We introduce a novel rich local descriptor of an image point, we call the (labeled) distance set, which is determined by the spatial arrangement of image features around that point. We describe a two-dimensional (2D) visual object by the set of (labeled) distance sets associated with the feature points of that object. Based on a dissimilarity measure between (labeled) distance sets and a dissimilarity measure between sets of (labeled) distance sets, we address two problems that are often encountered in object recognition: object segmentation, for which we formulate a distance sets shape filter, and shape matching. The use of the shape filter is illustrated on printed and handwritten character recognition and detection of traffic signs in complex scenes. The shape comparison procedure is illustrated on handwritten character classification, COIL-20 database object recognition and MPEG-7 silhouette database retrieval.