Constraint relaxing on topological operators in pictorial queries with null answer

This paper proposes an approach for relaxing constraints of a pictorial query when the answer returns a null value. In particular this approach, similarl y with the 9-intersection matrix between two sets point, proposes to extend the representation of the symboli c graphical objects (SGO) in terms of interior, boundary, and complement points, applied to any configurati on of two SGO. The suggested method considers three matrices: the first for representing the points cardin ality of the intersection of interior, boundary and exterior of a polyline with the analogous three intersectio ns of a polygon, the second for representing the polylines cardinality of the same intersection sets and the third for representing the polygons cardinality of the same intersection sets. Moreover, in order to relax topo logical constraints of any configuration, conceptual neighbourhood graphs between topological operators valid for the different pairs of SGO are proposed, as well as the connected complex matrices which enlarge the above me ntioned 9-intersection matrix. A computational model for determining relations that are conceptually more similar for each configuration is also proposed and the polyline-polygon relation is studied.