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This paper presents a novel method for the free-space characterization and shape recognition of dielectric objects using multivariate calibration methods and linear discriminant analysis. The dimensions of the variously shaped objects are comparable with some of the transmitted wavelengths of the ultra-wideband (UWB) time-domain pulses used. A system illuminating the objects under test by a subnanosecond UWB pulse has been built. An array of receiving antennas receives the scattered pulses that contain information about the shape, the size, and the dielectric or related material properties of the objects. Multivariate analysis is applied to separate geometric effects from those due to the dielectric properties. Results are shown for two measurement series determining the amount of carbon and weight or the dielectric constant of the objects under test, independent of their shape, size, and orientation. Furthermore, a classification algorithm is applied, separating the objects into geometrical classes independent of all other varied parameters.