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Dual-energy computerized tomography has gained great interest because of its ability to characterize the chemical composition of a material rather than simply providing relative attenuation images as in conventional tomography. The purpose of this paper is to introduce a novel polychromatic dual-energy processing algorithm, with an emphasis on detection and characterization of piecewise constant objects embedded in an unknown cluttered background. Physical properties of the objects, particularly the Compton scattering and photoelectric absorption coefficients, are assumed to be known with some level of uncertainty. Our approach is based on a level-set representation of the characteristic function of the object and encompasses a number of regularization techniques for addressing both the prior information we have concerning the physical properties of the object and the fundamental physics-based limitations associated with our ability to jointly recover the Compton scattering and photoelectric absorption properties of the scene. In the absence of an object with appropriate physical properties, our approach returns a null characteristic function and, thus, can be viewed as simultaneously solving the detection and characterization problems. Unlike the vast majority of methods that define the level-set function nonparametrically, i.e., as a dense set of pixel values, we define our level set parametrically via radial basis functions and employ a Gauss-Newton-type algorithm for cost minimization. Numerical results show that the algorithm successfully detects objects of interest, finds their shape and location, and gives an adequate reconstruction of the background.