Fractal Metrology for images, signals and time series processing in Geosciences

The comparative study of Geosystems fractal behavior requires harmonizing statistics and integral information management. A core set of fractal parameters extracted from multiscale images and time series, as well as by signal processing, is uncertain, scale and measurement algorithm dependent, dynamic and variable in space. The aim of our research is to standardize the polifacetic information coming from fractal approach to Geosciences and to harmonize statistically the different measurement proposals and standards. For this purpose we design the Fractal Metrology (Oleschko, 2006). The box of numerous reference techniques, useful for unbiased fractal parameters extraction from different sources, is calibrated. The Geosystem scale invariance is documented by simple measurement of histogram roughness and estimated in terms of Hurst exponent. The lacunarity is used as the precise measure of data translation invariance. A set of contrasting examples of fractal metrology application to satellite imaginary, georadargrams analysis, as well as to optical and scanning electron microscopy is providing. In order to unify these multiscale and heterogeneous data banks we introduce a new branch of Fractal Geometry: Fractal Image Informatics (Oleschko et al., 2004).