Geometrically Invariant Image Watermarking Using Connected Objects and Gravity Centers

Abstract

The design of geometrically invariant watermarking is one of the most challenging work in digital image watermarking research area. To achieve the robustness to geometrical attacks, the inherent characteristic of an image is usually used. In this paper, a geometrically invariant image watermarking scheme using connected objects and gravity center is proposed. First, the gray-scale image is converted into the binary one, and the connected objects according to the connectedness of binary image are obtained, then the coordinates of these connected objects are mapped to the gray-scale image, and the gravity centers of those bigger objects are chosen as the feature points for watermark embedding. After that, the line between each gravity center and the center of the whole image is rotated an angle to form a sector, and finally the same version of watermark is embedded into these sectors. Because the image connectedness is topologically invariant to geometrical attacks such as scaling and rotation, and the gravity center of the connected object as feature points is very stable, the watermark synchronization is realized successfully under the geometrical distortion. The proposed scheme can extract the watermark information without using the original image or template. The simulation results show the proposed scheme has a good invisibility for watermarking application, and stronger robustness than previous feature-based watermarking schemes against geometrical attacks such as rotation, scaling and cropping, and can also resist common image processing operations including JPEG compression, adding noise, median filtering, and histogram equalization, etc.

1. Introduction

Recently, with the development of computer network and information technology, lots of digital multimedia data are stored, transmitted and distributed through Internet, which lead to illegal copy, manipulation or use without any control for the electronic content. As an important information security technique, the digital watermarking has become an efficient way to the copyright protection and content authentication [1]. For different purposes, digital watermarking can be broadly classified into two categories: robust watermarking and fragile watermarking. The former is used to protect ownership of the digital media, while the latter is used to authenticate the integrity and verity of the digital content [2]. The robust watermarking is generally designed to withstand various attacks. The attacks in watermarking systems can be roughly classified into signal processing attacks and geometrical attacks [3]. Traditional signal processing attacks include JPEG compression, adding noise, histogram equalization, image filtering, etc., while typical geometrical attacks consist of rotation, scaling, translation (RST), cropping, etc. Signal processing attacks act by reducing the watermark energy so that the watermark may disappear after attacks. By comparison, geometrical attacks can destroy the synchronization between watermark embedding and extraction. In other words, the position of the watermark has changed although it still exists in the image. Many existing robust watermarking techniques have successfully resisted traditional signal processing attacks [4] [5] [6]. However, the ability to resist geometrical attacks is still one of the most challenging issues [7]. Current geometrically invariant watermarking techniques include template-based embedding, invariant-transform domain (e.g. Fourier-Mellin transform) embedding, and feature-based embedding.

In [8], S. Pereira et al proposed a geometrically invariant watermarking algorithm based on polar maps for the accurate and efficient recovery of the template in an image which had undergone an arbitrary linear transformation. The main idea consists of adding structure to the template, and the experimental results demonstrate the robustness against common image processing operations such as JPEG compression, rotation, scaling, and aspect ratio changes. However, the template-based watermarking schemes immune to rotation, scale and translation (RST) attacks are not secure because the fixed structure of the template may be removed and destroyed easily. In [9], A. R. Manuel et al improved the algorithms belonging to the family of those exploiting the template with a regular structure by using the Levenberg-Marquardt’s method for nonlinear least-squares estimation, and an estimate of the affine synchronization parameters after geometrical distortions could be obtained. Another common method is based on invariant-transform domains to design geometrically invariant watermarking schemes. RST resilient watermarking for image exploiting Fourier-Mellin transform was proposed in [10]. But the scheme is less effective to other types of geometrical distortion such as local warping due to the interpolation and quantization effect of inverse DFT transform.

Robustness can be also achieved by applying the geometrically invariant feature. Up to now, feature-based embedding has been widely applied in geometrically invariant watermarking schemes. In [11], an statistical feature-based geometrically invariant watermarking scheme was presented, which can resist both geometrical attacks and signal processing attacks Unfortunately, this scheme cannot resist image cropping. To tackle the issue of geometrical distortions, a robust blind watermarking in quaternion Fourier transform domain was proposed in [12]. In this scheme, the fast quaternion Fourier transform is performed on the image block, and some low-order pseudo-Zernike moments of the real quaternion Fourier transform coefficient matrix are computed, which are regarded as the effective feature vectors. Experimental results show the robustness to common image processing operations and geometrical distortions. However, this scheme is not very robust against median filtering and light lowering for texture image. In addition, the computational complexity is slightly high for least squares support vector machine training and pseudo-Zernike moments computation. In [13], I. Nasir et al adopted a feature extraction method based on end-stopped wavelets to extract significant geometry preserving feature points, which was robust against various types of common image processing and geometrical attacks. Ref. [14] developed a watermarking method to jointly enhance the robustness and security of feature-based image watermarking schemes. The controlled randomization is incorporated in determining the feature regions of an image for mitigating the leakage of secret information. The experimental results of robustness evaluation demonstrate that the method can effectively resist various attacks, including noise-like signal processing and geometrical distortions. In [15], Niu et al presented a geometrically invariant watermarking using the invariant centroid theory and the support vector regression (SVR). The geometrically invariant space is constructed based on color image normalization, and the watermark is embedded into host color image by modifying the low frequency nonsubsampled contourlet transform coefficients. The watermark can be blindly extracted and automatically re-synchronized under geometrical distortions. However, SVR training process expends a lot of time to get an optimal regression function, which drops the computational efficiency. In addition, a robust digital color image watermarking algorithm which combines color image feature point extraction and shape image normalization was proposed in [16] The feature point extraction method called Mexican Hat wavelet scale interaction is used to select the points which can survive a variety of geometry attacks.

In this paper, we develop a geometrically invariant watermarking scheme based on the connected object and gravity center of an image aiming at better performances. This paper is organized as follows: Section 2 overviews the connected object and gravity center of the image. Section 3 describes the proposed geometrically invariant watermarking for digital images. In Section 4, we theoretically analyze the geometrical invariability. Simulation results and comparison with previous works are shown in Section 5. Finally, we draw our conclusions in Section 6.

 

2. Connected Object and Gravity Center of Digital Image

2.1 Connected Object

The connectedness is used to describe the regions and boundaries of an image. To identify connected objects in a digital image, we need to locate groups of the correlative pixels that are ‘connected’ to each other. In fact, the connected objects growing of an image according to the connectedness is a kind of feature-based image segmentation process that partitions a digital image into lots of disjoint regions. A region is a connected set of pixels, in which all the pixels are adjacent or touching.

For many operations, distinguishing connected objects depends on the convention used to decide whether pixels are connected. Typically, there are two types of connectedness patterns: 8-connectedness and 4-connectedness. For 8-connectedness pattern, all of the pixels that touch the pixel of interest are considered, including those on the diagonals. Thus, each pixel would have eight neighbors. For 4-connectedness pattern, the pixels along the diagonals are not considered, and each pixel has only four neighbors. Therefore, the selection of connectedness patterns affects the number of connected objects.

In a binary image, a pixel can either have a value of ‘1’ as the object or ‘0’ as the background, and the pixels with value ‘1’ are white while value ‘0’ are black. For example, the binary matrix A represents the binary image shown in Fig. 1(a). If we adopt the 8-connectedness pattern, the original binary image will consist of five connected objects shown in Fig. 1(b). But if we adopt the 4-connectedness pattern, there will be six connected objects shown in Fig. 1(c).

Fig. 1.An example of connected objects

2.2 Gravity Center

The gravity center is calculated by the low order moments of the image. The two-dimensional moment can be directly used in the interested regions and need not to separate it from the whole image. High order moments are more sensitive to noise, while the low order moments are insensitive to noise and quantization errors, which is beneficial to the characterization of collectivity for the regions.

The 2-D (p+q)th order origin moment of a continuous image Ω is defined as [17]

where f (x, y) represents the gray-level value at location (x, y). For digital image, the integrals are replaced by summations as follows:

The gravity center G(gx, gy) of the the image is easily defined in terms of the zero-order moment and first-order moments as follows [18]:

where the zero-order moment M00 represents the area of the image clearly. Similarly, the gravity center of the connected object can be work out when the set Ω is replaced with the connected object.

 

3. Proposed Geometrically Invariant Watermarking Scheme

3.1 Moderate Connected Objects

In order to resist the geometrical attacks such as rotation and scaling, watermark embedding is based on the inherent characteristics of image in general. In this paper, we use the connected objects as a characteristic, because the connected object of an image possesses topological invariability from morphology theory. The number of connected objects is invariable to the geometrical distortion of an image from a theoretical point of view, unless the image is torn up. However, if we directly use the original gray-scale image to convert to the binary version, the generated connected objects will contain the very big or small objects. For a very big connected object, only one gravity center can be obtained in a quite large area, while the gravity center of a very small connected object is instable. As well known, the median filtering is a simple and very effective noise removal filtering process. It usually causes significant loss of the detail and small objects in the image. Based on this performance, we can use median filtering to smooth original gray-scale image and remove some details and small objects. After that, the generated connected objects are more moderate. For the filter window Sxy, after performing the median filtering, each output pixel contains the median value in the Sxy neighborhood around the corresponding pixel in the input image f(x, y), namely

Then, we convert by a threshold T1 as following

By this way, the background and object pixels have gray levels grouped into two dominant modes by the threshold T1 ∈ [0,1]. The pixels signed ‘1’ is corresponding to the objects, whereas those pixels signed ‘0’ is corresponding to the background. Suppose that the area size of the moderate connected objects is limited in the interval [C1, C2], the pixels number in a connected object will be If the principal density of is the Gaussian distributing with mean μ and variance σ. Then, the optimal threshold T1 satisfies [18]:

Here, P1 and P2 are the probabilities of the object pixels and background pixels, respectively, and μ1 and μ2 are the means of the Gaussian distributing for two types of pixels. Suppose the variances of two types of pixels are all σ2. Thus, the moderate connected object can be obtained by selecting the optimal threshold T1.

3.2 Feature Points for Watermark Embedding

The generated connected objects’ coordinates are mapped to the gray-scale image, thus the original image is also composed of lots of connected objects. Let Ωi(i=1,2, …, u) represent u connected objects in the gray-scale image, and N(Ωi) represent the number of pixels in each object. We define another threshold T2 satisfying

The threshold T2 partly controls the number of connected objects. Fig. 2 shows some test images, and Fig. 3 shows the number of connected objects of these images with different threshold T2 under median filtering window 5×5 and 15×15, respectively. The larger T2, the less number of connected objects will be. This leads to the bigger connected objects are held. In general, the gravity centers of bigger connected objects are stable. To obtain stable gravity centers as the feature points, we select the number of connected objects is 3~11. From Fig. 3, we see that when the number of connected objects for most of the images is 3~11 under different filtering windows, T2 value falls into the interval [140, 300]. So the appropriate T2 value should be in the interval [140, 300] according to the experiment results.

Fig. 2.Test images

Fig. 3.Number of connected objects with different threshold T2 under median filtering

To obtain stable feature points, we choose those bigger objects satisfying N(Ωi) ≥ T2 to calculate their gravity centers as the feature points Mi (mix, miy) for watermark embedding as bellows

For each irregular connected object Ωi, since

So if the connected object Ωi is convex, the location of the feature points Mi, will fall into the inside of the connected object, otherwise the feature points will fall into either the inside or outside of the concave connected objects.

3.3 Watermark Embedding

Firstly, the generated connected objects are sorted in descending order according to the number of pixels in each connected object. The connected objects including maximal number of pixels is at the forefront of the sorting result, and is the biggest connected object. According to T2, we select anterior v bigger connected objects whose corresponding gravity centers Gi (i=1,2, ...,v) are worked out. Assume the center of the whole image is C. As shown in Fig. 4, let be the starting radial, and its rotating α degree forms a sector. Then, we embed the same version of watermarks into each sector. The detailed watermark embedding method is as follows. First, We divide equally each sector into L parts using L-1 straight lines. Adding two angle lines, there will be total L + 1 lines used for embedding watermark information in a sector, and then the length of the radial line is as the reference length Lref. For watermarking synchronization purpose, we use as the starting line, and equally embed N watermark bits on each line. Thus, the distance between two adjacent embedding points is Lref / N. Thus, each sector will accommodate total (L+1)N watermark bits. Because the watermark embedded into each sector is identical, so the distribution of watermark bits is thick for the sector with smaller area, while for those with bigger area, is sparse.

In general, the occurrence probability that two sectors overlap each other is very small. The cause is that the gravity centers of several bigger connected objects are used to form sectors, thus the distribution of these gravity centers is sparse, and it is not easy to make two sectors formed by these gravity centers overlapping.To avoid the small probability event that sectors are overlapped, we adopt the following method. If any sector i created from gravity center Gi (i=1,2, …,v) overlaps one of its previous sectors 1, 2, …, i - 1, the gravity center Gi is just discarded and a new gravity center Gv+1 is added whenever there are some gravity centers not yet been added.

In each embedding point, we note the gray-scale value f ∈ Z, and 0 ≤ f ≤ 255, and use the odd-even quantization method to embed the watermark bit wi, i=1,2…, (L+1)N into an image as follows:

When wi = 0, the watermarked gray-scale value fw satisfy

When wi = 1, than the watermarked gray-scale value fw satisfy

where ⎿ • ⏌ denotes the floor function. Δ > 0 is quantization step, which controls the watermark strength and can be set reasonably by the users. In general, the larger Δ will result in stronger robustness, while the quality of the watermarked image is degraded. So the selection of Δ values should be a reasonable trade-off between the perceptual transparency and the robustness. Consequenctly, to achieve this goal, the magnitude of the modified gray-scale value should locate at the middle of the quantization interval. In generally, the more suitable values of Δ are in the interval [15, 23] according to the experiment results.

For example, we set the quantization step Δ =20, and assume the watermark bit 0 is embedded into the pixel point with gray-scale value f = 242. Due to ⎿ 242/20 ⏌mod2 = 0, the watermarked gray-scale value will be fw ⎿ 242/20 ⏌ × 20 + ⎿ 20/2 ⏌= 250 according to Eq.(13). However, if the watermark bit 0 is embedded into another gray-scale value f = 135, due to ⎿ 145/20 ⏌mod2 = 1 and 145 ∈[⎿ 145/20 ⏌ × 20, ⎿ 145/20 ⏌ × 20 + ⎿ 20/2 ⏌), the watermarked gray-scale value will be fw =(⎿ 145/20 ⏌-1) × 20 + ⎿ 20/2 ⏌ + 130 according to Eq. (13). Similarly, the embedding process of watermark bit 1 is similar to that of watermark bit 0 according to Eq. (14).]undefined

Now we describe an example of the underflow and overflow about the value of fw. Assume the watermark bit 1 is embedded into the pixel point with gray-scale value f = 8. Due to ⎿ 8/20 ⏌mod2 = 0 and 8 < ⎿ Δ/20 ⏌, the underflow would happen, and the watermarked gray-scale value will be fw = Δ = 20 according to Eq.(14). On the contrary, when f = 240, due to ⎿ 240/20 ⏌mode2 = 0 and (⎿ 240/20 ⏌ + 1) × 20 + ⎿ 20/2 ⏌ > 255, the overflow would happen, and the watermarked gray-scale value will be fw = (⎿ 240/20 ⏌ - 1) × 20 + ⎿ 20/2 ⏌ = 230 according to Eq.(14).

Fig. 4.Sector formed by the gravity center of connected object

3.4 Watermark Extracting

In the watermark retrieval process, first, we convert the gray-scale image into the binary one, and then obtain the moderate connected objects based on the median filtering and the connectedness technique. According to the threshold T2, we can calculate the gravity centers of bigger connected objects used to embed watermark information. Like the watermark embedding process, several sectors are generated for watermark embedding. In each sector, we can extract a watermark version on L + 1 lines. Because we use the center of the whole image and the gravity centers of connected objects as the feature points for watermark embedding in each sector, which is geometrically invariant, no matter how the image is rotated, scaled and translated, the watermark will be synchronized. The watermark is extracted as follows

where fw denotes the watermarked gray-scale value. According to quantization method, when the difference between quantized gray-scale values and the original ones varies within [ −Δ/2,Δ/2), watermark bits will be correctly extracted, and the robustness is ensured.

 

4. Geometrical Invariability Analysis

The connected objects growing of an image according to the connectedness is a kind of feature-based image segmentation process that partitions a digital image into lots of disjoint regions. In addition, the gravity center of the connected object has the property of geometrically invariant. Based on the fact that connectedness and the gravity center are all geometrical invariability, the watermark can survive under geometrical attacks.

4.1 Rotation

After a rotation by an angle θ about the origin, the first-order moments are given by

and the zero-order moment So after rotating with an angle θ, the gravity center is changed as

Namely

4.2 Scaling

After scaling with a factor α in the x-direction and β in the y-direction, the size of the image (object) is correspondingly changed. Let Ωs represent the scaled image (object), then the first-order moments after scaling are given by

Similarly,

In addition, the zero-order moment So the relation of gravity center between before and after scaling is

Namely

4.3 Translation

After translation of coordinates shifted in position Δx in the x-direction and Δy in the y-direction, the first-order moments are given by

and the zero-order moment So the relation of gravity center between before and after translations is

From above analysis, we see the gravity center of an image (object) is invariant under RST transform.

To further explain that the proposed scheme is invariant after scaling, rotation and translation, we show a sketch map of the watermark embedding locations in Fig. 5. From Fig. 5(a), there are five sectors are formed. The points in each sector are the watermark embedding locations, which are obtained according to the gravity centers based on the connected objects content. Therefore, the straight line (i=1,2,3,4,5) between the center of the whole image and the gravity center of each connected object rotates, scales and translates synchronously with the whole image. Consequently, the watermark embedding points can be find correctly after geometrical attacks to the watermarked image. For example, Fig. 5 (b) shows the watermark embedding points after rotating α degree. From Fig. 5 (b), we see the watermark embedding points can be ratated adptively α degree with the whole image. Fig. 5 (c) and (d) show the watermark embedding points after scaling with factors 0.5 and 1.5, respectively. From Fig. 5 (c) and (d), we see the interval of watermark embedding points can be scaled synchronously. Similarly, the watermark embedding points can also be translated synchronously with the whole image. In addition, the watermark bits hiding by the quantization in each embedding point can tolerate change of gray-scale values in certain extent, so our watermarking scheme can also survive other common image processing attacks such as JPEG compression, adding noise, median filtering, and histogram equalization.

Fig. 5.Sketch map of the watermark embedding locations under image rotation and scaling

 

5. Experimental Results

To evaluate the performances of the proposed scheme, we used the standard gray-scale image of size 512 × 512 ‘Lena’ and ‘Barbara’ as the test images shown in Fig. 6. In the test, the window size of median filtering is set to 15 × 15, and T1 is set to 0.79 for ‘Lena’, and 0.82 for ‘Barbara’, respectively. Then, we obtain the corresponding moderate connected components under 8-connectedness pattern shown in Fig. 7. When T2 is set to 230, we can get six connected objects for ‘Lena’, and eight connected objects for ‘Barbara’, and then we calculate the gravity center coordinates of connected objects. They are (373,477), (35, 431), (146, 390), (456, 354), (234, 330), (105, 295) and (38, 298), (156, 229), (193, 194), (175, 181), (175, 144), (261, 132), (253, 71), (206, 84) for ‘Lena’ and ‘Barbara’, respectively. Set α =10°, we can obtain the corresponding sectors for watermark embedding based on these gravity centers of connected objects and the center of the whole image.

Fig. 6.Original image

Fig. 7.Moderate connected objects

We embed the same version of 512-bit watermarks into each sector, and obtain the watermarked image. For a good watermarking scheme, the PSNR values of watermarked image should be greater than 36 dB, which is an experiential value. In this paper, the quantization step can be selected to meet the invisibility and robustness for watermarking application. Set the quantization step Δ =16, the resulting peak-signal-to-noise ratio (PSNR) due to watermark embedding is calculated. The PSNR values between the original and watermarked images are 50.72dB and 53.80dB for ‘Lena’ and ‘Barbara’, respectively, indicating that invisibility of the watermark is satisfactory. Table 1 shows the invisibility performance comparison between our scheme and other feature-based geometrically invariant watermarking schemes.

Table 1.PSNR(dB) for various watermarking schemes

The robustness of the proposed scheme is demonstrated under both geometrical distortion and common image processing operations. Rotation, scaling and cropping are tested for geometrical distortion, while median filtering, adding Gaussian noise, JPEG compression, and histogram equalization are tested for common image processing operations. In this paper, the robustness is measured as the bit error rate (BER) of extracted watermark. For the extracted watermark and the original watermark BER is defined as

Obviously, a low BER indicates that the extracted watermark has a stronger robustness. In the proposed scheme, the same version of watermarks is embedded into each sector, thus there are multi-version watermarks are extracted, and the lowest BER value of multi-version watermarks is as the valid BER value.

To examine the invariance against geometrical attack, we perform some geometrical attacks on ‘Lena’ and ‘Barbara’ images, respectively. As an example, Fig. 8 shows some geometrically attacked ‘Lena’ images such as rotation, scalling and cropping. The watermark can be detected after the watermarked image suffered geometrical attacks. In order to demonstrate the robustness advantages of the proposed scheme, the watermark detection results are compared with methods [11][12][15], which are all feature-based geometrically invariant watermarking schemes.

Fig. 8.Several geometrical attacked ‘Lena’ images

Fig. 9~Fig. 12 show the simulation results under image rotation, scaling, cropping, and JPEG compression respectively. It is seen from Fig. 9 that both the proposed method and the methods [11][12][15] can survive under different rotation degrees. For the proposed method, the BERs are extremely low, and the watermark can be accurately extracted regardless of rotation degrees. The reason is that when the watermarked image is rotated, the shapes of connected objects are invariable, so the gravity center of each connected object will be located synchronously with any rotation degrees. In this regard, the proposed scheme outperforms the methods [11][12][15].

Fig. 9.Watermark detection results under different rotation degree

When the watermark image suffer scaling attack, the size of connected objects will be scaled synchronously following the image, and the reference length is scaled synchronously. Thus the watermark detection will be synchronized for scaling on the watermarked image. From Fig. 10, we know that both methods can resist scaling attacks. Especially, we find that when the image is scaled greater, the proposed method performs better, and the BERs are lower than that of the methods [11][12][15]. The underlying reason is that the connected objects are magnified, and gravity centers (feature points) are more stable, so the BERs are lower, and the extracted watermarks are more robust. On the contrary, in the case that an image is diminished, the stability of the feature points may be gone down when the related objects disappear. Therefore, the BERs will be risen. Although the BERs are higher than other three watermarking schemes when the scaling factor is less than 1, the proposed scheme is effective. By comparison, the overall performance of the proposed method is better than that of methods [11][12][15].

Fig. 10.Watermark detection results under different scaling factor

Cropping attack is a kind of local geometrical distortion. Fig. 11 shows the watermark detection results under cropping attack. From Fig. 11, we see that the BERs of our scheme are the lowest, which implies that our scheme resists cropping attack well. However, the method [11] cannot deal with image cropping, because Polar Harmonic Transforms is a statistical based image feature extraction method.

Fig. 11.Watermark detection results under cropping attack

In our scheme, the same version of watermarks is embedded into each sector, and the lowest BER value of all the extracted watermark versions is as the valid BER value. Even if only one extracted watermark version is well extracted under different attacks, the proposed scheme will be still valid and robust. As an example, we embed the same version of 512-bit watermarks into each sector formed by the connected objects in Fig. 7(b). If the image ‘Barbara’ is cropped by (H 50%, V 50%) like Fig. 8(f), two gravity centers of the corresponding connected objects are still remained shown in Fig. 12. So the lowest BER value of two extracted watermark versions is as the valid BER result. In addition, the connectedness and gravity center of the image are stable to the cropping attack, so the BER values are low shown in Fig. 11(b).

Fig. 12.Two gravity centers of ‘Barbara’are still remained under cropping attack (H 50%, V 50%)

JPEG compression is a kind of common image processing operation. Fig. 13 shows the watermark detection results under JPEG compression. From Fig. 13, we know that both methods can extract the watermark with high accuracy when the quality factors are greater than 30. Therefore, these methods are all robust to JPEG compression. In addition, the watermark detection results under other common image processing operations are listed in Table 2.

Fig. 13.Watermark detection results under JPEG compression

To sum up, the robustness to most geometrical attacks and common image processing operations is ensured because the connectedness and gravity center of the image is beneficial to immune to the considered attacks. In addition, If the rotation angles for forming the sectors are unknown, the watermark embedding location will not found by the illegal user. Consequently, the embedded watermark information is secure. Furthermore, as long as the connected objects are intact, their gravity centers will be not destroyed, and the extracted watermark will also be survived under local geometrical attacks. The experimental results show that the proposed scheme has a great improvement in the performance of extracted watermarks compared with the previous feature-based watermarking schemes.

Table 2.Watermark detection results under common image processing operations (BER)

 

6. Conclusions

In this paper, we have presented a robust geometrically invariant watermarking scheme by using the connected object and gravity center of the digital image. The irregular connected objects contact tightly with the spatial image content, which is changed adaptive synchronously with the image. We use the gravity centers of connected objects to be as the feature points for watermarking synchronization purpose, and improve the robustness to geometrical attacks. The experimental results demonstrate the proposed watermarking scheme is robust to most geometrical attacks, such as rotation, scaling and cropping, etc, and can also resist common image processing operations.