Indexing Planar Point Quartets Via Geometric Attributes

An index is devised to support position-independent search for images containing quartets of icons. Point quartets exist that do not unambiguously map to quadrilaterals, however, four points do unambiguously determine a set of six interpoint line segments. Values for the “size”, “shape”, and “orientation ” attributes of an icon quartet can be derived as functions of this interpoint line set, and can be used to construct a point-based index, in which each point quartet maps to a single point in the resulting hyperdimensional index space. Orientation can be represented by a single, spatially closed dimension. However, assignment of a reference direction for quartets possessing a k-fold rotational symmetry presents a significant challenge. Methods are described for determining shape and orientation attributes for point quartets, and for mapping these attributes onto a set of attribute axes to form a combined index. The orientation computation supplies, as a byproduct, one component of the shape attribute. All attributes are continuous with respect to small variations in the indexed point quartets. 1