Fractal filtering method

Lima, A., De Vivo, B., Cicchella, D., Cortini, M., and Albanese, S. (2003). Multifractal IDW interpolation and fractal filtering method in environmental studies An application on regional stream sediments of Campania Region (Italy). Appl. Geochem. 18, 1853—1865. 

In this chapter, the application of multifractal inverse distance weighted (MIDW) interpolation method and a fractal filtering technique, named spatial and spectral analysis or simply (S-A) method (Cheng, 2003), will be illustrated to evaluate geochemical background at the regional and local scale. For this purpose, two case studies will be discussed for two different Italian areas ... 

To decompose the MIDW interpolated map to obtain background/baseline and anomaly maps, a fractal filtering technique, named spatial and spectral analysis or simply (S-A) method, is applied. 

Figure 7.5 Pb (A) and U (B) background/baseline maps compiled using spatial and spectral analysis (S—A method). The values have been obtained by decomposition of the Pb and U geochemical maps (Fig. 7.1A and B, respectively) into separate components using the fractal filters selected on the S—A plot. Pb background/baseline map is generated only with signals with power spectrum (E) >15,713 (selected cutoff in Fig. 7.6A). U background/baseline map is generated only with signals with power spectrum (E)>706 (selected cutoff in Fig. 7.6B). For both maps pixel values have been reclassified by fractal C—A plot (see text).

---