Reference no: EM133244719
Case: LSB embedding in two LSBs Assume that the cover is an 8-bit grayscale image with pixel values in the set {0, ..., 255}. Consider two different embedding schemes: LSBR2 and LSBM2. LSBR2 embeds two bits into each pixel by replacing the two least LSBs (the 8th and the 7th bit) with message bits: Emb: Two bits are embedded into each pixel by replacing its two least significant bits with two message bits. For example, if the cover pixel value is ci = 14 = (00001110)2 and we want to embed message bit pairs 00, 01, 10, 11, we change ci to 12, 13, 14, 15, respectively. If ci = 32 = (00100000)2, we embed the same bit pairs by changing ci to 32, 33, 34, and 35, etc. Ext: Two bits are extracted as the least two LSBs from the pixels to form the message. Assuming that the message is a random bit-stream of maximal length (2 number of pixels) and the pixel values are uniformly distributed in {0, ..., 255}, compute the expected L1 distortion per pixel. Hint: Realize that you have essentially only four types of pixels depending on their last two LSBs or, equivalently, the remainder after dividing by 4 (ci = 4k, 4k+1, 4k+2, and 4k+3, k = 0, 1, ..., 63).
The expected distortion will depend on the type into which the pixel belongs. Assuming that the pixel values are uniformly distributed means that the expected distortion per pixel will be the arithmetic average of the expected distortion per each pixel type. LSBM2 is a version of LSBM also capable of embedding two bits per pixel: Emb: Two bits are embedded at each pixel by always modifying the pixel value to the closest value with the required least two LSBs.
Example: if ci = 14 = (00001110)2 and we want to embed message bit pairs 00, 01, 10, 11, we change ci to 12, 13, 14, 15, respectively. If ci = 32 = (00100000)2, we embed the same bit pairs by changing ci to 32, 33, 34, and 31, etc. Note that the last change from 32 to 31 will lead to modification of six LSBs! Ext: Again, two bits are extracted from the least two LSBs of pixels to form the message. Assuming that the message is a random bit-stream of maximal length (2 x number of pixels) and the pixel values are uniformly distributed in {0, ..., 255}, compute the expected L1 embedding distortion per pixel. For simplicity, in this problem ignore the boundary issues. Which scheme has a lower expected distortion and why?