Point cloud registration is a fundamental problem in computer vision with a wide range of applications. The problem mainly consists of three parts: feature estimation, correspondence matching and transformation estimation. We introduced the Quan-tile Assignment problem and proposed a solution algorithm to be used in a point cloud registration framework for establishing the correspondence set between the source and the target point clouds. We analyzed different common feature descriptors and transformation estimation methods to combine with our Quantile Assignment algorithm. The performance of these approaches together with our algorithm are tested with controlled experiments on a dataset we constructed using well-known 3D models. We detected the most suitable methods to combine with our approach and proposed a new end-to-end pairwise point cloud registration framework. Finally, we tested our framework on both indoor and outdoor benchmark datasets and compared our results with state-of-the-art point cloud registration methods in the literature.