Border extrapolation using fractal attributes in remote sensing images

Abstract

In management, monitoring and rational use of natural resources the knowledge of precise and updated information is essential. Satellite images have become an attractive option for quantitative data extraction and morphologic studies, assuring a wide coverage without exerting negative environmental influence over the study area. However, the precision of such practice is limited by the spatial resolution of the sensors and the additional processing algorithms. The use of high resolution imagery (i.e., Ikonos) is very expensive for studies involving large geographic areas or requiring long term monitoring, while the use of less expensive or freely available imagery poses a limit in the geographic accuracy and physical precision that may be obtained. We developed a methodology for accurate border estimation that can be used for establishing high quality measurements with low resolution imagery. The method is based on the original theory by Richardson, taking advantage of the fractal nature of geographic features. The area of interest is downsampled at different scales and, at each scale, the border is segmented and measured. Finally, a regression of the dependence of the measured length with respect to scale is computed, which then allows for a precise extrapolation of the expected length at scales much finer than the originally available. The method is tested with both synthetic and satellite imagery, producing accurate results in both cases.