Determining the relationship between the dendritic spine morphology and its functional properties is a fundamental challenge in neurobiology research. In particular, how to accurately and automatically analyse meaningful structural information from a large microscopy image data set is far away from being resolved. As pointed out in existing literature, one remaining challenge in spine detection and segmentation is how to automatically separate touching spines. In this paper, based on various global and local geometric features of the dendrite structure, we propose a novel approach to detect and segment neuronal spines, in particular, a breaking-down and stitching-up algorithm to accurately separate touching spines. Extensive performance comparisons show that our approach is more accurate and robust than two state-of-the-art spine detection and segmentation algorithms.