Fractal Image Informatics: from SEM to DEM

Land cover monitoring by fractal analysis of digital images

“…This can be observed by comparing different parts of the same image both at the local scale (reference lines) and at the global scale (firmagrams). As an example of the efficiency of the proposed comparison technique (Fractal Image Informatics, Oleschko et al, 2004Oleschko et al, , 2008, we discuss the case of the L33 firmagram (Fig. 6).…”

“…The algorithm Histo_Gen (Parrot, 2003) was applied to the .raw image, transforming it to a column of intensity values, following the original pixel arrangement across the 2-dimensional image. The roughness of this linear array (.ts extension), called firmagram (from the Spanish firma = signature, Oleschko et al, 2008) and of some segments of the column data, called reference lines (Oleschko et al, 2004) were measured. The fractal analysis of the complete firmagram (global scale) and of selected reference lines (local scale) was performed by the Rescaled Range technique (R/S) of the commercial software, Benoit v1.2 (1999).…”

“…For this purpose, the gray level intensity distribution across each studied image was translated into an Excel file consisting of a single column of intensity values. The 2-D diagram of this column was called firmagram (from the Spanish firma = signature) by Oleschko et al (2004Oleschko et al ( , 2008. The roughness of the time series was quantified by the Hurst exponent via the RescaledRange (R/S) method (Oleschko et al, 2004(Oleschko et al, , 2008.…”

“…Notwithstanding, the scale invariance of the main natural scenes' attributes becomes especially useful for this type of multi-scale and multi-temporal researches, being a simplified alternative to the quantitative analysis of land cover. In this study, we used the non-invasive, instantaneous and less time-consuming fractal technique designed by Oleschko et al (2004Oleschko et al ( , 2008 in order to measure the soil cover patterns under contrasting management conditions. The degree of surface occupation by plant residues was correlated with the fractal descriptors of their spatial heterogeneity, continuity, and tortuosity.…”

Fractal Metrology for biogeosystems analysis

“…The lack of reference techniques, standards and quality control for the measurements of these basic attributes of complex systems, makes difficult any intergroup comparisons of the usually extensive data surveys, resulting in unsustainable decision-making. In this study, we combine some principles and techniques of Fractal Geometry, Metrology, Informatics, Probability Theory and Statistics to create a new branch of Metrology, what we propose to call Fractal Metrology, and introduce scale invariant roughness as the main measurand of SI, UNI, NL, COM and CR of complex systems (Oleschko et al, 2008).…”