The structure of neuronal dendrites and their spines underlie the connectivity of neural networks. Dendrites, spines, and their dynamics are shaped by genetic programs as well as sensory experience. Dendritic structures and dynamics may therefore be important predictors of the function of neural networks. Based on new imaging approaches and increases in the speed of computation, it has become possible to acquire large sets of high-resolution optical micrographs of neuron structure at length scales small enough to resolve spines. This advance in data acquisition has not been accompanied by comparable advances in data analysis techniques; the analysis of dendritic and spine morphology is still accomplished largely manually. In addition to being extremely time intensive, manual analysis also introduces systematic and hard-to-characterize biases. We present a geometric approach for automatically detecting and quantifying the three-dimensional structure of dendritic spines from stacks of image data acquired using laser scanning microscopy. We present results on the measurement of dendritic spine length, volume, density, and shape classification for both static and time-lapse images of dendrites of hippocampal pyramidal neurons. For spine length and density, the automated measurements in static images are compared with manual measurements. Comparisons are also made between automated and manual spine length measurements for a time-series data set. The algorithm performs well compared to a human analyzer, especially on time-series data. Automated analysis of dendritic spine morphology will enable objective analysis of large morphological data sets. The approaches presented here are generalizable to other aspects of neuronal morphology.