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This paper addresses the problem of recognizing free-form 3D objects in point clouds. Compared to traditional approaches based on point descriptors, which depend on local information around points, we propose a novel method that creates a global model description based on oriented point pair features and matches that model locally using a fast voting scheme. The global model description consists of all model point pair features and represents a mapping from the point pair feature space to the model, where similar features on the model are grouped together. Such representation allows using much sparser object and scene point clouds, resulting in very fast performance. Recognition is done locally using an efficient voting scheme on a reduced two-dimensional search space. We demonstrate the efficiency of our approach and show its high recognition performance in the case of noise, clutter and partial occlusions. Compared to state of the art approaches we achieve better recognition rates, and demonstrate that with a slight or even no sacrifice of the recognition performance our method is much faster then the current state of the art approaches.