Abstract: The transparency of traditional digital watermarking algorithms decreases with the increase of embedding strength, and their robustness and stability are poor. To solve these problems a frequency centroid zero watermarking algorithm based on polarization code and two-dimensional interleaving algorithm is proposed. In the proposed algorithm,the watermark information is encoded by polarization code in turn,and the interleaving matrix is constructed by two-dimensional interleaving. Then, the low-frequency coefficients of the carrier image are obtained by non-subsampled contour transform. Next, the one-dimensional matrix is obtained by block non-negative matrix decomposition. According to the characteristics of frequency distribution,the local frequency centroid is calculated to construct the feature matrix. Finally, the exclusive or operation of the interlaced matrix and the feature matrix containing watermark information are carried out to generate zero watermark. Experimental results show that the zero watermarking algorithm can effectively resist conventional signal processing attacks,geometric attacks and combinatorial attacks,and the normalized coefficient of watermark extraction is more than 0.88,which is robust and stable for practical applications.

Key words: polar code, two-dimensional interleaving, non-subsampled contour transform, frequency centroid, zero watermark