A Voronoi-based 9-intersection model for spatial relations

The technological progress in the field of artificial intelligence (AI) has brought new opportunities and challenges to the intelligent development and innovative research in fuzzy spatial relations, fuzzy theory is the basic theory of intelligent information processing, and the paper gives a brief analysis of fuzzy calculation method in spatial analysis and spatial relation calculation. In particular, the spatial relations of fuzzy objects are more difficult to express and describe accurately. This paper proposes a method to calculate the topological relations between fuzzy objects with 4-Intersection model and 9-Intersection model, in the analysis of spatial relations, the extension from deterministic entity to uncertain entity is realized with fuzzy set theory, the fuzzy space matrix is constructed, then fuzzy topological relations and fuzzy membership are calculated and output, the model simplifies many complex relations, and it can describe eight topological relations including disjoint, meet, overlap, covers, contains, covered-by, inside and equal. In practical application, the position of spatial objects can be controlled and adjusted according to topological relations. Through analysis of algorithm and fuzzy membership calculation, the model is effective in theory.

While both linguistic semantics and geographic information science have struggled to accurately and usefully define the meanings of natural language prepositions, there has been less dialogue between these disciplines than one might expect. In this paper we set out to describe the meaning of the English preposition at using well-established formal models of qualitative spatial relations within geographic information science (GIScience), ultimately proposing an account for its meaning which is novel for both discipline areas, and we relate this description to previous definitions of at from within linguistic semantics. The investigation in this paper illustrates that at cannot be handled using the mathematical formalizations of crisp spatial relations in GIScience. However, the model proposed in this paper based on contrast sets, Voronoi Diagrams and Galton & Hood's (2005) Anchoring theory, contributes to a better understanding of the meaning of at. The model also enables improved automatic interpretations of the preposition by partitioning space into contrast sets and representing at as indicating that a spatial entity is more closely related to a reference object than to any other in the set. We show how the model can be framed within a formal semantics account and how it can in principle be extended to account for spatial uses of other prepositions as well. The paper demonstrates potential areas of fruitful cross-fertilisation between GIScience and linguistic semantics. EARLY ACCESS

In recent years, models of spatial relations, especially topological relations, have attracted much attention from the GIS community. In this paper, some basic topologic models for spatial entities in both vector and raster spaces are discussed. It has been suggested that, in vector space, an open set in 1-D space may not be an open set any more in 2-D and 3-D spaces. Similarly, an open set in 2-D vector space may also not be an open set any more in 3-D vector spaces. As a result, fundamental topological concepts such as boundary and interior are not valid any more when a lower dimensional spatial entity is embedded in higher dimensional space. For example, in 2-D, a line has no interior and the line itself (not its two end-points) forms a boundary. Failure to recognize this fundamental topological property will lead to topological paradox. It has also been stated that the topological models for raster entities are different in Z^{2} and R^{2}. There are different types of possible boundaries depending on the definition of adjacency or connectedness. If connectedness is not carefully defined, topological paradox may also occur. In raster space, the basic topological concept in vector space—connectedness—is implicitly inherited. This is why the topological properties of spatial entities can also be studied in raster space. Study of entities in raster (discrete) space could be a more efficient method than in vector space, as the expression of spatial entities in discrete space is more explicit than that in connected space.

Spatial Information Extraction from Short Messages

Directional relations, topological relations and metric relations are the basic spatial constraint in the geometric space. The three kinds of spatial relations are not isolated and restrict each other. In this paper, we focus on the effect of topology and distance on the representation of directional relations and present a description mechanism of directional relations considering topology and distance. In this new model, (1)topological constraint is analyzed as the basis of directional relations categories; (2)distance relations is the other factor of representation of directional relations and distinguish the directional relations of different positions in the same ray line; (3)depending on the analysis of the capability of exiting directional relations models to represent the restraint from the topological relations and distance, a category mechanism based on the topological relations and distance is proposed to improve the accuracy of the directional description. This model combines the restraint from topological and distance relations and consummates the representation of directional relations. Experiments show excellent efficiency in view of directional description.

9-intersection model is the most popular framework used for formalizing the spatial relations between two spatial objectsA andB. It transforms the topological relationships between two simple spatial objectsA andB into point-set topology problem in terms of the intersections ofA’s boundary (∂A), interior (A0) and (A−) withB’s boundary (∂B), interior (B0) and exterior (B−). It is shown in this paper that there exist some limitations of the original 9-intersection model due to its definition of an object’s exterior as its complement, and it is difficult to distinguish different disjoint relations and relations between complex objects with holes, difficult or even impossible to compute the intersections with the two object’s complements (∂A∩B−,A0∩∂B−,A−∩∂B,A−∩B0 andA−∩B−)since the complements are infinitive. The authors suggest to re-define the exterior of spatial object by replacing the complement with its Voronoi region. A new Voronoi-based 9-intersection (VNI) is proposed and used for formalizing topological relations between spatial bojects. By improving the 9-intersection model, it is now possible to distinguish disjoint relations and to deal with objects with holes. Also it is possible to compute the exterior-based intersections and manipulate spatial relations with the VNI.

Spatial modeling is one of the most important parts in the area of spatial relations, and it is necessary to develop a new model with high practicality. Firstly this paper analyzes the characteristics and defects of present models; secondly introduces in detail the construction method of quadtree histogram; thirdly cloud model are used to judge spatial directional relation. The experimental results show that the model is feasible. Computer vision is concerned with automatic extraction of useful information from images. The description for human space perception is an important task of the computer vision research. The description of spatial relation is a basic ability of human cognition, it is an important basic task for computer audio-visual information processing to build automatically the description of spatial relation between objects in the image. Spatial relation is mainly constituted of directional relation, topological relation and distance relation. The fundamental theories of topology relation and distance relation are comparatively perfect, but the fundamental theories of directional relation have not any unified standard. There are three main approaches for assessing the basic directional relation. The first one is based on cone model (1) which assimilates an object to the centroid, but it doesn't take into account shape, size and distance information. The second one is based on projection model such as minimum bounding rectangles (2), and directional relation matrix (3), etc., but these models assimilate an object to the minimum bounding rectangle, so shape, size and distance information also can't be taken into account. The third one is based on angle-histogram model (4). Given an object of target A and a reference object B, the angle-histogram is computed from the angles between any two points in both objects and normalized by the maximum frequency. This histogram represents the directional relations of the object A with respect to the reference object B. This model has taken into account shape, size and distance information. But this model has high computational complexity, so it is not practical. Numerous studies are based on this notion of angle-histogram, e.g., (5-8). In (5-7), R-histogram, R*-histogram and F-histogram are proposed, and they can reduce the computational complexity. In (8), a quadtree histogram model of spatial directional relation is proposed, and it can get high accuracy and small computational complexity together.

5 - Geographic Relations

The integration of the raster data cube alongside another form of geospatial data (e.g., vector data) raises considerable challenges when it comes to managing and representing it using knowledge graphs. Such integration can play an invaluable role in handling the heterogeneity of geospatial data and linking the raster data cube to semantic technology standards. Many recent approaches have been attempted to address this issue, but they often lack robust formal elaboration or solely concentrate on integrating raster data cubes without considering the inclusion of semantic spatial entities along with their spatial relationships. This may constitute a major shortcoming when it comes to performing advanced geospatial queries and semantically enriching geospatial models. In this paper, we propose a framework that can enable such semantic integration and advanced querying of raster data cubes based on the virtual knowledge graph (VKG) paradigm. This framework defines a semantic representation model for raster data cubes that extends the GeoSPARQL ontology. With such a model, we can combine the semantics of raster data cubes with features-based models that involve geometries as well as spatial and topological relationships. This could allow us to formulate spatiotemporal queries using SPARQL in a natural way by using ontological concepts at an appropriate level of abstraction. We propose an implementation of the proposed framework based on a VKG system architecture. In addition, we perform an experimental evaluation to compare our framework with other existing systems in terms of performance and scalability. Finally, we show the potential and the limitations of our implementation and we discuss several possible future works.

For qualitative spatial reasoning, there are various dimensions of objects. A considerable amount of effort has been devoted to 2D representation and analysis of spatial relations. Here we present an exposition for 3D objects. There are three types of binary relations between pairs of objects: topological connectivity, cardinal directions, and distance relations. The combinations of these relations can provide additional useful knowledge. The spatial databases include data and the spatial relations to facilitate end-user spatial querying, it also is important to associate natural language with these relations. Some work has been done in this regard for line-region and region-region topological relations in 2D, and very recent work has initiated the association between natural language, topology, and metrics for 3D objects. However, prior efforts have lacked rigorous analysis, expressive power, and completeness of the associated metrics. Herein we present a detailed study of new metrics required to bridge the gap between topological connectivity and size information for integrating reasoning in spatial databases. The complete set of metrics that we present should be useful for a variety of applications dealing with 3D objects including regions with vague boundaries.

Human-subjects testing based on a sound formal model is outlined as an effective way to evaluate and refine computational models of spatial relations. The cognitive response of a subject (person) to a real-world situation depends on the characteristic of the situation and the characteristics of the subject. Spatial entities can be characterized by topological relations, metric, scale (scope), kinds of phenomena (semantics), motion (time), and (for maps and displays) graphic presentation. Subjects' responses may vary according to their natural languages, their cultures, and individual characteristics such as gender, age, and handedness. Given this conceptual background, seven human-subjects testing protocols are introduced. Each test is described, and results of applications of these tests are summarized where possible. The tests are compared with their requirements, and the different aspects of human spatial cognition that they might test. Lastly, a program for applying these tests and refining the formal models based on test results is presented.

In order to better meet the needs of stomatology teaching demonstration, the paper conducts a research on the modified bionic design of the traditional dental articulator. Topology is introduced into the morphological bionic design for quantitative analysis. Starting from shape, the common point of topology and bionic design, to analyze the topological structure of human craniofacial bone based on the existing structure of dental articulator. This paper simply divides the complex topological relationships into five topological relationships (separation, adjacency, intersection, containment, and equality) based on the 9IM model, and set topological weight for these five representative topological relationships. Topological weight can be used to quantify the relationship between spatial entities and extract important features. The stability of topological properties in morphological cognition and extraction is used to better rationally restrict the bionic design process, finally establish a preliminary bionic morphological model.

Topological relation is invariant under continuous transformations of space, which incarnates the global characteristics of entity. The topological relation is an important spatial relationship in GIS. The three-dimensional space can be described with the simplex model, and a complex entity can be divided into simplexes whose dimensions are equal to or less than the dimension of entity in GIS. The topological relations among 0-simplix (point), 1-simplex (line), 2-simplex (triangle), and 3-simplex (tetrahedron) in the three-dimensional GIS are described with the 9-intersition matrix model. Topological relations that the 9-intersection matrix can classify are 11 topological relations between lines, 13 topological relations between line and triangle, 11 topological relations between line and tetrahedron, 18 topological relations between triangles, 9 topological relations between triangle and tetrahedron, and 8 topological relations between tetrahedron. Base on the set theory, the qualitative reasoning of topological relation is studied, whose results are listed in the composition table.

Chapter 13 Qualitative Spatial Representation and Reasoning

The relationship between sense of place, social capital and civic engagement has been studied in different disciplines. However, their association has been less examined, and their spatial relationship has been analyzed even less. This study contributes to a better understanding of the relationship between these three concepts (i.e., sense of place, social capital and civic engagement). Furthermore, we analyze the crucial role that the spatial relationship between them plays. Using spatial data collected through a web map-based application, we adopt structural equation modeling (SEM) techniques to assess the repercussion that sense of place has on social capital and how the latter affects civic engagement. We find that sense of place is significant and positively correlated with social capital, while the latter also significantly explains civic engagement at the individual level. Furthermore, we observe a better statistical performance in almost all cases when a spatial relationship between the three constructs exists. Our research leverages SEM techniques, Geographic Information Science (GISc) methods, and participatory methodology to show the spatial connection between sense of place and social capital to explain civic engagement. Deriving and quantifying such meaning allows us to highlight the importance of their spatial dimension in city processes such as participation.