Fractal Image Informatics: from SEM to DEM
Klaudia Oleschko, Jean François Parrot, Gábor Korvin, M. Esteves, M. Vauclin, V. Torres-Argüelles, C. Gaona Salado, Sergei Cherkasov, Klaudia Oleschko, Sergei Cherkasov, José Luís Palacio Prieto, Vianey Torres Argüelles, Claudia I. Gaona Salado, Ana Gabriela Castañeda Miranda, Sergio Aurelio Zamora Castro · AIP conference proceedings · 2008
In this paper, we introduce a new branch of Fractal Geometry: Fractal Image Informatics, devoted to the systematic and standardized fractal analysis of images of natural systems. The methods of this discipline are based on the properties of multiscale images of selfaffine fractal surfaces. As proved in the paper, the image inherits the scaling and lacunarity of the surface and of its reflectance distribution [Korvin, 2005]. We claim that the fractal analysis of these images must be done without any smoothing, thresholding or binarization. Two new tools of Fractal Image Informatics, firmagram analysis (FA) and generalized lacunarity (GL), are presented and discussed in details. These techniques are applicable to any kind of image or to any observed positive‐valued physical field, and can be used to correlate between images. It will be shown, by a modified Grassberger‐Hentschel‐Procaccia approach [Phys. Lett. 97A, 227 (1983); Physica 8D, 435 (1983)] that GL obeys the same scaling law as the Allain‐Cloitre lacunarity [Phys. Rev. A 44, 3552 (1991)] but is free of the problems associated with gliding boxes. Several applications are shown from Soil Physics, Surface Science, and other fields.