Given the success of convolutional neural networks (CNNs) during recent years in numerous object recognition tasks, it seems logical to further extend their applicability to the treatment of three-dimensional data such as point clouds provided by depth sensors. To this end, we present an approach exploiting the CNN's ability of automated feature generation and combine it with a novel 3D feature computation technique , preserving local information contained in the data. Experiments are conducted on a large data set of 600.000 samples of hand postures obtained via ToF (time-of-flight) sensors from 20 different persons, after an extensive parameter search in order to optimize network structure. Generalization performance, measured by a leave-one-person-out scheme, exceeds that of any other method presented for this specific task, bringing the error for some persons down to 1.5%.