Yang et al.’s method

Yang et al. propose a data hiding method to improve the accuracy of predictive errors in complex image.

Before transporting secret data B to the receiver, the sender embeds secret data into cover image using Yang et al.'s method as follows. The sender divides the cover image into white and black segments like a chessboard. Figure 2 is the two segments of Yang et al.’s method

Figure 2. Two segments of Yang et al.’s method.

The sender compiles the embedded algorithm with one segment at once. In first part of embedded algorithms, the sender computes all the predictive errors in white segment by Formula (2-11).

 shifted by Formula (2-12) to make the spaces nearby peak points.

13 predictive errors are scanned. When scanned predictive errors are equal to peak points (H ,₁₁ H ), the sender shifts predictive errors and embeds secret data into cover image ₂₁ by Formula (2-13).



Predictive errors are scanned again and reversed into pixel values by Formula (2-14).

 sender outputs the numbers of predictive errors of black segment and gets histogram of predictive errors. The sender finds (H ,₁₂ H ,₂₂ Z ,₁₂ Z ) where ₂₂ Z₁₂H₁₂H₂₂Z₂₂. The predictive errors in the range of (H ,₁₂ Z ) and (₁₂ H ,₂₂ Z ) are shifted by Formula (2-15) ₂₂ to generate the spaces nearby peak points.

 predictive errors are scanned. When scanned predictive errors are equal to peak points (H ,₁₂ H ), the sender shifts predictive errors and embeds secret data into cover image ₂₂

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When receiving the information, the receiver divides stego-image into white and black segments as Figure 2 and compiles the extracted algorithm with one segment at once. In first part of extracted algorithms, the receiver computes all the predictive errors in black segment by Formula (2-11). The receiver scans the predictive errors from up to down and left to right until all the predictive values are scanned. When the scanned predictive errors are equal to peak points (H ,₁₂ H ), the receiver extracts embedded data ₂₂ by Formula (2-17).



After extracting embedded data, the receiver shifts predictive errors by Formula (2-18).

 segment for white segment and computes second part of extracted algorithms as follows.

In second part of extracted algorithms, the receiver computes all the predictive errors in white segment by Formula (2-11). The receiver scans the predictive errors from up to down and left to right until all the predictive values are scanned. When the scanned

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predictive errors are equal to peak points (H ,₁₁ H ), the receiver extracts embedded data ₂₁ by Formula (2-19).



After extracting embedded data, the receiver shifts predictive errors by Formula (2-20).

 real secret data.

To understand Yang et al.’s method, we give the following example. Assume that the sender wants to embed the secret data B{01101111010100) into the cover image in Figure 3.

Figure 3. The cover image.

The sender divides the cover image into white and black segments and computes all the predictive errors of white segment by Formula (2-11). The results are shown in Figure 4.

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Figure 4. The predictive errors of white segment.

The sender outputs the numbers of predictive errors in white segment and gets histogram of predictive errors as Figure 5.

Figure 5. The histogram of predictive errors of white segment.

Obviously, the sender gets H₁₁ 0, H₂₁1, Z₁₁1 and Z₂₁2. Then the sender shifts predictive errors in the range (-1,0) and (0,2) to generate the spaces nearby peak points (H₁₁, H ₂₁) by Formula (2-12). The sender scans predictive errors of white segment from up to down and left to right. Predictive errors are shifted to embed secret data (0110111101) into the image in Figure 4 by Formula (2-13). After shifting predictive errors, the sender gets the embedded histogram and shifted predictive errors as Figure 6.

0 1 2

-1 -2

2 2

8

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Figure 6. Embedded histogram and shifted predictive errors of white segment.

The sender scanned predictive errors again and reverses the predictive errors into pixel values by Formula (2-14). The results are shown in Figure 7.

Figure 7. The stego-image after first algorithm.

To embed remained secret data (0100), the sender swaps white segment for black segment and computes all predictive errors of black segment by Formula (2-11). The results are shown in Figure 8.

Figure 8. The predictive errors of black segment.

0 1 2 -1

-2

1 2 6

2 1

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The sender outputs the numbers of predictive errors in black segment and gets histogram of predictive errors as Figure 9.

Figure 9. The histogram of predictive errors in black segment.

Obviously, the sender gets H₁₂ 0, H₂₂1, Z₁₂ 2 and Z₂₂ 3. Then the sender shifts predictive errors in the range (-2,0) and (0,3) to generate the spaces nearby peak points H₁₁ and H₁₂ by Formula (2-15). The sender scans predictive errors of black segment from up to down and left to right. Predictive errors are shifted to embed secret data (0100) into the image in Figure 8 by Formula (2-16). After shifting predictive errors, the sender gets the embedded histogram and shifted predictive errors as Figure 10.

Figure 10. Embedded histogram and shifted predictive errors of black segment.

The sender scans predictive errors again and reverses the predictive errors into pixel values by Formula (2-14). The results are shown as Figure 11.

0 1 2

-1 -2

3 4

2

3 4 5

2 1 1

0 1 2

-1 -2

4 3 3

3 4 5 2 1

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Figure 11. The stego-image.

The secret data are completely embedded into cover image so far. The sender transports stego-image, L, H₁₁, H₂₁, Z₁₁, Z₂₁, H₁₂, H₂₂, Z₁₂ and Z₂₂ to the receiver.

When receiving the information, the receiver divides the stego-image into white and black segments as Figure 11. In the first part of extracted algorithms, the receiver computes all the predictive errors of black segment by Formula (2-11). The results are shown in Figure 12.

Figure 12. The shifted predictive errors of black segment.

The receiver scans predictive errors from up to down and left to right. The embedded data are extracted by Formula (2-17). After extracting embedded data, predictive errors are shifted by Formula (2-18). The receiver scans predictive errors again and reverses the predictive errors into pixel values by Formula (2-14). The results are shown in Figure 7. After compiling first part of extracted algorithms, the receiver gets the

20 embedded data (0100000).

In second part of extracted algorithms, the receiver swaps black segment for white segment and computes all the predictive errors of white segment by Formula (2-11).

The results are shown in Figure 13.

Figure 13. The shifted predictive errors of white segment.

The receiver scans predictive errors from up to down and left to right. The embedded data are extracted by Formula (2-19). After extracting embedded data, predictive errors are shifted by Formula (2-20). The receiver scans predictive errors again and reverses the predictive errors into pixel values by Formula (2-14). The results are as Figure 3.

After compiling second part of extracted algorithms, the receiver gets the embedded data (0110111101) . Since the redundant secret data are extracted when

22 12 21

11 H H H

H

L    , the receiver has to combine the extracted data of two segments and delete redundant B where _k k L to get real secret data. Finally, the receiver gets the cover image and secret data B(01101111010100).

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