The fully automated analysis of 3D point clouds is of great importance in photogrammetry, remote sensing and computer vision. For reliably extracting objects such as buildings, road inventory or vegetation, many approaches rely on the results of a point cloud classification, where each 3D point is assigned a respective semantic class label. Such an assignment, in turn, typically involves statistical methods for feature extraction and machine learning. Whereas the different components in the processing workflow have extensively, but separately been investigated in recent years, the respective connection by sharing the results of crucial tasks across all components has not yet been addressed. This connection not only encapsulates the interrelated issues of neighborhood selection and feature extraction, but also the issue of how to involve spatial context in the classification step. In this paper, we present a novel and generic approach for 3D scene analysis which relies on (i) individually optimized 3D neighborhoods for (ii) the extraction of distinctive geometric features and (iii) the contextual classification of point cloud data. For a labeled benchmark dataset, we demonstrate the beneficial impact of involving contextual information in the classification process and that using individual 3D neighborhoods of optimal size significantly increases the quality of the results for both pointwise and contextual classification.