In neurobiology, the 3D reconstruction of neurons followed by the identification of dendritic spines is essential for studying neuronal morphology, function and biophysical properties. Most existing methods suffer from problems of low reliability, poor accuracy and require much user interaction. In this paper, we present a method to reconstruct dendrites using a surface representation of the neuron. The skeleton of the dendrite is extracted by a procedure based on the medial geodesic function that is robust and topology preserving, and it is used to accurately identify spines. The sensitivity of the algorithm on the various parameters is explored in detail and the method is shown to be robust.