In this paper we address the loop closure detection problem in simultaneous localization and mapping ( slam ), and present a method for solving the problem using pairwise comparison of point clouds in both two and three dimensions. The point clouds are mathematically described using features that capture important geometric and statistical properties. The features are used as input to the machine learning algorithm AdaBoost, which is used to build a non-linear classifier capable of detecting loop closure from pairs of point clouds. Vantage point dependency in the detection process is eliminated by only using rotation invariant features, thus loop closure can be detected from an arbitrary direction. The classifier is evaluated using publicly available data, and is shown to generalize well between environments. Detection rates of 66%, 63% and 53% for 0% false alarm rate are achieved for 2D outdoor data, 3D outdoor data and 3D indoor data, respectively. In both two and three dimensions, experiments are performed using publicly available data, showing that the proposed algorithm compares favourably with related work.