Acquisition and quantitative analysis of high resolution images of dendritic spines are challenging tasks but are necessary for the study of animal models of neurological and psychiatric diseases. Currently available methods for automated dendritic spine detection are for the most part customized for 2D image slices, not volumetric 3D images. In this work, a fully automated method is proposed to detect and segment dendritic spines from 3D confocal microscopy images of medium-sized spiny neurons (MSNs). MSNs constitute a major neuronal population in striatum, and abnormalities in their function are associated with several neurological and psychiatric diseases. Such automated detection is critical for the development of new 3D neuronal assays which can be used for the screening of drugs and the studies of their therapeutic effects. The proposed method utilizes a generalized gradient vector flow (GGVF) with a new smoothing constraint and then detects feature points near the central regions of dendrites and spines. Then, the central regions are refined and separated based on eigen-analysis and multiple shape measurements. Finally, the spines are segmented in 3D space using the fast marching algorithm, taking the detected central regions of spines as initial points. The proposed method is compared with three popular existing methods for centerline extraction and also with manual results for dendritic spine detection in 3D space. The experimental results and comparisons show that the proposed method is able to automatically and accurately detect, segment, and quantitate dendritic spines in 3D images of MSNs.