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Dendritic spines are considered a morphological proxy for excitatory synapses, rendering them a target of many different lines of research. Over recent years, it has become possible to image simultaneously large numbers of dendritic spines in 3D volumes of neural tissue. In contrast, currently no automated method for spine detection exists that comes close to the detection performance reached by human experts. However, exploiting such datasets requires new tools for the fully automated detection and analysis of large numbers of spines. Here, we developed an efficient analysis pipeline to detect large numbers of dendritic spines in volumetric fluorescence imaging data. The core of our pipeline is a deep convolutional neural network, which was pretrained on a general-purpose image library, and then optimized on the spine detection task. This transfer learning approach is data efficient while achieving a high detection precision. To train and validate the model we generated a labelled dataset using five human expert annotators to account for the variability in human spine detection. The pipeline enables fully automated dendritic spine detection and reaches a near human-level detection performance. Our method for spine detection is fast, accurate and robust, and thus well suited for large-scale datasets with thousands of spines. The code is easily applicable to new datasets, achieving high detection performance, even without any retraining or adjustment of model parameters.