We present a probabilistic framework for matching of point clouds. Variants of the ICP algorithm typically pair points to points or points to lines. Instead, we pair data points to probability functions that are thought of having generated the data points. Then an energy function is derived from a maximum likelihood formulation. Each such distribution is a mixture of a bivariate Normal Distribution to capture the local structure of points and an explicit outlier term to achieve robustness. We apply our approach to the SLAM problem in robotics using a 2D laser range scanner.