepper noise, cropping,
rotation, and JPEG compression.

(a) Baboon

(b) Lenna

(d) Airplane

(c) Pepper

(e) House

TABLE III.

NC VALUES OF THE PROPOSED METHOD FOR DIFFERENT
IMAGES AGAINST VARIOUS ATTACKS
Attacks
Salt &
Pepper(0.02)
Cropping
(25%)
Content
Changing
Rotatation(35)
JPEG(30)
JPEG(90)
Lossless
compression
Format
Conversion
Brightness
Adjustment
No Attack

Fig. 5 Watermarked images obtained by the proposed method
TABLE II.

COMPARISON OF
AND SEVERAL RECENT METHODS

PSNR RESULT BETWEEN THE PROPOSED

Proposed

Zhao et al. [7]

Liu et al. [8]

Chamlawi et al. [14]

45.69

37.13

39

36.23

(a) Salt & Pepper

(d)Watermark after salt
& pepper attack

(b) Cropping

(e) Watermark after
cropping attack

(c) Content change

(f) Watermark after
content change

(i) Lossless
Compression

(k) Watermark after
JPEG attack

[3]
[4]

(l) Watermark after
lossless compression

Fig. 6 Watermarked ‘Lena’ image after applying various attacks

Lenna
0.3766

House
0.3199

0.7647

0.7587

0.7590

0.7419

0.7059

0.9719

0.9643

0.9660

0.9677

0.9485

0.0143
0.0033
0.0139
1

0.0119
0.0224
0.0479
1

0.0158
0.0152
0.0099
1

0.0127
0.0043
0.0360
0.9991

0.0035
0.0094
0.0225
0.9974

1

1

1

0.9991

0.9974

1

1

1

0.9991

0.9974

1

1

1

0.9991

0.9835

REFERENCES

[5]
(j) Watermark after
rotation attack

Pepper
0.3422

In this paper, a semi-fragile image authentication
scheme based on ST and LUD has been proposed. The
proposed method is computationally fast and simple. The
proposed method is secured because encryption and private
key based randomness has been used in both watermark
preprocessing and embedding. This method has produced high
quality watermarked image and also effectively detected
malicious alterations done on image while being resistant to
various content preserving manipulation. These results verify
that the proposed watermarking method can be a suitable
candidate for image authentication. There are several
directions for future work on the proposed scheme introduced
in this paper. A comparison between the proposed scheme and
several state-of-the-art methods in terms of robustness will be
carried out. In addition, computational complexity of the
proposed scheme will be calculated.

[2]

(h) JPEG 30

Airplane
0.3515

V. CONCLUSION

[1]

(g) Rotation

Baboon
0.3628

[6]

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[8]
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[13]

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A. Phadikar, S. P. Maity, and M. Mandal, “Novel wavelet-based QIM
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K. Maeno, Q. Sun, S. F. Chang, M. Suto. "New Semi-Fragile Image
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