In this paper, a robust image watermarking method in two-dimensional space/spatial-frequency distributions domain is proposed which is robust against geometric distortion. This watermarking is detected by a linear frequency change. The dopplerlet transformation is used to detect the watermark. The chirp signals are used as watermarks and this type of signals is resistant to all stationary filtering methods and exhibits geometrical symmetry. In the two-dimensional Radon-Wigner transformation domain, the chirp signals used as watermarks change only its position in space/spatial-frequency distribution, after applying linear geometrical attack, such as scale rotation and cropping. But the two-dimensional Radon-Wigner transformation needs too much difficult computing. So the image is put into a series of 1D signal by choosing scalable local time windows. The watermark embedded in the dopplerlet transformation domain. The watermark thus generated is invisible and performs well in StirMark test and is robust to geometrical attacks. Compared with other watermarking algorithms, this algorithm is more robust, especially against geometric distortion, while having excellent frequency properties.
Contrast and spatial frequency modulation for diagnosis of amblyopia: An electrophysiological approach
