A New Perspective in Shape from Shading from Sar Images

In this paper we propose a new technique for Shape from Shading (SfS) from Synthetic Aperture Radar (SAR) images based on fractals. In particular, the present paper shows that, introducing proper models both for surface and scattering mechanisms, it is possible to estimate with sufficient accuracy the underlying topography also with a very simple and low computational complexity inversion technique. Natural surfaces, which are here of concern, are modeled via fractal geometry, in particular a 2-D fractional Brownian motion (fBm) is used. The scattering mechanisms are described through solutions suitable for fractal surface models; in particular, the Small Perturbation Method (SPM) is used. Considering a simple SAR image model, an appropriate and extremely low-computational inversion technique is used to invert the direct model and estimate the underlying topography. The proposed SAR SfS method is tested and numerically evaluated using an actual SAR image.