Issue 1: Finding the better transform

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In the search for an efficient data-hiding algorithm for the printing and scanning process, the first issue we addressed was how to get from the spatial domain to the frequency domain. The question looked into was whether one transfrom might be better (be subject to less error from the printing and scanning process) than another transform. From the background reading and research in preparing for this project, we found the two most commonly used transforms were the FFT and the DCT.

The FFT and DCT were compared by examining them before and after the printing and scanning process. The FFT and DCT of the original image (without any alterations) were taken and the spectrum was saved. The image was then printed out and scanned back into the computer. The FFT and DCT were taken of the scanned in image. The frequency spectrums of the image after scanning were subtracted from the frequency spectrums before scanning to examine differences. These plots corresponded to error, with greater differences correlating to greater error. The error plots of both the FFT and DCT are shown above. The DCT was found to have less error from the printing and scanning process.