Topological relationship is the most important spatial relationship at the semantic level. There are two basic methods to study topological reasoning: RCC method based on region connection and "N-intersection" model based on point set. The key problem of GIS spatial reasoning is how to use the basic data information stored in the database and combine the relevant spatial constraints to obtain the required unknown spatial information. The reasoning of topological relations is the basis of spatial reasoning, query and analysis of GIS, which directly affects the development and application of GIS. It is the development trend of spatial topological reasoning to combine human cognitive model with topological relations such as space-time, fuzziness and hierarchy, so that the description of the model is more in line with people's expression and cognition of topological information, and it will become networked and popular.
Abstract: Topology is one of the most important spatial relationships at the semantic level. There are two basic methods of topological reasoning: RCC method based on region and N-intersection model based on point. One of the key problems of GIS spatial reasoning is how to use the basic data and related spatial constraint information in the database to obtain the required spatial information. In addition, topological reasoning is the basis of g is spatial reasoning, query and analysis, which directly affects the development and application of GIS. Combining spatial reasoning with spatial reasoning methods such as spatio-temporal, fuzzy and hierarchical topology of GIS makes the model easier to understand when expressing topological information and cognitive style. This is the trend of pushing topological reasoning to network and popularization.
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Key words: topological relation, spatial reasoning, spatial query, spatial analysis.
Introduction: In recent years, the spatial relationship theory has attracted extensive attention in the fields of geographic information system, intelligent navigation, robotics, computer vision, image understanding, image database and CAD/CAM. At present, the relevant research in the international geographic information science community mainly focuses on the semantic problems of spatial relations, the formal description of spatial relations, the query and analysis based on spatial relations, spatial reasoning and so on. Because topological relation is the most important spatial relation at the semantic level, most of the existing researches are aimed at topological relation.
The topological relationship between two spatial objects refers to the spatial relationship that remains unchanged under topological transformation (rotation, translation, scaling, etc.). ), that is, topological invariants, such as the adjacency and connectivity of spatial objects. Topological relations express the interrelationships between spatial data that satisfy the principles of topological geometry. That is, the adjacency, association, inclusion and connectivity between entities represented by nodes, arcs and polygons. Such as: the adjacency relationship between points, the inclusion relationship between points and faces, the separation relationship between lines and faces, and the coincidence relationship between faces. Topological relationship is the basis of spatial reasoning, query and analysis, and the progress of topological relationship research directly affects the application of GIS.
1. Description model of spatial topological relations
Spatial reasoning (mainly qualitative spatial reasoning) is used to study and analyze topological spatial relations, which is called topological reasoning for short. At present, there are two basic methods to study topological reasoning: RCC method based on regional connection and "N-intersection" model based on point set.
1. 1 RCC model
RCC model is an algebraic topological relation model proposed by Randell et al. It uses the theory of regional connectivity calculus (RCC) to express the topological characteristics and topological relations of spatial regions. The RCC model is based on the region in the point set topology, not the point. The region can have any dimension, but in a specific formal model, the dimensions of all regions are the same. For example, when considering the 2-dimensional case, the boundaries between regions and the intersections between regions will not be considered. The RCC model assumes that an original binary relation C(P, q) represents the connection between areas P and Q, and gives the topological explanation of relation C according to the points in the area. Using relation c, eight basic relations can be defined. If the boundary of the region is not considered, only five relationships can be distinguished, which are called RCC-8 and RCC-5 relationship sets respectively.
1.2 "n-crossing" model
From the perspective of mutually exclusive rows and completeness, with the deepening of people's understanding of the topological relationship of things, the descriptive model of topological relationship has also developed from the four-intersection model (4I model) to the nine-intersection model (9I model), and then to the nine-intersection model based on Voronoi diagram (V9I model). V9I model not only considers the interior and boundary of spatial entities, but also regards Voronoi region as a whole. Therefore, this model organically combines the advantages of intersection and interaction methods, and can overcome some shortcomings of the original 9-tuple model, including the difficulty of not distinguishing separation relations and calculating the complement of targets.
"N-crossing" model
In recent years, the regional topological relationship in grid space has also been studied. Such as Eigenhofer &; Referring to the construction method of 9- intersection model in vector space, Sharma proposed to define the target boundary based on the concept of 4- neighborhood (or 4- connectivity), thus establishing the topological relationship model between grid regions. Subsequently, Winter proposed an improved grid region topology definition method. This method uses the 9-intersection model in vector space to describe the topological relationship of grid areas, which can better distinguish the intersection relationship, connection relationship and separation relationship.
The nine-intersection model based on dimension expansion can well distinguish four situations in which two spatial objects intersect as empty, point, line and surface. However, in the current formal description methods of spatial topology, there are still some cases where the model description is wrong or can't be described, such as the description of the topological relationship of polygons with islands. One development direction of topological relationship description model is to combine the theoretical model research of people's spatial cognition, integrate different methods of spatial relationship description, further improve the theoretical model of spatial relationship, such as the criterion of directional relationship and the formal description of measurement relationship, and establish a unified spatial relationship description system that is more in line with human cognitive model, so as to make the relationship description between geospatial objects more accurate and comprehensive.
2. The application of topological relation reasoning in GIS.
Topological relationship is the basis of spatial reasoning, query and analysis of GIS, which directly affects the development and application of GIS. The following mainly discusses the application of topological relation theory in GIS from three aspects: GIS spatial reasoning, query and analysis.
2. 1 Topological relations and spatial reasoning
Reasoning is the process of inferring new facts according to known facts and laws. The key problem of GIS spatial reasoning is how to use the basic data information stored in the database and combine the relevant spatial constraints to obtain the required unknown spatial information. It involves the characteristics of spatial objects and the logical expression of reasoning, in which spatial characteristics include topological properties, shapes, sizes, directions and distances. The logical expression of reasoning is like a mathematical operation, which formally expresses the spatial relationship between two objects. The comprehensive reasoning of topological relations and directional relations is becoming the main research direction of spatial reasoning. In the application of GIS, what we need is to invert the spatial information such as spatial distribution, size and shape between objects through some constraints. For example, the conceptual adjacency model between spatial relations is established by 9 tuples, and the gradual change process of spatial relations is deduced to reflect the deformation process of spatial entities. On the left of Figure 4 below is the application of spatial reasoning in school location; On the right is the spatial reasoning used to analyze the relationship between soil pollution and the incidence of thyroid cancer.
2.2 Topological relationship and spatial query
GIS spatial data modeling and spatial database design should not only express spatial entities, but also express the spatial relationship between spatial entities. At present, the traditional query language of relational database can not effectively support spatial query because it only provides operations such as equality or sorting of simple data types (such as integers or characters). In order to solve the application problems of spatial database in spatial query, analysis and processing, the support of spatial query language is needed. For example, Arc/Info, Tiger and other systems use relational tables to express the spatial relationships between endpoints and arcs, arcs and tiles, so that the coordinates of overlapping endpoints and tiles only need to be stored once, which not only saves storage space, but also facilitates topological consistency check and query analysis. For example, it will be very simple to query the names of provinces where the Yangtze River flows and borders Hubei Province. In ARC/INFO, the results described by 9-tuple model (i.e. separation, connection, intersection, inclusion/inclusion, overlay/overlay, equality) are added to the query command through macro language.
2.3 Topological relations and spatial analysis
To some extent, spatial analysis deals with the relationship between spatial entities, which can also be said to be the application of spatial relationship theory. For example, point pattern recognition deals with the proximity and distribution between point objects, overlay analysis deals with the intersection and coverage of multiple spatial objects, and network analysis deals with the topological adjacency and association of spatial objects.
Topological relationship is the basis of spatial relationship, and it also involves the consistency of spatial graphic structure in various expressions. Consistency analysis is to test whether the same target has topological contradictions in multiple expressions. From the point of view of time and space, geospatial information changes with time, not only the geometric position, shape and size of spatial objects, but also the topological relationship between objects. Based on the change of topological relationship, the similarity of two spatial graphic structures at different times can be quantitatively analyzed, and based on topological change and geometric change, the data quality of two data sets representing the same area can be compared and analyzed.
Spatial reasoning is widely used in geographic information system, robot navigation, advanced vision, natural language understanding, engineering design and common sense reasoning of physical location. , but also continue to penetrate into other fields, the connotation is very extensive. As the most basic spatial information, topological information is the basis of all spatial relations. Spatial reasoning based on topological relations is a hot issue in GIS.
3. Conclusion
When modeling topological relations, people's cognitive model should be fully integrated, so that the description of the model is more in line with people's expression and cognition of topological information, and the difference between cognition and model description should be minimized. When expressing the model, we need to describe the relationship between spatial objects more accurately and comprehensively, which depends on various mathematical theories and methods, or the comprehensive application of several theories and methods. At the same time, we should also consider the full combination with GIS to enhance the practicability of the model, so as to better solve the practical application problems. In the field of GIS spatial relations, the formal description model and expression method of three-dimensional, spatio-temporal, fuzzy and hierarchical topological relations, as well as cognition, reasoning and access based on spatial relations are the recent research directions.