1. Reversible Data Hiding using Histogram Shifting
Sai Saketh Nandagiri

2. Need for reversible data hiding
Restoring the original cover image after extraction of payload from the stego image in which the payload is hidden. E.g., in medical images it is required that the image is losslessly reconstructed after extraction of payload.
Content authentication to verify the authenticity of the multimedia material. E.g., to verify the authenticity of a bank check transmitted over the internet.
A watermarked image is deemed to be authentic if pixel values in the stego image are not altered after embedding the data.

3. Reversible Data Hiding-Histogram Shifting
Original image is modified based on tonal distribution to hide the payload.
The peak and zero points in the histogram are used for embedding data.
The peak and zero values should be transmitted as side-information to the receiver for payload extraction.

4. Algorithm-I
First reversible data hiding algorithm as proposed by Ni et al [25].
Steps:
Find the peak and zero point in the histogram of cover image.
Scan the whole image in a sequential order, such as row-by-row, from top to bottom.
Shift the histogram to left/right based on the location of zero point. If zero point is on the left side of histogram, i.e. v_zero < v_peak, shift the histogram towards left.
Embed data in the shifted histogram.

5. Step 1:
From the original image matrix f, histogram is plotted to locate zero and peak values.
Figure 1: Original image f
Figure 2: Original histogram h

6. Step 2:
Figure 3: (a)Original image f (left)
(b)Shifted image 𝑓 (right)
Shift the histogram to the left as the zero point is located on the left side of the histogram using equation 1.
𝑓 𝑥 = 𝑓 𝑥,𝑦 −1, 𝑣 𝑧𝑒𝑟𝑜 <𝑓 𝑥,𝑦 < 𝑣 𝑝𝑒𝑎𝑘 𝑓(𝑥,𝑦), 𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒 Eq. 1
Figure 4: (a)Original histogram h (left)
(b)Shifted histogram ℎ (right)

7. Step 3:
Figure 5: (a)Shifted image 𝑓 (left)
(b)Stego image 𝑓 (right)
Embed payload p = ‘ ’ in the shifted image using equation 2.
𝑓 𝑥,𝑦 = 𝑓 𝑥,𝑦 −1, 𝑓 𝑥,𝑦 = 𝑣 𝑝𝑒𝑎𝑘 𝑎𝑛𝑑 𝑝 𝑙 =0 𝑓 (𝑥,𝑦), 𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒 Eq. 2
Figure 6: (a)Shifted histogram ℎ (right) (b)Stego histogram ℎ (left)

8. Algorithm-II
Reversible data hiding algorithm proposed by Pan et al [26].
Steps:
Divide the cover image into blocks of size s x s.
For each block B, the peak value v_peak is located from its histogram. The neighboring points v_peak-1 and v_peak+1 are also located.
Histogram is shifted to the left and right based on v_peak-2 and v_peak+2
Embed data in the shifted histogram.

9. Histogram is shifted to the left and right using equation 3.
𝐵′ 𝑖,𝑗 = 𝐵 𝑖,𝑗 +1, 𝑣 𝑝𝑒𝑎𝑘 +2≤𝐵(𝑖,𝑗)≤254 𝐵 𝑖,𝑗 −1, ≤𝐵(𝑖,𝑗)≤ 𝑣 𝑝𝑒𝑎𝑘 −2
Eq. 3
Binary bit stream is embedded in the cover image using equation 4.
𝐵′′ 𝑖,𝑗 = 𝐵′ 𝑖,𝑗 +1, & 𝐵 ′ 𝑖,𝑗 =𝑣 𝑝𝑒𝑎𝑘 +1, 𝑝 𝑙 =1 𝐵′ 𝑖,𝑗 −1, & 𝐵 ′ 𝑖,𝑗 =𝑣 𝑝𝑒𝑎𝑘 −1, 𝑝 𝑙 =1
Eq. 4

10. Proposed method to achieve RDH-HS
Fig 7: Flowchart of the proposed data hiding method

11. Proposed method to achieve RDH(cont.)
Steps:
At the transmitter:
The cover image (512 × 512) is 8 bits quantized as shown in fig. 7, is split into four blocks, each of size (256 × 256) as shown in fig. 8. The histogram of each block is shown in fig. 9.
Then the histogram of each block is inverted as shown in fig. 10 using eq 𝐵 𝑖,𝑗 =255−𝐼 𝑖,𝑗 , 1≤𝑖≤𝑟𝑜𝑤𝑠;1≤𝑗≤𝑐𝑜𝑙𝑢𝑚𝑛𝑠 Eq. 5
Fig 8: Cover image

12. Fig 9: Cover image split into blocks
Fig 10: Histogram of individual blocks(see fig. 9)
Fig 11: Inverted histogram of individual blocks(see fig. 10)

13. Continued
Histogram shifting of each block as proposed by Pan et al. [26].
𝐵′ 𝑖,𝑗 = 𝐵 𝑖,𝑗 +1, 𝑣 𝑝𝑒𝑎𝑘 +2≤𝐵(𝑖,𝑗)≤254 𝐵 𝑖,𝑗 −1, ≤𝐵(𝑖,𝑗)≤ 𝑣 𝑝𝑒𝑎𝑘 −2
Eq. 6
Fig 12

14. Continued
The data is embedded in each block along using eq. 7.
𝐵′′ 𝑖,𝑗 = 𝐵′ 𝑖,𝑗 +1, & 𝐵 ′ 𝑖,𝑗 =𝑣 𝑝𝑒𝑎𝑘 +1, 𝑝 𝑙 =1 𝐵′ 𝑖,𝑗 −1, & 𝐵 ′ 𝑖,𝑗 =𝑣 𝑝𝑒𝑎𝑘 −1, 𝑝 𝑙 =1
Eq. 7
Fig 13

15. Continued
The histograms of each block are inverted and stitched to form a stego image of size (512 × 512).
𝐵′′′ 𝑖,𝑗 =255−𝐵′′ 𝑖,𝑗 , 1≤𝑖≤𝑟𝑜𝑤𝑠;1≤𝑗≤𝑐𝑜𝑙𝑢𝑚𝑛𝑠
Eq. 8
Fig 14

16. Fig 15

17. Continued Fig 16 At the receiver:
The stego image (512 × 512) is split into four blocks, each of size (256 × 256).
Fig 16

18. Continued Eq. 9 Fig 17 Invert the histogram of each block using eq. 9.
𝐶 𝑖,𝑗 =255−𝐵′′′ 𝑖,𝑗 , 1≤𝑖≤𝑟𝑜𝑤𝑠;1≤𝑗≤𝑐𝑜𝑙𝑢𝑚𝑛𝑠
Eq. 9
Fig 17

19. Continued
The data is extracted from each block and shifted histogram is obtained using equation 𝐶 ′ (𝑖,𝑗)= 𝐶 𝑖,𝑗 −1, 𝐶 𝑖,𝑗 =𝑣 𝑝𝑒𝑎𝑘 +2, 𝑝 𝑙 =1 𝐶 𝑖,𝑗 +1, 𝐶 𝑖,𝑗 =𝑣 𝑝𝑒𝑎𝑘 −2, 𝑝 𝑙 =1 𝐶 𝑖,𝑗 , 𝐶 𝑖,𝑗 = 𝑣 𝑝𝑒𝑎𝑘 ±1 ,𝑝 𝑙 = Eq. 10
Fig 18

20. Continued
The shifted blocks are re-shifted using equation 11.
𝐶′′ 𝑖,𝑗 = 𝐶′ 𝑖,𝑗 −1, 𝑣 𝑝𝑒𝑎𝑘 +3≤𝐶′(𝑖,𝑗)≤255 𝐶′ 𝑖,𝑗 +1, ≤𝐶′(𝑖,𝑗)≤ 𝑣 𝑝𝑒𝑎𝑘 −3
Eq. 11
Fig 19

21. Continued
The histogram of each block is inverted using equation 12.
𝐶′′′ 𝑖,𝑗 =255−𝐶′′ 𝑖,𝑗 , 1≤𝑖≤𝑟𝑜𝑤𝑠;1≤𝑗≤𝑐𝑜𝑙𝑢𝑚𝑛𝑠
Eq. 12
Fig 20

22. Continued
The inverted blocks are stitched together to get the original cover image.
Fig 21

23. PSNR of stego image (in dB)
Results
Block size
PSNR of stego image (in dB)
Max number of bits
256 x 256
8987
128 x 128
12675
32 x 32
24209
16 x 16
29579
8x8
33960
Table 1: Results for Lena image

24. PSNR of stego image (in dB)
Continued
Block size
PSNR of stego image (in dB)
Max number of bits
256 x 256
5797
128 x 128
8322
32 x 32
17438
16 x 16
21798
8x8
24808
Table 2: Results for Barbara image

25. PSNR of stego image (in dB)
Continued
Block size
PSNR of stego image (in dB)
Max number of bits
256 x 256
7160
128 x 128
9966
32 x 32
17385
16 x 16
21806
8x8
24237
Table 3: Results for Goldhill image

26. PSNR of stego image (in dB)
Continued
Block size
PSNR of stego image (in dB)
Max number of bits
256 x 256
22754
128 x 128
27149
32 x 32
38959
16 x 16
44047
8x8
47568
Table 4: Results for Airplane image

27. PSNR of stego image (in dB)
Cont.
Block size
PSNR of stego image (in dB)
Max number of bits
256 x 256
16409
128 x 128
21617
32 x 32
35272
16 x 16
40449
8x8
44490
Table 5: Results for Tiffany image

28. Conclusions & Future work
The objective of this research is to improve the security of the present data hiding algorithms. This is achieved using histogram inversion before embedding the data in the cover image. In the results section it is also clear that the PSNR of the image improves with decrease in block size.
The only tradeoff is, when the block size decreases, there is significant increase in number of blocks to be processed. This leads to increase in the embedding time.
This research is mainly based on algorithm proposed by Pan et al [26]. Future work can be, extending the present algorithm by using the stego image to embed data again. This is defined as multi-layer embedding.

29. Acronyms and Abbreviations
HS-RDH – Histogram shifting based RDH
ICMP – Internet Control Message Protocol
IWT – Integer Wavelet Transform
JPEG – Joint Photographic Experts Group
LSB – Least Significant Bit
PSNR – Peak Signal to Noise Ratio 
QIM – Quantization Index Modulation
RDH - Reversible Data Hiding

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38. Thank You!