Rate-distortion analysis of steganography for conveying stereovision disparity maps

Umeda, Toshiyuki [UCL] Batalomeu, Ana B. [] Francob, Filipe [] Delannay, Damien [UCL] Macq, Benoît [UCL]

3-D images transmission in a way which is compliant with traditional 2-D representations can be done through the embedding of disparity maps within the 2-D signal. This approach enables the transmission of stereoscopic video sequences or images on traditional analogue TV channels (PAL or NTSC) or printed photographic images. The aim of this work is to study the achievable performances of such a technique. The embedding of disparity maps has to be seen as a global rate-distortion problem. The embedding capacity through steganography is determined by the transmission channel noise and by the bearable distortion on the watermarked image. The distortion of the 3-D image displayed as two stereo views depends on the rate allocated to the complementary information required to build those two views from one reference 2-D image. Results from the works on the scalar Costa scheme are used to optimize the embedding of the disparity map compressed bit stream into the reference image. A method for computing the optimal trade off between the disparity map distortion and embedding distortion as a function of the channel impairments is proposed. The goal is to get a similar distortion on the left (the reference image) and the right (the disparity compensated image) images. We show that in typical situations the embedding of 2 bits/pixels in the left image, while the disparity map is compressed at 1 bit per pixel leads to a good trade-off. The disparity map is encoded with a strong error correcting code, including synchronisation bits.