INTRODUCTION
Recently, digital contents can be easily accessed by using computer networks and the problem of protecting multimedia information has become more and more important. As a solution to this problem, digital watermark technology is now drawing the attention as a new method of protecting copyrights for digital data^{[1,2]}. It is realized by embedding information data with an insensible form for human audio/visual systems. We call the embedded information data watermark.
In general, a digital watermark technique must satisfy the following two properties.
First, the embedded watermark does not spoil the quality of the image and should
be perceptually invisible. The second property is that it doesn’t require
the original image for watermark detection. It is also robust to common image
processing and geometric distortions.
Today, almost all of the proposed watermark algorithms could not meet the above requirements simultaneously, especially resistance to rotation, cropping, etc. A binary watermark sequence is embedded into the highest magnitude DCT coefficients^{[3]}. Hence, this algorithm is robust against image processing and common geometric transformations. Hsu and Wu^{[4,5]} proposed discrete cosine/wavelet transform algorithms to embed a binary watermark by modifying the middlefrequency coefficients. This algorithm is resistant to common image processing; but geometric distortions are still challenges. The main drawback^{[35]} is requiring the original image to detect/extract the watermark.
Recently, a grayscale digital watermarking technique was proposed by Niu et al.^{[6]}. The grayscale watermark, a visually recognizable pattern, is decomposed into eight binary bitplanes^{[6]}. Some binary bitplanes are embedded into the middle DCT components of the original image, with the remainder used as the secret keys. The main disadvantages of this private watermarking algorithm are: (1) the original image is required to verify the existence of the watermark; (2) the robustness property is resistant to JPEG compression and general image processing, but geometric distortions are still challenges.
Base on the above facts, we propose an image watermarking algorithm based on the Discrete Wavelet Transform (DWT). The features of our algorithm are as follows. We do not require the original image for watermark detection and it is robust to common image processing and geometric attacks.
PRELIMINARIES
Wavelet transform: The wavelet transform is a mathematical tool for decomposing.
We briefly review the DWT model (Fig. 1), which shows a 2scale
wavelet transform. The image is first decomposed into four subbands denoting
LL_{1}, LH_{1}, HL_{1} and HH_{1}. LH_{1},
HL_{1} and HH_{1} contain the finest scale detailed wavelet
coefficients, i.e., the higher frequency detailed information.

Fig. 1: 
The image is divided into seven subbands through 2scale level
wavelet transform 
LL_{1}, the coarse overall shape, is the low frequency component containing
most of the energy in the image. The wavelet transform is then applied to obtain
the next coarser scale by further decomposing LL_{1} into LL_{2},
LH_{2}, HL_{2} and HH_{2}. If the process is repeated
t times, we can obtain the subband LL_{t} through tscale level wavelet
transform.
In the human visual system, people are more sensitive to low frequency components than high frequency components. Under reasonable attacks, the low frequency components can survive. Consequently, LL_{t} of the original image is very close to that of the altered image.
QUANTIZATION
Quantization is a lossy data compression method. A quantization is nothing more than an approximator. A simple example of quantization is shown in Fig. 2.
Here, every number less than 2 is approximated by 3. Every number between 2 and 0 are approximated by 1. Every number between 0 and 2 are approximated by +1. Every number greater than 2 is approximated by +3. Note that the approximate values are uniquely represented.
PROPOSED ALGORITHM
Although the low frequency components can survive after reasonable attacks, they are perceptible to the human eye. For this reason, most frequencydomain watermarking algorithms try to insert the watermark into the middlerange frequencies. However, that the low frequency components can survive under considerable attacks is a good property for watermark security. Hence, in this paper, we will apply the low frequency component for inserting watermark.

Fig. 2: 
A example of quantization 
Usually the watermark is a pseudorandom sequence of real numbers. This kind of watermark can be used only to determine whether the watermark is present or not by detector, but the watermark oneself has no actual meaning. Along with request of the copyright protection increasing gradually, many scientists focus on meaningful watermark. Therefore, in this paper, meaningful binary pattern is used to the watermark.
The proposed new robust watermarking algorithm has the advantages of robustness for common image processing and not requiring the original image for watermark detection. The stages for this algorithm can be grouped into embedding stages and detection stages.
EMBEDDING WATERMARKING STAGES
We firstly introduce the following notation. Integer I(i, j), I΄(i, j) indicate (grayscale or) luminance of the original image I and the watermarked image I’ with eight bits per pixel, respectively. The original image I is defined as follows:
Where, W_{I} and H_{1} is the width and height of I, respectively.
Where, W_{W} and H_{W} is the width and height of W, respectively.
Without losing the generality, let W_{I} and H_{I} are a power
of 2. Let meaningful binary watermark W be stored into a onedimension vector,
defined as .
Step 1. Wavelet transforming of the original image: Mallal^{[7]} stated that we know that wavelet Haar has very good performance. Since filter length of wavelet Haar is the most short, computational complexity of its decomposing and reconstructing is lower than other wavelet. At the same time, Mallat algorithm is to infinite signal, but natural image is finite, therefore wavelet need be continued when processing image. However, it is very special for wavelet Haar, its boundary needn’t be continued. Further, Liuetal^{[8]} also stated that we know that wavelet Haar is the most suitable for digital watermarking. Therefore, in this study, wavelet Haar is used.
In the wavelet transform phase, assume that the original grayscale image is
decomposed into t scale subbands and LL_{t} is obtained. Here t is a
predetermined constant. The owner can determine the value of t according to
the tradeoff between the efficiency and the robustness. The size of the coarse
overall shape, i.e., subband LL_{t} (L for short), is W_{L}
by H_{L}, where:
and
All wavelet coefficients in the L were stored into a onedimension vector C.
Step 2. Selection of embedding coefficient: A random sequence Index
is generated firstly by secret key K. Only algorithm’s designer owns this
secret key and position of embedding ith watermark bit (i)
is determined by Index(i), i.e., the wavelet coefficient of embedding watermark
bit is C(j)(j = Index(i)). Therefore, it are required that Index’s element
is mutually inequality and the Index’s value don’t exceed number of
the wavelet coefficients.
Step 3. Embedding watermark method: By modifying selected the wavelet
coefficient C(j), the watermark bit flow (i)
is embedded. After selected the wavelet coefficient C(j) is quantized by step
length q, which is a predetermined positive integer, if (i)
= 0, then quantization value is modified into an even number of the nearest
C(j)/q; and if (i)
= 1, then quantization value is modified into an odd number of the nearest C(j)/q.
And inverse quantization is adopted. Based on the above, the embedding watermark
method was described as follows:
• 
By step length q, whole real field were divided into some
small subintervals, i.e.,[kAq,(k+1)Aq], (k = 0,±1,±2,...).
Without losing the generality, let real number C(j) ∈ [NAq,(N+1)Aq]
where N is integer. 
• 
Let quantization value of C(j) be Q(j). If one of N and N+1 is an even
number inevitably, then let Q(j) equal to this even number and if (i)
= 0, one of N and N+1 is an odd number inevitably, then let Q(j) equal to
this odd number. 
• 
After Q(j) inverted quantization, modified wavelet coefficient C΄(j)
= Q(j)Aq is obtained. 
Step 4. Wavelet inverse transform: For the wavelet coefficients of have
embedded watermark, tscale level wavelet inverse transform were adopted and
watermarked image is obtained.
Detect watermarking stages: The original image isn’t required to detect the existence of the watermark. The detect process have four steps as follows:
Step 1: The tested image is tscale level discrete wavelet transform.
Step 2: By secret key K, the same with embedding watermark, the positions of embedding watermark were determined and corresponding coefficients were obtained.
Step 3: Let C΄(j) be an obtained coefficient and N = round .
Watermark bit values were extracted by using N’s odevity.
Step 4: Let onedimension watermark bit flow be stored into a twodimensional meaningful binary watermark.
RELEVANT QUESTIONS DISCUSSING
Decide quantization step length q: To improve
the robustness of our algorithm for to common image processing and geometric
distortions, the quantization step length q have to be decided.
For the low frequency coefficients, according to the strong or weak of the locally texture in the corresponding position, it will be divided into two classes, defined as S_{1} and S_{2}, respectively. Where, S_{1} is a point set with the strong texture and S_{2} is other point set with the weak texture. Embed points of corresponding different class should adopt different the quantization step length.
Because subbands LH_{t}, HL_{t} and HH_{t} contain the finest scale detailed wavelet coefficients, i.e., LH_{t}, HL_{t} and HH_{t} contain texture or edges information of the image, texture of embedding coefficients was classed by using them. For embedding coefficient L(i,j), let corresponding subbands wavelet coefficients be LH(i, j), HL(i, j) and HH(i, j), respectively. Let the average of corresponding subbands wavelet coefficient amplitudes be mean LH, mean HL and mean HH, respectively.
We know that the bigger the absolute value of coefficient, the stronger the texture of corresponding position. Therefore, to judge the texture strong or weak of corresponding position by using subbands, mean LH, mean HL and mean HH will be used. Judgment method is described as follows:
If (LH(i, j)≥ mean LH) or (HL(i, j)≥ mean HL) or (HH(i, j) ≥ mean
HH),
Then LH(i, j)∈S_{1}, else LH(i, j)∈S_{2}.
If LH(i, j)∈S_{1}, then q = q_{1}, else q = q_{2},
where, q_{1} > q_{2}.
Selection of the wavelet decomposing scale t: We know that, as the wavelet
decomposed scale t increasing, the amplitude of low frequency coefficient increases
with the approximate 2 multiple. Usually, the watermark is thought to be a weak
signal added to strong background (i.e., the original image). So long as the
weak signal added is lower than the contrast sensitivity threshold, the human
vision system can't feel its existence. According to Weber’s law^{[9]},
the contrast sensitivity threshold is proportional to amplitude of the background
signal. This shows that, as the wavelet decomposed scale t increasing, strength
of embedding watermark can increase with approximate 2 multiple.
According to the above consider, as the wavelet decomposed scale t increasing, strength of embedding watermark will increase significantly. Thus, robustness of the watermark may be improved. Moreover, the more wavelet decomposed scale t, the better components of watermark can be spread. So, for the watermark algorithms, the wavelet decompose scales should be improved possibly according to the amount of the watermark data.
RESULTS AND DISCUSSION
To prove the robustness of our algorithm for common image processing and geometric
distortions, we performed some experiments with some grayscale standard images.
Here, we describe experimental results using the standard image baboon (512x512
pixels, 8 bits/pixel) in Fig. 3a. The watermark is (64x64
pixels) in Fig. 3b and the watermarked image I΄ after
embedding Fig. 3b into Fig. 3a according
to our algorithm is shown in Fig. 3c.
In present experiments, the original image is 4scale level wavelet transformed and the quantization step lengths are q_{1} = 16 and q_{2} = 8, respectively.
For evaluate the quality the test image and the original image using the Peak Signaltonoise Ratio (PSNR), where
Here, similarity between the original watermark and extracted watermark is simply expressed in terms of the fraction y = X/M, where, M is the total number of original watermark points in both figures and X is the count of points from either original watermark that have at least one point from other original watermark in their 3x3 neighborhood.
PSNR of Fig. 3c is 41.8757dB. Figure 3d
is a extracted watermark from Fig. 3c using our algorithm.
Similarity between Fig. 3b and d is 1. This shows that the
extracted watermark using our algorithm is very accurate.
TO TEST ROBUSTNESS
Image JPEG compression: The extracted watermarks are shown Fig.
4af, after JPEG compression version of Fig. 3c with
parameters of 60, 50, 40, 30, 20 and 10 qualities, respectively and all 0% smoothing.

Fig. 3b: 
Original watermark 

Fig. 3c: 
Watermarked image 

Fig. 3d: 
Detected watermark 
Their PSNRs are reduced to 33.0483, 29.7978, 29.1957, 28.3831, 26.2983 and
23.8089, respectively.
Image noising: We add Gaussian noise (zeromean and variance 0.001)
to Fig. 3c, its PSNR is reduced to 29.9573 dB. The extracted
watermark image are still recognizable and shown in Fig. 5a.
We add Salt and Pepper noise (noise density 0.005) to Fig. 3c,
its PSNR is reduced to 28.5867 dB. The extracted watermark image are still recognizable
( Fig. 5b).
Similarity measures between Fig. 5a, b and Fig.
3b shown in Table 1.

Fig. 6a: 
This is an image by cropping Fig. 3c irregularly 

Fig. 6b: 
This is an image by cropping Fig. 3c 

Fig. 6c: 
Cropped irregularly 
Table 1: 
Similarity measure 

Image rotation: Most watermarking schemes cannot survive after rotation.
We rotate Fig. 3c 2° and resize it to 512x512. The PSNR
is seriously reduced to 14.8170 dB. However, the extracted recognizable watermark
image shown in Fig. 5c is still extracted.
Image cropping: Figure 6a shows an irregularly cropped
version of Fig. 3c and Fig. 6b shows a
cropped version of Fig. 3c where only the central region,
containing the face of baboon remains. Their PSNRs are reduced to 11.3662 dB
and 8.7647, respectively. We can still clearly retrieve the watermark image,
as shown in Fig. 6c and d.
Image filtering: The detected watermarks are shown in the Fig.
7a, b and c, after highpass filtering,
3x3 median filtering and 3x3 mean filtering versions of Fig.
3c.

Fig. 7a: 
Highpass filtering 

Fig. 7b: 
3x3 median filtering 

Fig. 7c: 
3x3 mean filtering 
StirMark attack: Figure 3c is attacked using the
StirMark attack one time with default parameters. Although Fig.
3c suffers an attack from the most powerful watermarking benchmark and the
PSNR is reduced to 18.2970 dB, the retrieved watermark image is still recognizable
to the human eyes. Figure 8a show the result.
UnZign attack: Figure 3c is attacked using the unZign
process one time with default parameters and then the unZignattacked Fig.
3c image is resized back to 512x512. Although Fig. 3c
suffers the unZign attack and the PSNR is reduced to 23 dB, present watermark
image is still recognizable. The retrieved watermark is shown in Fig.
8b.
Besides above experiments, we let other images be original images selected from USCSIPI Image Database^{[10]} for testing new algorithm. The experiment results show that this algorithm is still robustness for resisting various attacks.
In our algorithm, the exact ownership is verified if the retrieved watermark image is meaningful to the verifier. Through the experimental results, our algorithm has the following properties:
Robustness: Under standard attacks, our algorithm is robust to various image processing and geometric translations, such as JPEG compression, noising, rotation, cropping and filtering attacks.
Blindness: The extraction watermark does not require the original image. In practice, this is an essential property of the copyright protection and covert communication.
StirMark and unZign attacks: Experiment 6 and experiment 7 show that our algorithm survives under the StirMark and unZign attacks.
CONCLUSIONS
We believe that wavelet transform can play an important role in the digital image watermark. Based on this idea, we apply wavelet transform and quantization in our algorithm. This novel algorithm can be resistant to common image processing and simple geometric attacks. Furthermore, our algorithm can also resist StirMark and unZign attacks. It shows that our algorithm can apply in the copyright protection and covert communication.