### Transactions on data hiding and multimedia security VI

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The watermark embedding process is detailed step by step as follows: 1. The last several nondivisible rows and columns are not used for embedding. Choose the subimages that have a large number of feature points to be embedding blocks. These blocks are perceptually high textured. For each perceptually high textured subimage SubA: 3. The same changes are carried out at center-based symmetric positions due to the constraints in the DFT domain for obtaining a real image. The proposed robust and improved Harris detector is finally used to find strong IFPs in the watermarked image. The position of each strong IFP, the bipolar watermark message bit sequence Wi, the number of embedding positions Len, two secret keys n and K for our one-way hash function in each subimage, two middle frequency ratios, and the secret key for generating the PN-sequence are saved for watermark detection.

Since strong IFPs are obtained via the intersection operation, the number of IFPs is optimized and the storage is minimal compared to the cost of saving the image itself. If all the information is compressed, the storage cost will be further minimized. The relatively strong IFPs are first extracted by intersecting the IFPs obtained by applying our proposed improved Harris corner detector on the probe image and a few randomly rotated probe images. Two sets of Delaunay tessellation-based triangles [27] are generated using the strong IFPs found in the probe image and the saved strong IFPs, respectively.

These two sets of triangles are then matched to determine the possible geometric transformations the probe image has undergone. These geometric transformations are further utilized to restore the probe image so synchronization errors are minimized in the detection. A Desynchronization Resilient Watermarking Scheme 39 The choice of Delaunay tessellation is based on two attractive properties: 1 Local property: If a vertex disappears, the tessellation is only modified on connected triangles.

That is, the tessellation patterns of other triangles remain the same even though losing or shifting an IFP affects the triangle s connected to it. In addition, two properties of the Delaunay tessellation always ensure that an identical generation of triangles can be obtained if the relative positions of the IFPs do not change.

We implemented the Qhull algorithm [28] to generate the IFPs-based triangles due to its fast speed and less memory constraints. In our system, the angle radians are used to match Delaunay tessellation-based triangles. That is, if two triangles have very similar angle radians i. The possible geometric transformations are determined from the matched triangle pairs since the IFPs-based triangles undergo the same transformation as the image itself.

## Transactions on Data Hiding and Multimedia Security X

The detailed steps are: 1. Calculate the scaling factor SF by resizing the probe triangle to the same size as the target matched triangle. Calculate the translation factor TF by registering one of the vertices of the matched triangle pair. Calculate the rotation factor RF by aligning the other two unregistered vertices of the matched triangle pair. Since an image and the within triangles undergo exactly the same transformation, we use the majority of the identical 3-element tuples obtained from all matched triangle pairs to restore the probe image.

That is, the number of matched bits in a potential embedding subimage is compared with a threshold to determine whether the watermark is present in the probe image.

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This threshold is calculated based on the false-alarm probability that may occur in watermark detection. We further simplify Eq. This is a low false alarm probability so we can confidently claim the watermark exists. In our system, we will check the perfect match in any embedding subimage to indicate the presence of the watermark. We then illustrate the effectiveness of the proposed strong IFPs-based image restoration scheme, which functions as a self-synchronization scheme to align the possibly geometrically distorted watermarked image with the original one.

Next, we perform extensive comparisons with three well designed feature-based RST resilient watermarking schemes proposed by Tang and Hang [19], Wang et al. Finally, we summarize the performance of our proposed scheme under a variety of Stirmark attacks on 8-bit watermarked grayscale images. These four images correspond to several texture categories.

For example, Baboon includes textured areas with high frequency components; Lena and Airplane include large homogeneous areas whereas Lena has sharp edges; and Pepper falls in a low-textured category. The PSNRs of these four watermarked images are These PSNR values are all greater than In general, we apply the Delaunay tessellation on the strong IFPs to generate triangles, and use angle degrees to find the matched triangles between the original and probe A Desynchronization Resilient Watermarking Scheme 41 images.

We further use these matched triangles to find the possible geometric attacks. Table 1 lists four image texture dependent parameters and the number of strong IFPs determined by applying our image-texture-based improved and robust Harris corner detector on four images with different textures. These four parameters are Ratio the factor for classifying image textures , Type the texture decided by Eq.

It clearly shows that diameter D is determined by the image texture. That is, the more complicate the texture, the larger the diameter D. The value of SNum indicates the distribution of the perceptually high texture within an image. These adaptive parameters are automatically determined based on image textures. They improve the accuracy in finding the image-content-based strong IFPs and the robustness in resisting geometric and common image processing attacks on different textured images. We also observe that the number of IFPs is less than 35 for all the test images with different textures.

This observation clearly demonstrates that our improved and robust Harris corner detector does regulate the number of IFPs. It also indicates that the cost of saving IFPs for watermark synchronization is minimal compared with the cost of saving the host image.

## Bibliography - Machine Learning in Image Steganalysis - Wiley Online Library

Table 1 also lists the ratios between the number of matched triangle pairs for determining the geometric transformation and the total number of matched triangle pairs under four random geometric attacks. When comparing the results between the images, it should be noted that the number of matched triangle pairs is not linearly related to the number of strong IFPs due to the sensitivity of the IFPs to different attacks. However, our improved and robust Harris corner detector generates relatively strong IFPs to reduce the synchronization errors. In addition, two properties of the Delaunay tessellation always ensure that there are enough matched triangles, as indicated by high ratios in Table 1, for restoring the probe image.

Each gray cell indicates that the corresponding method fails to detect the watermark under the corresponding distortion. Table 2 summarizes the 42 X. Qi detection results compared with the schemes of Tang [19] and Wang [20] against common image processing attacks. Table 3 summarizes the detection results compared with the schemes of Tang [19] and Wang [20] against desynchronization attacks.

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These two tables show the ratio between the number of correctly detected watermarked embedding regions and the number of original embedded watermarked embedding regions. Table 2. Comparison of the detection rates i. One reason is that our relatively strong IFPs are more stable than those found by the Mexican hat detector and the scale invariant Harris-Laplace detector. These robust IFPs ensure more accurate synchronization between the probe and original watermarked images. Another reason is that the watermark is embedded in the mid-frequencies, which are in positions that are unlikely changed by common image processing attacks.

Table 3 clearly shows that our scheme performs the best in all the desynchronization attacks except the large cropping and local random bending attacks. These successes are mainly due to the following three reasons: 1 Our proposed robust and improved Harris corner detector finds relatively strong IFPs which are more resistant to desynchronization attacks. Our scheme is also more vulnerable to large cropping attacks since the potential embedding regions may be removed.

Comparison of the detection rate i. Qi Table 4. All these tests are performed on images of Lena, Airplane, and Car for a fair comparison. The comparison results upon various common image processing attacks and geometric distortions are listed side by side in Table 4. As shown in Table 4, both methods successfully pass the small shearing, rotation, scaling, and Stirmark general attacks. This makes the method vulnerable to image processing distortions.

These images are evenly distributed with high, medium, and low textures according to Eq.

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That is, the database contains 35 images for each texture level. The overall average PSNR value for these watermarked images is Each distortion category i. The yaxis summarizes the average detection rates of all images in each texture level under each distortion category. Specifically, the average detection rates for all simulated geometric attacks are The average detection rates for all simulated attacks are The overall average detection rate for all images under all simulated attacks is In summary, the all-around result of our proposed watermark scheme outperforms the peer feature-based schemes.