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This paper addresses the problem of generic object classification from three-dimensional depth or meshed data. First, surface patches are segmented on the basis of differential geometry and quadratic surface fitting. These are represented by a modified Gaussian image that includes the well-known shape index. Learning is an interactive process in which a human teacher indicates corresponding patches, but the formation of generic classes is unaided. Classification of unknown objects is based on the measurement of similarities between feature sets of the objects and the generic classes. The process is demonstrated on a group of three-dimensional (3-D) objects built from both CAD and laser-scanned depth data.