Towards Applying the OPRA Theory to Shape Similarity

Qualitative spatial reasoning (QSR) abstracts metrical details of the physical world and enables computers to make predictions about spatial relations even when precise quantitative information is unavailable [2]. From a practical viewpoint QSR is an abstraction that summarizes similar quantitative states into one qualitative characterization. A complementary view from the cognitive perspective is that the qualitative method compares features within the object domain rather than by measuring them in terms of some artificial external scale [6]. As a result, qualitative descriptions are quite natural for humans. For instance, when contemplating the distance to two different destinations, the relative notion “A is closer than B” is typically more natural than the quantitative alternative, “A is 160 meters away, and B is 200 meters away.” Similarly with direction, one may more naturally think of things as “to the left” or “to the right” instead of in terms of compass bearings or degrees of rotation. The two main directions in QSR are topological reasoning about regions [14, 15, 18] and positional reasoning about point configurations, like reasoning about orientation and distance [1, 6, 8, 11, 19]. More information on the historical evolution of QSR calculi is presented by Moratz in a chapter about Qualitative Spatial Reasoning in the Encyclopedia of GIS [10]. Additionally, see [3] for an in-depth discussion of the various aspects and approaches in QSR. There is also considerable work about using positional reasoning to describe the qualitative shape of 2D regions [9, 16, 17]. Many of these approaches represent qualitative shape by listing the relative positions of the adjacent vertices of polygons enumerating the outline of the polygon [7]. However, these previous approaches make limited use of concepts relating