Abstract:Abstract-This paper introduces a reasoning system based on a previously developed model for ternary projective relations between spatial objects. The model applies to spatial objects of the kind point and region, is based on basic projective invariants and takes into account the size and shape of the three objects that are involved in a relation. The reasoning system proposes a set of permutation and composition rules, which allow the inference of unknown relations from given ones.
I. INTRODUCTIONThe field of … Show more
“…This model gives a classification of projective relations between three geometric objects in the plane, distinguishing 34 relations that form a JEPD set ( jointly-exhaustive and pair-wise disjoint). The latter property is essential for developing reasoning systems of relations [6,28]. As far as metric relations are concerned, such as the distance between two points, they are normally meant as quantitative relations, but there are qualitative approaches to describe distances that could be further investigated [26].…”
Section: Geometric Space Propertiesmentioning
confidence: 99%
“…The results on reasoning mechanisms with ternary relations, such as composition tables [46], have yet to be developed. Qualitative spatial reasoning on ternary relations is a topic of active research [6,28,66]. More rarely, in the literature, quaternary relations are envisaged: for example, in order to illustrate the notion of surrounding [59].…”
Various approaches lie behind the modelling of spatial relations, which is a heterogeneous and interdisciplinary field. In this paper, we introduce a conceptual framework to describe the characteristics of various models and how they relate each other. A first categorization is made among three representation levels: geometric, computational, and user. At the geometric level, spatial objects can be seen as point-sets and relations can be formally defined at the mathematical level. At the computational level, objects are represented as data types and relations are computed via spatial operators. At the user level, objects and relations belong to a context-dependent user ontology. Another way of providing a categorization is following the underlying geometric space that describes the relations: we distinguish among topologic, projective, and metric relations. Then, we consider the cardinality of spatial relations, which is defined as the number of objects that participate in the relation. Another issue is the granularity at which the relation is described, ranging from general descriptions to very detailed ones. We also consider the dimension of the various geometric objects and the embedding space as a fundamental way of categorizing relations.
“…This model gives a classification of projective relations between three geometric objects in the plane, distinguishing 34 relations that form a JEPD set ( jointly-exhaustive and pair-wise disjoint). The latter property is essential for developing reasoning systems of relations [6,28]. As far as metric relations are concerned, such as the distance between two points, they are normally meant as quantitative relations, but there are qualitative approaches to describe distances that could be further investigated [26].…”
Section: Geometric Space Propertiesmentioning
confidence: 99%
“…The results on reasoning mechanisms with ternary relations, such as composition tables [46], have yet to be developed. Qualitative spatial reasoning on ternary relations is a topic of active research [6,28,66]. More rarely, in the literature, quaternary relations are envisaged: for example, in order to illustrate the notion of surrounding [59].…”
Various approaches lie behind the modelling of spatial relations, which is a heterogeneous and interdisciplinary field. In this paper, we introduce a conceptual framework to describe the characteristics of various models and how they relate each other. A first categorization is made among three representation levels: geometric, computational, and user. At the geometric level, spatial objects can be seen as point-sets and relations can be formally defined at the mathematical level. At the computational level, objects are represented as data types and relations are computed via spatial operators. At the user level, objects and relations belong to a context-dependent user ontology. Another way of providing a categorization is following the underlying geometric space that describes the relations: we distinguish among topologic, projective, and metric relations. Then, we consider the cardinality of spatial relations, which is defined as the number of objects that participate in the relation. Another issue is the granularity at which the relation is described, ranging from general descriptions to very detailed ones. We also consider the dimension of the various geometric objects and the embedding space as a fundamental way of categorizing relations.
“…The qualitative spatial aspect refers to changes in the qualitative spatial relations holding between a feature and its neighbors. According to Clementini (2013), qualitative spatial relations belong to one of three classes: topological (Egenhofer 1989;Randell and Cohn 1989;Tarquini and Clementini 2008), projective (Clementini et al 2010;Tarquini et al 2007;Fogliaroni and Clementini 2015;Billen and Clementini 2006, 2005b, 2005a, and metric (Hernández, Clementini, and Di Felice 1995;Moratz and Ragni 2008).…”
Volunteered geographic information (VGI) has entered a phase where there are both a substantial amount of crowdsourced information available and a big interest in using it by organizations. But the issue of deciding the quality of VGI without resorting to a comparison with authoritative data remains an open challenge. This article first formulates the problem of quality assessment of VGI data. Then presents a model to measure trustworthiness of information and reputation of contributors by analyzing geometric, qualitative, and semantic aspects of edits over time. An implementation of the model is running on a small data-set for a preliminary empirical validation. The results indicate that the computed trustworthiness provides a valid approximation of VGI quality.
ARTICLE HISTORY
“…Its extension to a spherical surface is addressed in (Clementini, 2008). The converse, rotation and composition rules are discussed in (Clementini et al, 2010).…”
Section: Directionmentioning
confidence: 99%
“…The converse, rotation and composition rules are discussed in Clementini et al . (2010). Figure 16A pictorial example of five separate zones in ternary projective relations, where a is on the left side and after b and c , denoted by ls:af ( a , b , c ) (Clementini & Billen, 2006: 805)…”
Section: Aspects Of Qualitative Spatial Relationsmentioning
Representation and reasoning with qualitative spatial relations is an important problem in artificial intelligence and has wide applications in the fields of geographic information system, computer vision, autonomous robot navigation, natural language understanding, and spatial databases etc. The reasons for this interest in using qualitative spatial relations include cognitive comprehensibility, efficiency and computational facility. This paper summarizes progress in qualitative spatial representation by describing key calculi representing different types of spatial relationships. The paper concludes with a discussion of current research and glimpse of future work.
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