scholarly journals Deriving topological relations from topologically augmented direction relation matrices

2021 ◽  
pp. 1-23
Author(s):  
Matthew P. Dube
Keyword(s):  
Spatial Reasoning ◽  
Qualitative Spatial Reasoning ◽  
Topological Relations ◽  
Topological Relation ◽  
Direction Relations ◽  
Relation Matrix

Topological relations and direction relations represent two pieces of the qualitative spatial reasoning triumvirate. Researchers have previously attempted to use the direction relation matrix to derive a topological relation, finding that no single direction relation matrix can isolate a particular topological relation. In this paper, the technique of topological augmentation is applied to the same problem, identifying a unique topological relation in 28.6% of all topologically augmented direction relation matrices, and furthermore achieving a reduction in a further 40.4% of topologically augmented direction relation matrices when compared to their vanilla direction relation matrix counterpart.

scholarly journals Qualitative Spatial Reasoning with Directional and Topological Relations

2015 ◽  
Vol 2015 ◽  
pp. 1-10 ◽  
Author(s):  
Sangha Nam ◽  
Incheol Kim
Keyword(s):  
Intelligent Systems ◽  
Spatial Reasoning ◽  
Cognitive Robotics ◽  
Qualitative Spatial Reasoning ◽  
Topological Relations ◽  
Topological Relation ◽  
Wide Range ◽  
Spatial Entities ◽  
Reasoning Algorithm ◽  
Ubiquitous Computing Environments

A wide range of application domains from cognitive robotics to intelligent systems encompassing diverse paradigms such as ambient intelligence and ubiquitous computing environments require the ability to represent and reason about the spatial aspects of the environment within which an agent or a system is functional. Many existing spatial reasoners share a common limitation that they do not provide any checking functions for cross-consistency between the directional and the topological relation set. They provide only the checking function for path-consistency within a directional or topological relation set. This paper presents an efficient spatial reasoning algorithm working on a mixture of directional and topological relations between spatial entities and then explains the implementation of a spatial reasoner based on the proposed algorithm. Our algorithm not only has the checking function for path-consistency within each directional or topological relation set, but also provides the checking function for cross-consistency between them. This paper also presents an application system developed to demonstrate the applicability of the spatial reasoner and then introduces the results of the experiment carried out to evaluate the performance of our spatial reasoner.

scholarly journals An approach to computing direction relations between separated object groups

2013 ◽  
Vol 6 (2) ◽  
pp. 3179-3210
Author(s):  
H. Yan ◽  
Z. Wang ◽  
J. Li
Keyword(s):  
Spatial Cognition ◽  
Spatial Reasoning ◽  
Point Of View ◽  
Qualitative Spatial Reasoning ◽  
Gestalt Principles ◽  
Quantitative Expression ◽  
Direction Relations ◽  
Triangular Network ◽  
Psychological Experiments ◽  
Spatial Recognition

Abstract. Direction relations between object groups play an important role in qualitative spatial reasoning, spatial computation and spatial recognition. However, none of existing models can be used to compute direction relations between object groups. To fill this gap, an approach to computing direction relations between separated object groups is proposed in this paper, which is theoretically based on Gestalt principles and the idea of multi-directions. The approach firstly triangulates the two object groups; and then it constructs the Voronoi Diagram between the two groups using the triangular network; after this, the normal of each Vornoi edge is calculated, and the quantitative expression of the direction relations is constructed; finally, the quantitative direction relations are transformed into qualitative ones. The psychological experiments show that the proposed approach can obtain direction relations both between two single objects and between two object groups, and the results are correct from the point of view of spatial cognition.

scholarly journals Reasoning about Topological and Cardinal Direction Relations Between 2-Dimensional Spatial Objects

2014 ◽  
Vol 51 ◽  
pp. 493-532 ◽  
Author(s):  
A. G. Cohn ◽  
S. Li ◽  
W. Liu ◽  
J. Renz
Keyword(s):  
Spatial Reasoning ◽  
Spatial Information ◽  
Qualitative Spatial Reasoning ◽  
Topological Information ◽  
Directional Information ◽  
Spatial Objects ◽  
Cardinal Direction ◽  
Direction Relations ◽  
Consistency Problem ◽  
Cardinal Direction Relations

Increasing the expressiveness of qualitative spatial calculi is an essential step towards meeting the requirements of applications. This can be achieved by combining existing calculi in a way that we can express spatial information using relations from multiple calculi. The great challenge is to develop reasoning algorithms that are correct and complete when reasoning over the combined information. Previous work has mainly studied cases where the interaction between the combined calculi was small, or where one of the two calculi was very simple. In this paper we tackle the important combination of topological and directional information for extended spatial objects. We combine some of the best known calculi in qualitative spatial reasoning, the RCC8 algebra for representing topological information, and the Rectangle Algebra (RA) and the Cardinal Direction Calculus (CDC) for directional information. We consider two different interpretations of the RCC8 algebra, one uses a weak connectedness relation, the other uses a strong connectedness relation. In both interpretations, we show that reasoning with topological and directional information is decidable and remains in NP. Our computational complexity results unveil the significant differences between RA and CDC, and that between weak and strong RCC8 models. Take the combination of basic RCC8 and basic CDC constraints as an example: we show that the consistency problem is in P only when we use the strong RCC8 algebra and explicitly know the corresponding basic RA constraints.

scholarly journals An approach to computing direction relations between separated object groups

2013 ◽  
Vol 6 (5) ◽  
pp. 1591-1599 ◽  
Author(s):  
H. Yan ◽  
Z. Wang ◽  
J. Li
Keyword(s):  
Spatial Cognition ◽  
Spatial Reasoning ◽  
Point Of View ◽  
Qualitative Spatial Reasoning ◽  
Gestalt Principles ◽  
Quantitative Expression ◽  
Direction Relations ◽  
Triangular Network ◽  
Psychological Experiments ◽  
Spatial Recognition

Abstract. Direction relations between object groups play an important role in qualitative spatial reasoning, spatial computation and spatial recognition. However, none of existing models can be used to compute direction relations between object groups. To fill this gap, an approach to computing direction relations between separated object groups is proposed in this paper, which is theoretically based on gestalt principles and the idea of multi-directions. The approach firstly triangulates the two object groups, and then it constructs the Voronoi diagram between the two groups using the triangular network. After this, the normal of each Voronoi edge is calculated, and the quantitative expression of the direction relations is constructed. Finally, the quantitative direction relations are transformed into qualitative ones. The psychological experiments show that the proposed approach can obtain direction relations both between two single objects and between two object groups, and the results are correct from the point of view of spatial cognition.

Enriching the Qualitative Spatial Reasoning System RCC8

2012 ◽  
pp. 203-254
Author(s):  
Ahed Alboody ◽  
Florence Sedes ◽  
Jordi Inglada
Keyword(s):  
Spatial Reasoning ◽  
Qualitative Spatial Reasoning ◽  
Topological Relations ◽  
Reasoning System ◽  
Gis Applications ◽  
Level 1 ◽  
Level 2

In this context, the authors develop definitions for the generalization of these detailed topological relations at these two levels (Level-1 and Level-2). The chapter presents two tables of these four detailed relations. Finally, examples for GIS applications are provided to illustrate the determination of the detailed topological relations studied in this chapter.

scholarly journals Modeling Imprecise and Bipolar Algebraic and Topological Relations using Morphological Dilations

2021 ◽  
Vol 5 (1) ◽  
pp. 1-20
Author(s):  
Isabelle Bloch
Keyword(s):  
Information Processing ◽  
Fuzzy Sets ◽  
Mathematical Morphology ◽  
Complete Lattice ◽  
Spatial Reasoning ◽  
Topological Relations ◽  
Preference Modeling ◽  
Logical Sense ◽  
Bipolar Fuzzy Sets ◽  
Core Features

Abstract In many domains of information processing, such as knowledge representation, preference modeling, argumentation, multi-criteria decision analysis, spatial reasoning, both vagueness, or imprecision, and bipolarity, encompassing positive and negative parts of information, are core features of the information to be modeled and processed. This led to the development of the concept of bipolar fuzzy sets, and of associated models and tools, such as fusion and aggregation, similarity and distances, mathematical morphology. Here we propose to extend these tools by defining algebraic and topological relations between bipolar fuzzy sets, including intersection, inclusion, adjacency and RCC relations widely used in mereotopology, based on bipolar connectives (in a logical sense) and on mathematical morphology operators. These definitions are shown to have the desired properties and to be consistent with existing definitions on sets and fuzzy sets, while providing an additional bipolar feature. The proposed relations can be used for instance for preference modeling or spatial reasoning. They apply more generally to any type of functions taking values in a poset or a complete lattice, such as L-fuzzy sets.

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