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In this paper, a wideband direct modeling and feature extraction method for two dimensional geometric objects with arbitrary local coordinate rotations is considered. In particular we focus on the problem of performing feature extraction for the case of electrically small objects which is particularly applicable to ground penetrating radar (GPR) applications. We first derive low frequency surface current density solutions for a class of simple two dimensional scatterers buried below a rough stochastic surface in a lossy half-space. Then for the inverse problem, a novel methodology is developed for pose and location invariant feature extraction derived from basis sets emerging from our proposed modeling framework. Our modeling and feature extraction algorithms are validated for different target shapes buried in lossy soil profiles.