Integrating existing cone-shaped and projection-based cardinal direction relations and a TCSP-like decidable generalisation

Integrating different knowledge representation languages is clearly an important topic. This allows, for instance, for a unified representation of knowledge coming from different sources, each source using one of the integrated languages for its knowledge representation. This is of special importance for QSR languages, for such a language makes only a finite number of distinctions: integrating QSR languages may be looked at as an answer to the well-known poverty conjecture. With these considerations in mind, we consider the integration of Frank’s cone-shaped and projection-based calculi of cardinal direction relations, well-known in QSR. The more general, integrating language we consider is based on convex constraints of the qualitative form r(x, y), r being a coneshaped or projection-based cardinal direction atomic relation, or of the quantitative form (α, β)(x, y), with α, β ∈ [0, 2π) and (β − α) ∈ [0, π]: the meaning of the quantitative constraint, in particular, is that point x belongs to the (convex) cone-shaped area rooted at y, and bounded by angles α and β. The general form of a constraint is a disjunction of the form [r1 ∨ · · · ∨ rn1 ∨ (α1, β1) ∨ · · · ∨ (αn2 , βn2)](x, y), with ri(x, y), i = 1 . . . n1, and (αi, βi)(x, y), i = 1 . . . n2, being convex constraints as described above: the meaning of such a general constraint is that, for some i = 1 . . . n1, ri(x, y) holds, or, for some i = 1 . . . n2, (αi, βi)(x, y) ⋆ TCSPs stands for Temporal Constraint Satisfaction Problems, a well-known constraint-based temporal framework [8]. ⋆⋆ This work was supported partly by the EU project “Cognitive Vision systems” (CogVis), under grant CogVis IST 2000-29375. 1 Qualitative Spatial Reasoning. holds. A conjunction of such general constraints is a TCSP-like CSP, which we will refer to as an SCSP (Spatial Constraint Satisfaction Problem). An effective solution search algorithm for an SCSP will be described, which uses (1) constraint propagation, based on a composition operation to be defined, as the filtering method during the search, and (2) the Simplex algorithm, guaranteeing completeness, at the leaves of the search tree. The approach is particularly suited for large-scale high-level vision, such as, e.g., satellite-like surveillance of a geographic area.