A statistical representation of three-dimensional shapes is introduced, based on a novel four-dimensional feature. The feature parameterizes the intrinsic geometrical relation of an oriented surface-point pair. The set of all such features represents both local and global characteristics of the surface. We compress this set into a histogram. A database of histograms, one per object, is sampled in a training phase. During recognition, sensed surface data, as may be acquired by stereo vision, a laser range-scanner, etc., are processed and compared to the stored histograms. We evaluate the match quality by six different criteria that are commonly used in statistical settings. Experiments with artificial data containing varying levels of noise and occlusion of the objects show that Kullback-Leibler and likelihood matching yield robust recognition rates. The present study proposes histograms of the geometric relation between two oriented surface points (surflets) as a compact yet distinctive representation of arbitrary three-dimensional shapes.