Imaging of dielectric objects buried under a rough surface via distorted born iterative method

A method is given for the shape, permittivity and conductivity reconstruction of lossy dielectric objects buried under rough surfaces using the Distorted Born Iterative Method (DBIM). The method is based on the refreshing of the Green's function of the two-part space media with rough interface by updating the complex permittivity of the reconstruction domain at each iteration step. The scattered field data are measured at multiple locations for multiple transmitters operating at a single frequency where both transmitters and receivers are located above the rough surface interface. The Green's function of the problem is obtained by using the buried object approach (BOA) method where the fluctuations of the rough surface from the flat one are assumed to be buried objects in a two-part space with planar interface. The performance of the method is tested by some numerical applications and satisfactory results are obtained

Ray-Affine Functions: A General Dual Form to Describe Curves, Surfaces, and Volumes

In computer graphics modeling, two different forms are used to represent curves and surfaces: implicit and parametric. Functions that can be expressed both in implicit and parametric forms are called dual forms. To date, the only known dual forms are monoids and superquadrics. In this paper, we introduce a new dual form: ray-affine functions. Ray-affines include both monoids and superquadrics and provide a wide range of other modeling functions including exponentials and sinusoidals. Ray-affines are closed under operations that implement morphing, union, and interpolation. This feature of ray-affine functions lets the user construct a ray-affine function to model a shape as a smooth aproximation of a control shape given by set union or set intersection of shapes defined by simpler ray-affine functions