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The paper considers the problem of shape-based recognition and pose estimation of 3D free-form objects in scenes that contain occlusion and clutter. Our approach is based on a novel set of discriminating descriptors called spherical spin images, which encode the shape information conveyed by classes of distributions of surface points constructed with respect to reference points on the surface of an object. The key to this approach is the relationship that exists between the l2 metric, which compares n-dimensional signatures in Euclidean space, and the metric of the compact space on which the class representatives (spherical spin images) are defined. The connection allows us to efficiently utilize the linear correlation coefficient to discriminate scene points which have spherical spin images that are similar to the spherical spin images of points on the object being sought. The paper also addresses the problem of compressed spherical-spin-image representation by means of a random projection of the original descriptors that reduces the dimensionality without a significant loss of recognition/localization performance. Finally, the efficacy of the proposed representation is validated in a comparative study of the two algorithms presented that use uncompressed and compressed spherical spin images versus two previous spin image algorithms reported previously (A.E. Johnson and M. Hebert, 1999). The results of 2012 experiments suggest that the performance of our proposed algorithms is significantly better with respect to accuracy and speed than the performance of the other algorithms tested.