This paper proposes a novel way of characterizing the local geometry of 3D points, using persistent feature histograms. The relationships between the neighbors of a point are analyzed and the resulted values are stored in a 16-bin histogram. The histograms are pose and point cloud density invariant and cope well with noisy datasets. We show that geometric primitives have unique signatures in this feature space, preserved even in the presence of additive noise. To extract a compact subset of points which characterizes a point cloud dataset, we perform an in-depth analysis of all point feature histograms using different distance metrics. Preliminary results show that point clouds can be roughly segmented based on the uniqueness of geometric primitives feature histograms. We validate our approach on datasets acquired from laser sensors in indoor (kitchen) environments.