In this paper, a new method of rigid point cloud registration called Points Registration Learning (PREL) is presented. This algorithm is based on Deep Neural Networks trained by sparse autoencoders and fed with a set of Euclidean and Mahalanobis distance maps. Unlike other reported methods, we do not assume closeness between point clouds or point pairs. This allows registering point clouds with a high degree of displacement or occlusion. PREL algorithm does not require an iterative process, it estimates points distribution non-parametrically and it does not require a finer adjustment using other methods such as Iterative Closest Point (ICP). To evaluate the proposed algorithm, two kinds of point cloud sets were used: one of them corresponds to real scenes acquired with an RGB-D camera and the other set are surface reconstructions. When comparing PREL, ICP and Deep Closest Point (DCP) with Root Mean Square Error (RMSE), using points sets with a high degree of occlusion and displacement, ICP method shows an average RMSE of 98.8, followed by DCP with 32.51 and PREL with 0.75. These results suggest that PREL algorithm can be useful to reconstruct scenes, to scan objects and to register point clouds in any application, given the learning ability of the proposed algorithm.