Error-Correction Coding of Spatial Image Watermarks in Gray Code

This paper deals with robustness of a spatial-domain-based digital watermark against signal distortions caused by lossy data compression usually used in digital communication systems, and presents a method for encoding a watermark bit in the Gray codeword representing a spatial signal by a (3, 1, 3) single-error-correcting (SEC) code. The two code words in the SEC code corresponding to respective watermark bits are determined so as to minimize the expected amount of embedding distortions. The stochastic analyses also show a capacity of the SEC code for changes in signal code words. Experiments using 8-bit monochrome images were carried out to evaluate the performance of the proposed method, where the watermarked images were distorted by the JPEG DCT-baseline coding scheme. The results demonstrate that, compared with a conventional method, the proposed method yields watermarked images with less distortions and achieves the comparable robustness.