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The iterative closest point (ICP) algorithm is a widely used method for aligning three-dimensional point sets. The quality of alignment obtained by this algorithm depends heavily on choosing good pairs of corresponding points in the two datasets. If too many points are chosen from featureless regions of the data, the algorithm converges slowly, finds the wrong pose, or even diverges, especially in the presence of noise or miscalibration in the input data. We describe a method for detecting uncertainty in pose, and we propose a point selection strategy for ICP that minimizes this uncertainty by choosing samples that constrain potentially unstable transformations.