Chapter 4 Synthetic Image Authentication
4.3 Proposed Scheme
4.3.1 Pixel Classification
non-flippable pixels. Flippable pixels can be changed to embed the watermark without causing noticeable artifacts.
For simplicity, we start with binary images to identify the flippable pixels. For instance, Figure 4-3 shows a part of the binary document image of Figure 4-1 and gives examples of flippable pixels and non-flippable pixels. The dotted lines indicate the flipping of the blue pixels and the dashed lines indicate the red ones. It can be easily observed that after flipping the blue and red pixels in the left image the caused artifacts in the right image are quite different. The flipping of the two red pixels causes distinct noticeable discontinuousness while the flipping of blue pixels doesn’t. So the blue pixels are identified as flippable pixels whose change will cause less noticeable artifacts and we should avoid changing the red pixels in order to keep the image quality.
Figure 4-3 Diagram of the proposed authentication watermark system
Embedding Authentication
Original Image Pixel Classification Pixel Permutation Pixel Grouping
Secret Key Authentication code
Watermarked Image Inverse Permutation Watermark Embedding
Pixel Permutation Divide Blocks Watermark Detection Integrity Check
Noise Filter Unverified Pixels
Inverse Shuffle Unverified Verified Tamper Localization
Orgin Recovery
Secret Key Authentication code
In a binary image, the flippability of a pixel can be determined by analyzing the local property in its neighborhood, for example in an n×n block. This is not a complex problem if the used block is small, such as in a 3×3 block. In [WL04], a flippability score, which indicates the pixel’s flippability, is given to each pixel by analyzing the smoothness and connectivity of the neighborhood around it in a 3×3 window. The smoothness is measured by the total number of the pixel transitions in horizontal, vertical, diagonal and anti-diagonal directions and the connectivity by the number of the black and white pixel clusters. A higher flippability score indicates that changing the pixel will cause less noticeable artifacts. Based on the similar idea, Yang and Kot proposed a new flippability criterion in [YK07]. According to this criterion, the flipping of a pixel should preserve the pixel connectivity in its 3×3 neighborhood.
These two methods achieve similar results. Figure 4-5 lists the 3×3 patterns in which the change of the center pixel is less noticeable. All of the listed patterns have a flippability score larger than 0.25. The patterns (a)-(b) and (i)-(l) comply with the connectivity-preserving criterion in [YK07].
However, although the patterns listed in Figure 4-5 are relatively suitable for changing among all the possible patterns, some of them will still cause noticeable artifacts to some extent. In our watermarking scheme, we propose a statistical detection strategy that allows watermark embedding and detection errors to exist up to a reasonable rate.
Thus, we can reduce the watermark payload by bearing some unsuccessful embeddings when the watermark capacity of the whole image is less than what is required. In
Figure 4-4 Examples of flippable and non-flippable pixels
addition, this strategy enables us to utilize every embedded watermark bit to monitor more image pixels, which will further reduce the watermark payload. Therefore, in the proposed watermarking scheme, the required number of flippable pixels is reduced. To further reduce the impact of the watermark embedding on the image fidelity, we formulate a new set of rules to determine the flippable pixels as follows, which is simpler but much stricter. Because the rules to determine the flippable pixels are simplified, the computation cost is consequently reduced. Hence in our scheme neither offline computation nor storage of a look-up table of flippable patterns is needed. All flippable pixels can be identified online quickly.
In a 3×3 neighborhood, the center pixel will be considered as flippable when the following three rules hold.
1. Both the horizontal and the vertical transition of the center pixel must be equal to one,
2. Both the diagonal and the anti-diagonal transition of the center pixel must be equal to one and
3. There must be at least one row or column whose transition is equal to zero.
The transition of the center pixel p(i,j) is calculated as follows:
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k a
k d
k v
k h
k j k i p k j k i p D t
l antidiagno
k j k i p k j k i p D t
diagnol
j k i p j k i p D t
vertical
k j i p k j i p D t
horizontal
(4-1)
where ]D[⋅ is a differential operator. D[a,b]=1 if a≠b and D[a,b]=0 if a=b.
Rule 1 ensures that the center pixel is not in a straight line and there is one and only one pixel in both directions having the same color as the center pixel, which means the center pixel is an edge pixel. Rule 2 ensures that the center pixel is not a corner pixel.
Rule 3 guarantees that the center pixel is along a straight line and not surrounded by pixels with different colors. According to these three rules, among the patterns listed in Figure 4-5, only the patterns (a) and (b) can be considered as flippable. In [WL04]
these two patterns have the largest flippability score of 0.625. They also comply with the connectivity-preserving criterion proposed in [YK07]. If we unleash Rule 3, the patterns (c) and (d) will become flippable while other patterns (e)-(l) still remain non-flippable. Therefore, Rule 3 can be deemed as optional when a higher watermark capacity is required.
If the targeted synthetic image is not binary but has a limited number of colors, a pixel classification process is performed before identifying the flippable pixels. All pixels are classified into two sets of colors, c1 and c2, corresponding to the black and white color in binary images. Every set contains one or more colors. This pixel classification is similar to the image binarization problem, but because we consider only the synthetic images with a limited number of colors, the problem becomes much simpler. Such
(a)
(j) (k) (l)
(i) (h)
(g)
(f) (e)
(d) (c)
(b)
Figure 4-5 List of the patterns in which the center pixel is suitable for flipping, excluding the symmetric cases of rotation, mirroring and complement.
synthetic color images usually have a discrete histogram distribution, so it is easy to find a suitable threshold to classify the pixels into two sets.
The threshold can be fixed or be chosen adaptively depending on the image content.
The middle value of all the possible pixel values, i.e. 128, is a suitable threshold for most images with moderate brightness/color distribution. For example, Figure 4-6 plots the luminance histogram of the color map image shown in Figure 4-2. The two highest peaks are the two background colors, green and white. Therefore, a threshold of 128 can separate the foreground pixels from the background. The background pixels are classified to set c2 and the foreground pixels to c1.
Nevertheless, if most pixels of the whole image are very light or dark, with this middle value we can not get enough distinct pixels to embed the watermark. In this case, the mean value can be used as the threshold to classify the pixels. Furthermore, according to the cover image’s property, this classification may be determined by the pixel luminance or hue or both. In most cases, the pixels can be classified based on the difference of the luminance. However, for special images in which the pixels have the same luminance and differ only in colors, the classification should depend on the histogram of the hue.
Figure 4-6 Histogram of the color map image
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