In this research the Hurst exponent H is used for quantifying the fractal features of LANDSAT images. The Hurst exponent is estimated by means of the Detrending Moving Average (DMA), an algorithm based on a generalized high-dimensional variance around a moving average low-pass filter. Hence, for a two-dimensional signal, the algorithm first generates an average response for different subarrays by varying the size of the moving low-pass filter. For each subarray the corresponding variance value is calculated by the difference between the original and the averaged signals. The value of the variance obtained at each subarray is then plotted on log-log axes, with the slope of the regression line corresponding to the Hurst exponent. The application of the algorithm to a set of LANDSAT imagery has allowed us to estimate the Hurst exponent of specific areas on Earth surface at subsequent time instances. According to the presented results, the value of the Hurst exponent is directly related to the changes in land use, showing a decreasing value when the area under study has been modified by natural processes or human intervention. Interestingly, natural areas presenting a gradual growth of man made activities or an increasing degree of pollution have a considerable reduction in their corresponding Hurst exponent.
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Juan C. Valdiviezo-N. ; Raul Castro ; Gabriel Cristóbal and Anna Carbone
Hurst exponent for fractal characterization of LANDSAT images
", Proc. SPIE 9221, Remote Sensing and Modeling of Ecosystems for Sustainability XI, 922103 (October 2, 2014); doi:10.1117/12.2060281; http://dx.doi.org/10.1117/12.2060281