A novel watermarking method is proposed to hide a binary watermark into image files compressed by fractal block coding. This watermarking method utilizes a special type of orthogonalization fractal coding method where the fractal affine transform is determined by the range block mean and contrast scaling. Such orthogonalization fractal decoding is a mean-invariant iteration. In contrast, the fractal parameters of classical fractal compression are very sensitive to any change of domain block pool and to common signal and geometric distortion. Hence, it is impossible to directly place a watermark in fractal parameters. The proposed watermark embedding procedure inserts a permutated pseudo-random binary sequence into the quantized range block means. The watermark is detected by computing the correlation coefficient between the original and the extracted watermark. Experimental results show that the proposed fractal watermarking scheme is robust against common signal and geometric distortion such as JPEG compression, low-pass filtering, rescaling, and clipping.

We present a general method, the δ-test, which establishes functional dependencies given a sequence of measurements. The approach is based on calculating conditional probabilities from vector component distances. Imposing the requirement of continuity of the underlying function, the obtained values of the conditional probabilities carry information on the embedding dimension and variable dependencies. The power of the method is illustrated on synthetic time-series with different time-lag dependencies and noise levels and on the sunspot data. The virtue of the method for preprocessing data in the context of feedforward neural networks is demonstrated. Also, its applicability for tracking residual errors in output units is stressed.