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Hyperbolae are common features in typical GPR scans that may result from localised reflectors (such as rocks), or from a buried cylindrical-shaped objects (such as pipes or drums). The shapes of these hyperbolae are influenced by both the nature of the subsurface reflector as well as the relative permittivity of the medium in which the objects are located. It is this uncertainty about what a hyperbola in a GPR scan actually represents, that has made it very difficult to make accurate estimations from GPR data, with regard to the buried object itself on one hand, and to the medium surrounding it on the other. In this paper, a novel general equation for hyperbolae which result from buried cylinders is presented which allows for cylinders of arbitrary radius, resulting in a more accurate estimation of the relative permittivity of the surrounding medium and of the depth, in addition to the radius information. This is achieved by subjecting the radargrams to a series of image processing stages followed by a curve-fitting procedure specifically developed for hyperbolae. The fitting technique is applied on a variety of synthetic hyperbolae that are generated to emulate reflections from targets of varying depth and radius and buried in a range of dielectrics. The results indicate this technique is fully capable of successfully estimating the depth and radius to within 1%. Further application to control site data has also given similar results, validating the method and justifying the assumptions used.