Topological relationships between a circular spatially extended point and a line : spatial relations and their conceptual neighborhoods

This paper presents the topological spatial relations that can exist in the geographical space between a Circular Spatially Extended Point and a Line and describes the use of those spatial relations in the identification of the conceptual neighbourhood graphs that state the transitions occurring among relations. The conceptual neighbourhood graphs were identified using the snapshot model and the smooth-transition model. In the snapshot model, the identification of neighbourhood relations is achieved looking at the topological distance existing between pairs of spatial relations. In the smooth-transition model, conceptual neighbours are identified analysing the topological deformations that may change a topological spatial relation. The graphs obtained were analysed as an alternative to map matching techniques in the prediction of the future positions of a mobile user in a road network.(undefined

Stability and statistical inferences in the space of topological spatial relationships

Modelling topological properties of the spatial relationship between objects, known as the extit{topological relationship}, represents a fundamental research problem in many domains including Artificial Intelligence (AI) and Geographical Information Science (GIS). Real world data is generally finite and exhibits uncertainty. Therefore, when attempting to model topological relationships from such data it is useful to do so in a manner which is both extit{stable} and facilitates extit{statistical inferences}. Current models of the topological relationships do not exhibit either of these properties. We propose a novel model of topological relationships between objects in the Euclidean plane which encodes topological information regarding connected components and holes. Specifically, a representation of the persistent homology, known as a persistence scale space, is used. This representation forms a Banach space that is stable and, as a consequence of the fact that it obeys the strong law of large numbers and the central limit theorem, facilitates statistical inferences. The utility of this model is demonstrated through a number of experiments

Topological augmentation: A step forward for qualitative partition reasoning

The current state of the art for partition based qualitative spatial reasoning systems such as the 9-intersection, 9+-intersection, direction relation matrix, and peripheral direction relations is that of the binary set intersection — either empty or non-empty — conveying the intersection (or lack thereof) of an object in the sets deriving the partition. While such representations are sufficient for topological components of objects, these representations are not sufficient for various tasks in qualitative spatial reasoning (composition, representation transfer, converse, etc.) regarding partitions as tiles. Topological augmentation expands the current binary status quo into a system of assigning topological relations between objects and tiles. A case study is presented in the form of the direction relation matrix, demonstrating that an increased vocabulary has benefits for spatial information systems, providing localized context within a qualitative embedding

Modeling fuzzy topological predicates for fuzzy regions

Spatial database systems and Geographical Information Systems (GIS) are currently only able to handle crisp spatial objects, i.e., objects whose extent, shape, and boundary are precisely determined. However, GIS applications are also interested in managing vague or fuzzy spatial objects. Spatial fuzziness captures the inherent property of many spatial objects in reality that do not have sharp boundaries and interiors or whose boundaries and interiors cannot be precisely determined. While topological relationships have been broadly explored for crisp spatial objects, this is not the case for fuzzy spatial objects. In this paper, we propose a novel model to formally define fuzzy topological predicates for simple and complex fuzzy regions. The model encompasses six fuzzy predicates (overlap, disjoint, inside, contains, equal and meet), wherein here we focus on the fuzzy overlap and the fuzzy disjoint predicates only. For their computation we consider two low-level measures, the degree of membership and the degree of coverage, and map them to high-level fuzzy modifiers and linguistic values respectively that are\ud deployed in spatial queries by end-users.FAPESP (grant numbers 2012/12299-8 and 2013/19633-3)CAPESCNPqNational Science Foundation (grant number NSF-IIS-0915914

Region Extraction and Verification for Spatial and Spatio-temporal Databases

Abstract. Newer spatial technologies, such as spatio-temporal databases, geo-sensor networks, and other remote sensing methods, require mecha-nisms to efficiently process spatial data and identify (and in some cases fix) data items that do not conform to rigorously defined spatial data type definitions. In this paper, we propose an O(n lg n) time complexity algorithm that examines a spatial configuration, eliminates any portions of the configuration that violate the definition of spatial regions, and constructs a valid region out of the remaining configuration.

Discovery of topological constraints on spatial object classes using a refined topological model

In a typical data collection process, a surveyed spatial object is annotated upon creation, and is classified based on its attributes. This annotation can also be guided by textual definitions of objects. However, interpretations of such definitions may differ among people, and thus result in subjective and inconsistent classification of objects. This problem becomes even more pronounced if the cultural and linguistic differences are considered. As a solution, this paper investigates the role of topology as the defining characteristic of a class of spatial objects. We propose a data mining approach based on frequent itemset mining to learn patterns in topological relations between objects of a given class and other spatial objects. In order to capture topological relations between more than two (linear) objects, this paper further proposes a refinement of the 9-intersection model for topological relations of line geometries. The discovered topological relations form topological constraints of an object class that can be used for spatial object classification. A case study has been carried out on bridges in the OpenStreetMap dataset for the state of Victoria, Australia. The results show that the proposed approach can successfully learn topological constraints for the class bridge, and that the proposed refined topological model for line geometries outperforms the 9-intersection model in this task

A survey of qualitative spatial representations

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, spatial databases and so on. 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

Embedding vague spatial objects into spatial databases using the VagueGeometry abstract data type

Spatial vagueness has been required by geoscientists to handle vague spatial objects, i.e., spatial objects that do not have exact locations, strict boundaries, or sharp interiors. However, there is a gap in the literature in how to handle these objects in spatial database management systems since they mainly provide support to crisp spatial objects, i.e., objects that have well-defined locations, boundaries, and interiors. In this paper, we fill this gap by proposing VagueGeometry, a novel abstract data type that handles vague spatial objects, includes an expressive set of vague spatial operations, and its implementation is open source. Experimental results show that VagueGeometry improved the performance of spatial queries with vague topological predicates from 23% up to 84% if compared with functionalities available in current spatial databases.FAPESPCAPESCNP

An abstract data type to handle vague spatial objects based on the fuzzy model

Crisp spatial data are geometric features with exact location on the extent and well-known boundaries. On the other hand, vague spatial data are characterized by inaccurate locations or uncertain boundaries. Despite the importance of vague spatial data in spatial applications, few related work indeed implement vague spatial data and they do not define abstract data types to enable the management of vague spatial data by using database management systems. In this sense, we propose the abstract data type FuzzyGeometry to handle vague spatial data based on the fuzzy model. FuzzyGeometry was developed as a PostgreSQL extension and its implementation is open source. It offers management for fuzzy points and fuzzy lines. As a result, spatial applications are able to access the PostgreSQL to handle vague spatial objects.FAPESPCAPESCNP

Extension of RCC*-9 to Complex and Three-Dimensional Features and Its Reasoning System

RCC*-9 is a mereotopological qualitative spatial calculus for simple lines and regions. RCC*-9 can be easily expressed in other existing models for topological relations and thus can be viewed as a candidate for being a “bridge” model among various approaches. In this paper, we present a revised and extended version of RCC*-9, which can handle non-simple geometric features, such as multipolygons, multipolylines, and multipoints, and 3D features, such as polyhedrons and lower-dimensional features embedded in ℝ3. We also run experiments to compute RCC*-9 relations among very large random datasets of spatial features to demonstrate the JEPD properties of the calculus and also to compute the composition tables for spatial reasoning with the calculus