The potential application of fractal approach for surface roughness retrieval: A study for simulated surfaces

Abstract

Natural surfaces can be modelled with fractals because fractals properly account for scale invariance and self similarity of these surfaces. The well-known measure, i.e. fractal dimension (D), is the property used to describe the roughness of fractal surfaces. Retrieving the Earth's surface roughness with satellite images, particularly synthetic aperture radar (SAR) images, is an interesting and challenging task. Consequently, many researchers are using electromagnetic models, various inversion techniques, semi-empirical models to retrieve the roughness parameters, i.e. RMS surface height (s) and autocorrelation length (l). Most of the models require some a priori information or some given values to solve the equations and retrieve l and s. Uncertainty still exists to retrieve these parameters with minimum or no a priori information. Therefore, in this paper, the fractal dimension approach has been applied to correlate l and s with fractal properties for development of a surface parameter retrieval algorithm. For this purpose, 1500 synthetic surfaces for known l and s have been generated, and their fractal dimension has been computed. D has also been computed after introducing Gaussian and speckle noise to the generated surfaces. The analysis among D, l and s shows the potentiality of relationship among these parameters and is helpful in developing a relationship among them by which l and s can be retrieved. The values of l and s are retrieved with the help of a look-up table for the synthetic surfaces which can be extended for retrieval of roughness parameters from the SAR images.