Dendritic spines are small, bulbous cellular compartments that carry synapses. Biologists have been studying the biochemical pathways by examining the morphological and statistical changes of the dendritic spines at the intracellular level. In this paper a novel approach is presented for automated detection of dendritic spines in neuron images. The dendritic spines are recognized as small objects of variable shape attached or detached to multiple dendritic backbones in the 2D projection of the image stack along the optical direction. We extend the curvilinear structure detector to extract the boundaries as well as the centerlines for the dendritic backbones and spines. We further build a classifier using Linear Discriminate Analysis (LDA) to classify the attached spines into valid and invalid types to improve the accuracy of the spine detection. We evaluate the proposed approach by comparing with the manual results in terms of backbone length, spine number, spine length, and spine density.