Fractal-Based Local Range Slope Estimation from Single SAR Image with Applications to SAR Despeckling and Topographic Mapping

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Abstract

In this paper, we propose a range slope estimation procedure from single synthetic aperture radar (SAR) images with both methodological and applicative innovations. The retrieval algorithm is based on an analytical linearized direct model, which relates the SAR intensity data to the range local slopes and encompasses both a surface model and an electromagnetic scattering model. Scene topography is described via fractal geometry, whereas the Small Perturbation Method is adopted to represent the scattering behavior of the surface. The range slope map is then used to estimate the surface topography and the local incidence angle map. For topographic mapping applications, also referred to as shape from shading, a regularization procedure is derived to recover the azimuth local slope and reduce distortions. Then we present a new intriguing application of the inversion procedure in the field of SAR despeckling. Proposed techniques and high-level products are tested in a wide series of experiments, where the algorithms are applied to both simulated (canonical) and actual SAR images. It is proved that the proposed range slope retrieval technique can (1) provide an estimate of the surface shape, with overall better performance w.r.t. typical models used in this field and (2) be useful in advanced despeckling techniques.

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Fractal-based description of natural scenes.

Alex P. Pentland (1984)

This paper addresses the problems of 1) representing natural shapes such as mountains, trees, and clouds, and 2) computing their description from image data. To solve these problems, we must be able to relate natural surfaces to their images; this requires a good model of natural surface shapes. Fractal functions are a good choice for modeling 3-D natural surfaces because 1) many physical processes produce a fractal surface shape, 2) fractals are widely used as a graphics tool for generating natural-looking shapes, and 3) a survey of natural imagery has shown that the 3-D fractal surface model, transformed by the image formation process, furnishes an accurate description of both textured and shaded image regions. The 3-D fractal model provides a characterization of 3-D surfaces and their images for which the appropriateness of the model is verifiable. Furthermore, this characterization is stable over transformations of scale and linear transforms of intensity. The 3-D fractal model has been successfully applied to the problems of 1) texture segmentation and classification, 2) estimation of 3-D shape information, and 3) distinguishing between perceptually ``smooth'' and perceptually ``textured'' surfaces in the scene.