Fractal algorithm for surface roughness parameters retrieval using multiband/polarization AIRSAR data

Surface roughness is an important characteristic in analyzing synthetic aperture radar images and three-dimensional (3-D) surfaces that influence the backscattering of electromagnetic waves. We propose an algorithm based on a fractal method for retrieving parameters of a surface. To estimate surface roughness parameters, 10,000 different 3-D surfaces with different rms-height and correlation length are simulated. 3-D simulation of surfaces is carried out based on fractal Brownian motion. The results show that the fractal method represents a good relationship between roughness parameters and fractal dimension. It can be seen that, in some cases, surfaces with different roughness have the same fractal dimension. Roughness index (RI) can be used as a complement to fractal dimension. We present empirical relationships among fractal dimension, roughness parameters, and RI. The method is implemented on L and C bands with HH and HV polarizations of AIRSAR data at different dates. The comparison between field measurement and estimated roughness showed that the accuracy of soil surface roughness estimation for band L with HH polarizations is better than bands L and C with polarizations HV and HH, respectively. The results of this method also are compared with the roughness estimates using the integral equation model (IEM). The analysis of outputs shows that the roughness estimation using the fractal and IEM is very similar in the low moisture at L band in HH polarization. The root mean square error of roughness for data at L band in HH polarization on July 1, 2002, is 0.54 and 0.53 cm for fractal and IEM, respectively. (C) 2019 Society of Photo-Optical Instrumentation Engineers (SPIE)