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We introduce 4PCS, a fast and robust alignment scheme for 3D point sets that uses wide bases, which are known to be resilient to noise and outliers. The algorithm allows registering raw noisy data, possibly contaminated with outliers, without pre-filtering or denoising the data. Further, the method significantly reduces the number of trials required to establish a reliable registration between the underlying surfaces in the presence of noise, without any assumptions about starting alignment. Our method is based on a novel technique to extract all coplanar 4-points sets from a 3D point set that are approximately congruent, under rigid transformation, to a given set of coplanar 4-points. This extraction procedure runs in roughly O(n² + k) time, where n is the number of candidate points and k is the number of reported 4-points sets. In practice, when noise level is low and there is sufficient overlap, using local descriptors the …