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In this paper we present a new approach for labeling 3D points with different geometric surface primitives using a novel feature descriptor - the Fast Point Feature Histograms, and discriminative graphical models. To build informative and robust 3D feature point representations, our descriptors encode the underlying surface geometry around a point p using multi-value histograms. This highly dimensional feature space copes well with noisy sensor data and is not dependent on pose or sampling density. By defining classes of 3D geometric surfaces and making use of contextual information using Conditional Random Fields (CRFs), our system is able to successfully segment and label 3D point clouds, based on the type of surfaces the points are lying on. We validate and demonstrate the method's efficiency by comparing it against similar initiatives as well as present results for table setting datasets acquired in indoor environments.