Implementation of modified level transformation for bit-plane watermarking

The inverting of signal bits is a basic operation for signal processing such as image watermarking. For performing the bit inversion for pixels, a level transformation that performs all the following three functions has been proposed in previous papers: first, inverting the bit associated with the chosen bit; second, reducing the change in the whole level caused by the inversion; and last, varying the transformed levels by a stochastic process. Procedures to implement the transformation are presented in this paper. Amounts of level change and changes of frequency distribution of levels caused by the transformation are also considered through simulations using real image data. The simulation results demonstrate that the stochastic properties of the transformation for real images can be approximately estimated from the properties obtained by an analysis under the assumption of a uniform frequency distribution of source levels.