Hurst exponent for fractal characterization of LANDSAT images

Abstract

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.

Discriminating image textures with the multiscale two-dimensional complexity-entropy causality plane

“…Actually, recent effective applications in heterogeneous fields confirm that these fractal techniques are highly valuable tools, e.g. identification of lesion regions of crop leaf affected by diseases [10], Hurst exponent estimation performed on satellite images to measure changes on the Earth's surface [11], and determination of scaling properties in encrypted images [12]. Despite all these significant efforts, the development of a robust methodology to detect and quantify spatial structures in images still represents an open and subtle problem.…”

Recurrence Plots of Geolocated Time Series from Satellite Maps of NOAA STAR Vegetation Health Index

“…Hurst and Lyapunov exponents have been used also in [13][14][15]. More generally, Hurst exponent can be involved in fractal analysis of LANDSAT images [16], to investigate the local changes in land uses.…”

Fractal analysis for natural resources management

“…The location of a specific region was determined according to the latitude and longitude coordinates of the image corners. 4 We then applied our algorithm to the grayscale version of each subimage in each sequence of the two geographical areas under investigation. Further, for each subimage, we estimated the generalized variance by applying square-moving-average windows of varying sizes n n, where n 2 f7; 11; : : : ; 256g.…”

“…The slope of the regression line represents the H value. 4 We used this algorithm to estimate the Hurst exponent to measure fractal changes from two image sets registered by the Landsat satellite, available through the US Geological Survey site. 5 For our simulations, we selected two scenes of particular interest, which show changes over time in land use and water management.…”