The advantages of terrestrial laser scanning (TLS) for geodetic monitoring of man-made and natural objects are not yet fully exploited. Herein we address one of the open challenges by proposing feature-based methods for identification of corresponding points in point clouds of two or more epochs. We propose a learned compact feature descriptor tailored for point clouds of natural outdoor scenes obtained using TLS. We evaluate our method both on a benchmark data set and on a specially acquired outdoor dataset resembling a simplified monitoring scenario where we successfully estimate 3D displacement vectors of a rock that has been displaced between the scans. We show that the proposed descriptor has the capacity to generalize to unseen data and achieves state-of-the-art performance while being time efficient at the matching step due the low dimension.