Although Point Clouds Registration is a very well studied problem, with many different solutions, most of the approaches in the literature aims at aligning two dense point clouds. Instead, we tackle the problem of aligning a dense point cloud with a sparse one: a problem that has to be solved, for example, to merge maps produced by different sensors, such as a vision-based sensor and laser scanner or two different laser-based sensors. The most used approach to point clouds registration, Iterative Closest Point (ICP), is also applicable to this sub-problem. We propose an improvement over the standard ICP data association policy and we called it Probabilistic Data Association. It was derived applying statistical inference techniques on a fully probabilistic model. In our proposal, each point in the source point cloud is associated with a set of points in the target point cloud; each association is then weighted so that the weights form a probability distribution. The result is an algorithm similar to ICP but more robust w.r.t. noise and outliers. While we designed our approach to deal with the problem of dense-sparse registration, it can be successfully applied also to standard point clouds registration.

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