Ground penetrating radar (GPR) is traditionally applied to smooth surfaces in which the assumption of half-space is an adequate approximation that does not deviate much from reality. Nonetheless, using GPR for internal structure characterization of tree trunks requires measurements on an irregularly shaped closed curve. A typical hyperbola fitting has no physical meaning in this new context since the reflection patterns are strongly associated with the shape of the tree trunk. Instead of a clinical hyperbola, the reflections give rise to complex-shaped patterns that are difficult to be analyzed even in the absence of clutter. In this paper, a novel processing scheme is described which can interpret complex reflection patterns assuming a circular target subject to any arbitrary shaped surface. The proposed methodology can be applied using commercial hand-held antennas in real time, avoiding computationally costly tomographic approaches that require the usage of custom-made bespoke antenna arrays. The validity of the current approach is illustrated both with numerical and real experiments.