On shape from shading and SAR images: An overview and a new perspective

In this paper, we first discuss some general problems and issues concerning Shape from Shading (SfS) from Synthetic Aperture Radar (SAR) images and present the state of the art. Starting from this general discussion, we propose a new perspective and introduce a novel approach to SAR SfS based on fractals. In particular, fractal geometry is used to model the shape of natural surfaces, which are here of concern. 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, the forward model is then inverted via an appropriate and extremely low-computational inversion approach and the underlying topography is estimated. The proposed SAR SfS technique is tested and numerically evaluated using an actual SAR image.