Classification of outdoor point clouds is an intensely studied topic, particularly with respect to the separation of vegetation from the terrain and manmade structures. In the presence of many overhanging and vertical structures, the (relative) height is no longer a reliable criterion for such a separation. An alternative would be to apply supervised classification; however, thousands of examples are typically required for appropriate training. In this paper, an unsupervised and rotation-invariant method is presented and evaluated for three datasets with very different characteristics. The method allows us to detect planar patches by filtering and clustering so-called superpoints, whereby the well-known but suitably modified random sampling and consensus (RANSAC) approach plays a key role for plane estimation in outlier-rich data. The performance of our method is compared to that produced by supervised classifiers common for remote sensing settings: random forest as learner and feature sets for point cloud processing, like covariance-based features or point descriptors. It is shown that for point clouds resulting from airborne laser scans, the detection accuracy of the proposed method is over 96% and, as such, higher than that of standard supervised classification approaches. Because of artifacts caused by interpolation during 3D stereo matching, the overall accuracy was lower for photogrammetric point clouds (74-77%). However, using additional salient features, such as the normalized green-red difference index, the results became more accurate and less dependent on the data source.