Qualitative Outline Theory

A theory of shape is important for AI both for recognition and description of objects and for reasoning about the possible behaviours of objects. Theories of shape may be loosely classified as either volume-based or outline-based. We present a theory of the latter type, initially confined to two-dimensional outlines. We represent outlines by means of strings over an alphabet of seven qualitative curvature types, and give a regular grammar which generates the strings corresponding to possible outlines. We use subsets of the curvature-type alphabet to characterise cognitively salient subclasses of outlines, with corresponding regular subgrammars, and use decusping, smoothing, and merging operators to simplify outlines for representation at coarser granularity. We give an algorithm for deriving the curvature sequence of an outline, using only local information obtained as the outline is traversed. Finally, we indicate how more detailed (including quantitative) information can be incorporated into the theory.