$$\mathcal {ALC({\mathbf {F}}})$$ : 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 ALC(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.

Fuzzy sets for image processing and understanding

“…Merging temporal and spatial information is also an important direction to pursue, for applications such as video analysis, change detection, etc. Several frameworks could be involved, such as modal logics [24], description logics [10,64,87], formal concept analysis [4,9,10], etc. Conversely, results obtained from images could be further exploited to provide a linguistic description of the observed scene, e.g.…”

Automatic Structuring of Photographic Collections for Spatio-Temporal Monitoring of Restoration Sites: Problem Statement and Challenges

“…Among topical applications of automatic analysis of an image visual content, we can mention the problem of visual-based localization whose objective is to geolocalize the content (or the camera), which is usually processed in an unsupervised way with content-based image retrieval tools (Pion et al, 2020) (Blettery et al, 2021). Other techniques include spatial reasoning based on computer vision and description logic (Hudelot et al, 2014).…”