Impact of LSBR2 and LSBM2 on the histogram Derive the formulas expressing the impact of embedding using LSBR2

Impact of LSBR2 and LSBM2 on the histogram Derive the formulas expressing the impact of embedding using LSBR2 and LSBM2 on the histogram h[i], i = 0, …, 255. Assume that the cover is an 8-bit grayscale image with pixel values in the set {0, …, 255} and that the secret message is a random bit-stream of relative length . Following the derivations from the lecture, find the expected value of h[i] as a function of the cover image histogram h0[i] and the relative message length . For LSBM2, work out also the correct formulas for the boundary bins. Note: In LSBM2, there can be ambiguous cases when there are two closest values with the same two LSBs, e.g., if the cover pixel value is 7 (the last two LSBs are 11) and if one needs to embed message bits 01, one could change 7 to either 9 or 5 with the same distortion (modifying by 2). Resolve this ambiguity by always selecting the option that disturbs fewer bits. In this case, it means changing 7 to 5 rather than 9.