Reversible Data Hiding using Histogram Shifting Sai Saketh Nandagiri 1001097897

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.

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.

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.

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

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)

Step 3: Figure 5: (a)Shifted image 𝑓 (left) (b)Stego image 𝑓 (right) Embed payload p = ‘1 0 1 1 0’ 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)

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.

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, 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

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

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. 5. 𝐵 𝑖,𝑗 =255−𝐼 𝑖,𝑗 , 1≤𝑖≤𝑟𝑜𝑤𝑠;1≤𝑗≤𝑐𝑜𝑙𝑢𝑚𝑛𝑠 Eq. 5 Fig 8: Cover image

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)

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, 1≤𝐵(𝑖,𝑗)≤ 𝑣 𝑝𝑒𝑎𝑘 −2 Eq. 6 Fig 12

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

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

Fig 15

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

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

Continued The data is extracted from each block and shifted histogram is obtained using equation 10. 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 =0 Eq. 10 Fig 18

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, 0≤𝐶′(𝑖,𝑗)≤ 𝑣 𝑝𝑒𝑎𝑘 −3 Eq. 11 Fig 19

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

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

PSNR of stego image (in dB) Results Block size PSNR of stego image (in dB) Max number of bits 256 x 256 48.3141 8987 128 x 128 48.3913 12675 32 x 32 48.6880 24209 16 x 16 48.8930 29579 8x8 49.1838 33960 Table 1: Results for Lena image

PSNR of stego image (in dB) Continued Block size PSNR of stego image (in dB) Max number of bits 256 x 256 48.2512 5797 128 x 128 48.3061 8322 32 x 32 48.5328 17438 16 x 16 48.6917 21798 8x8 48.9185 24808 Table 2: Results for Barbara image

PSNR of stego image (in dB) Continued Block size PSNR of stego image (in dB) Max number of bits 256 x 256 48.2750 7160 128 x 128 48.3358 9966 32 x 32 48.5343 17385 16 x 16 48.6937 21806 8x8 48.9157 24237 Table 3: Results for Goldhill image

PSNR of stego image (in dB) Continued Block size PSNR of stego image (in dB) Max number of bits 256 x 256 48.6141 22754 128 x 128 48.7194 27149 32 x 32 49.0965 38959 16 x 16 49.3330 44047 8x8 49.6595 47568 Table 4: Results for Airplane image

PSNR of stego image (in dB) Cont. Block size PSNR of stego image (in dB) Max number of bits 256 x 256 48.4693 16409 128 x 128 48.6105 21617 32 x 32 49.0057 35272 16 x 16 49.2274 40449 8x8 49.5564 44490 Table 5: Results for Tiffany image

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.

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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