$$\mathcal {ALC({\mathbf {F}}})$$ : A New Description Logic for Spatial Reasoning in Images

Abstract

In image interpretation and computer vision, spatial relations between objects and spatial reasoning are of prime importance for recognition and interpretation tasks. Quantitative representations of spatial knowledge have been proposed in the literature. In the Artificial Intelligence community, logical formalisms such as ontologies have also been proposed for spatial knowledge representation and reasoning, and a challenging and open problem consists in bridging the gap between these ontological representations and the quantitative ones used in image interpretation. In this paper, we propose a new description logic, named $$\mathcal {ALC({\mathbf {F}})}$$ , dedicated to spatial reasoning for image understanding. Our logic relies on the family of description logics equipped with concrete domains, a widely accepted way to integrate quantitative and qualitative qualities of real world objects in the conceptual domain, in which we have integrated mathematical morphological operators as predicates. Merging description logics with mathematical morphology enables us to provide new mechanisms to derive useful concrete representations of spatial concepts and new qualitative and quantitative spatial reasoning tools. It also enables imprecision and uncertainty of spatial knowledge to be taken into account through the fuzzy representation of spatial relations. We illustrate the benefits of our formalism on a model-guided cerebral image interpretation task.