Multifractal characterization of the spatial distribution of ulexite in a Bolivian salt flat

Abstract

Understanding spatial patterns is a critical and under-explored aspect of remote sensing. This paper describes how multifractal theory can be applied to characterize these heterogeneous patterns in remotely sensed data as well as to determine the operational scale. An example based on the characterization of ulexite distribution on the world's largest salt flat (10 000 km 2 ), located in Bolivia, using a binarized Landsat Thematic Mapper (TM) 4/7 ratio image, is used to describe the step-by-step procedure. Distribution was well characterized by the multifractal parameters and expressed through the f-a, t-q and D-q relationships. Moments from q522 to 5 showed a linear trend in scales from approximately 0.007 to 10 000 km 2 . This implies that the attribute analysed could be measured at different scales, within defined boundaries, and up-and down-scaled using the multifractal parameters. In addition, the asymmetry shown by the f-a spectrum indicates the presence of clusters with high probability of finding ulexite, and large areas where the mineral might be found in small patches. The areas with a high probability of finding ulexite were mapped to guide any future field survey. Using the maximum entropy concept, the operational scale to determine the mineral was obtained at 1062 m.

Detection of bacterial wilt infection caused by Ralstonia solanacearum in potato (Solanum tuberosum L.) through multifractal analysis applied to remotely sensed data

“…Moreover, the multifractal analysis gives a description of several physical properties of the observed signal such as the internal entropy, the anisotropy and the correlation among data. Indeed, multifractal analysis has been applied to signal data in several research fields such as solar flare X-ray emissions (McAteer et al 2007) soil science (Posadas et al 2003(Posadas et al , 2005, neurology (Yu et al 2001;Latka et al 2002) and cardiology (Ivanov et al 1999;Byalovskii et al 2005) among others. Hence, the objective of this work was to test the feasibility of using the multispectral light reflectance of plants, supported by conventional and wavelet-based multifractal analyses of the reflectance signal, for detecting R. solanacearum infection in potato crops, aiming at developing a practical field monitoring method for the spatial assessment of the health condition of the crop.…”

Multiscale characterization of pore spaces using multifractals analysis of scanning electronic microscopy images of carbonates

“…These two observations corroborate that generalized dimensions D q can provide an indicator of data heterogeneity degree, since their values would converge to a constant faster in images where pore distributions were less heterogeneous. Furthermore, Posadas et al (2005) have shown that homogeneous multifractal distributions have a narrow concave f(α)-spectra, whereas the opposite is true for heterogeneous structures. Thus, the wider is the magnitude of change of f(α) around the value f(α(0)), the higher is the heterogeneity of analyzed structures.…”

“…For multifractal pore distributions, the spectrum can be represented by a curve with a wide range of values for α. This interval increases with the increase of the distribution heterogeneity (Posadas et al, 2005;Xie et al, 2010). Multifractals generalized dimensions D q of the q −th order (Hentschel and Procaccia, 1983) are defined as:…”

“…The factor α i allows quantifying the distribution complexity in spatial location (Posadas et al, 2005). The number of boxes N(α), where the probability P i has singularity strengths between α and α+dα, can be related to the box size ε as:…”

“…where τ (q) is the q th mass exponent and f(α) the singularity spectrum (Halsey et al, 1986), are related as: D 0 , D 1 and D 2 can be computed using the following equations (Posadas et al, 2005):…”