Reversible color-to-gray mapping using subband domain texturization

The concept of reversible conversion of color images to gray ones has been recently introduced. Colors are mapped to textures and from the textures the receiver can recover the colors. This was done using the wavelet transform and replacing high-frequency subbands by the down-sampled chrominance planes. The idea is to print a color image with a black and white printer and, then, at a later time, to scan the document and recover colors. In this paper, we propose to use a more robust method, i.e. more resistant to the print-scan noise. We propose to use a largely redundant representation of the chrominance, embedding them into multiple subbands of a general subband transform. In other words, we spread the chrominance onto many subbands. We show theoretically that for minimizing the variance of the error caused by white noise, the chrominance should be replicated into many subbands and not linearly combined. We also demonstrate the method to find the best linear transform to embed the chrominance into the subbands in the more general case of colored noise. We carry a noise analysis to determine bounds to guide us on how many subbands into which to embed the chrominance. Experimental results were carried involving real printing and scanning, as well as using a simulated print-scan path.