Spatial Topological Relations Research Articles

A Model of Representing Extension and Shrinking for Spatial Relations

Aiming at region connection calculus (RCC) can only roughly represent spatial topological relations, and have difficulty in representing the distance, direction and so on. Therefore, based on RCC theory, Region Extension and Shrinking Calculus are proposed, and then a formalized metrization method using region as a basic unit is introduced. Based on RESC theory, taking the advantage such as application simplicity and easy realization of gird area method. The experiment proves the spatial relations can be easily obtained by Grid-Region method, and it is an effective way to repre- sent spatial relations.

Spatial chromatic tessellation: conception, interpretation, and implication

A novel spatial tessellation scheme, spatial chromatic tessellation (SCT), is proposed for representing and exploring space–entity relationship. The objective of this article is briefly introducing the basic concepts, structure, and properties of SCT. Our study mainly focuses on the arranged chromatic diagram (ACD), which is the most typical type of SCT. A few examples show that ACD can be used to analyze spatial topology, statistics, computations, database, and Voronoi diagrams. ACD also contains many implications on spatial analysis theory. With respect to each entity in a space, SCT partitions the space into a number of small unit cells and gives each cell a unique chromatic code. The spatial topological relationships among these cells are able to be represented and computed by their codes. Based on the different statistical rules on cellular codes, cells could be merged into larger clusters, such as a variety of Voronoi diagrams. Moreover, because cells are coded with the same data structure, it is easy to store and manage these codes in relational database, and then any spatial analytical operation could be realized simply by structured queries. SCT establishes a basic framework that not only provides a theoretical tool for spatial analysis and computations but also helps us to understand the space–entity relationship insightfully.

Spatial Topological Relationships: An Overview and Analysis

Spatial Topological Relationships: An Overview and Analysis

Watermarking geographical data on spatial topological relations

Geographical data is of great value for data producers. How to protect copyright of geographical data effectively using digital watermarking is a hot research issue. In this paper, spatial topological relation existing between polygons is chosen as cover data, and watermark is embedded by slightly modifying the metric measure of spatial topological relation, and some geographical objects are scaled to derive the watermarked data. Global Main Scaling Distance is introduced to measure the distortions caused by watermark embedding. Experimental results show that the proposed algorithm has a good robustness against geometrical attacks, simplification, interpolation and noise addition attacks, and preserves shape of the watermarked geographical objects. Furthermore, a good tradeoff between robustness and fidelity is acquired in the proposed algorithm.

Point cloud simplification with boundary points reservation

A non-uniform simplification approach with boundary points reservation was proposed concerning the boundary points loss caused by most point cloud simplification algorithms.First,kd-tree was used to represent the spatial topology relationship of the scattered point cloud and to calculate the k-nearest neighbors for each data point.Then an improved algorithm for boundary points detection of point cloud was presented to solve the low efficiency when the current algorithms extract boundary according to uniform distribution of point cloud.Consequently,all the resulted boundary points were reserved,while the non-boundary points were reserved for final non-uniform simplification according to the surface variation and their nearest neighbors.The experimental result shows that the proposed simplification approach has high accuracy and low space complexity,and can reserve the boundary points.

Methodology of feature change detection and matching in data updating

In the case of lack of correlation between identical entities in feature classes,the identical entity for the current feature and their change information was automatically identified by spatial analysis.When searching candidate matching collection for the current feature,a spatial query based on self-definition spatial topological relationship was designed,which narrowed the search scope,reduced the query time,and increased spatial analysis efficiency.When confirming the identical entity for the current feature,a weight-based similarity computing model was presented,and this effectively matched features in the circumstances of complex spatial relationships and improved the accuracy of matching.

GTP-based integral real-3D spatial model for engineering excavation GIS

Engineering excavation GIS (E2 GIS) is a real-3D GIS serving for geosciences related to geo-engineering, civil engineering and mining engineering based on generalized tri-prism (GTP) model. As two instances of GTP model, G-GTP is used for the real-3D modeling of subsurface geological bodies, and E-GTP is used for the real-3D modeling of subsurface engineering excavations. In the light of the discussions on the features and functions of E2GIS, the modeling principles of G-GTP and E-GTP are introduced. The two models couple together seamlessly to form an integral model for subsurface spatial objects including both geological bodies and excavations. An object-oriented integral real-3D data model and integral spatial topological relations are discussed.

이동객체 위치 일반화를 이용한 시공간 이동 패턴 탐사

현재의 이동객체를 기반으로 하는 다양한 시공간 응용환경에서의 서비스 지원 시스템 개발을 위하여 중요한 문제 중의 하나는 방대한 이동객체의 위치 이동 데이터로부터의 의미 있는 지식인 시공간 이동 패턴을 탐사하는 것이다. 이를 위하여 시간적 위상관계, 공간적 위상관계 그리고 시공간적 위상관계에 대한 접근이 지식 탐사를 위하여 고려되어야 한다. 이 논문에서는 효율적인 시공간 이동 패턴 탐사 기법인 MPMine 알고리즘을 제안하였다. 제안한 기법은 시간 제약조건과 공간 제약조건 등을 함께 괴려하며 또한 공간 위상 연산인 contain()을 이용한 공간 개념화를 수행할 수 있다. 제안한 기법은 기존의 일반적인 시간 패턴 탐사 기법과 달리 이동객체 데이터 집합으로부터 위치 및 일반화를 통하여 탐색 공간을 줄일 수 있어 효율적으로 유용한 이동 패턴을 탐사할 수 있다. Currently, one of the most critical issues in developing the service support system for various spatio-temporal applications is the discoverying of meaningful knowledge from the large volume of moving object data. This sort of knowledge refers to the spatiotemporal moving pattern. To discovery such knowledge, various relationships between moving objects such as temporal, spatial and spatiotemporal topological relationships needs to be considered in knowledge discovery. In this paper, we proposed an efficient method, MPMine, for discoverying spatiotemporal moving patterns. The method not only has considered both temporal constraint and spatial constrain but also performs the spatial generalization using a spatial topological operation, contain(). Different from the previous temporal pattern methods, the proposed method is able to save the search space by using the location summarization and generalization of the moving object data. Therefore, Efficient discoverying of the useful moving patterns is possible.

Application of radar-measured rain data in hydrological processes modeling during the intensified observation period of HUBEX

On the basis of Digital Elevation Model data, the raster flow vectors, watershed delineation, and spatial topological relationship are generated by the Martz and Garbrecht method for the upper area of Huangnizhuang station in the Shihe Catchment with 805 km2 of area, an intensified observation field for the HUBEX/GAME Project. Then, the Xin’anjiang Model is applied for runoff production in each grid element where rain data measured by radar at Fuyang station is utilized as the input of the hydrological model. The elements are connected by flow vectors to the outlet of the drainage catchment where runoff is routed by the Muskingum method from each grid element to the outlet according to the length between each grid and the outlet. The Nash-Sutcliffe model efficiency coefficient is 92.41% from 31 May to 3 August 1998, and 85.64%, 86.62%, 92.57%, and 83.91%, respectively for the 1st, 2nd, 3rd, and 4th flood events during the whole computational period. As compared with the case where rain-gauge data are used in simulating the hourly hydrograph at Huangnizhuang station in the Shihe Catchment, the index of model efficiency improvement is positive, ranging from 27.56% to 69.39%. This justifies the claim that radar-measured data are superior to rain-gauge data as inputs to hydrological modeling. As a result, the grid-based hydrological model provides a good platform for runoff computation when radar-measured rain data with highly spatiotemporal resolution are taken as the input of the hydrological model.

Geo-rough space

Rough set is a new approach to uncertainties in spatial analysis. In this paper, rough set symbols are simplified and standardized in terms of rough interpretation and specialized indication. Rough spatial entities and their topological relationships are also proposed in rough space, thus a universal intersected equation is developed, and rough membership function is further extended with the gray scale in our case study. We complete three works. First, a set of simplified rough symbols is advanced on the basis of existing rough symbols. Second, rough spatial entity is put forward to study the real world as it is, without forcing uncertainties into crisp set. Third, rough spatial topological relationships are studied by using rough matrix and their figures. The relationships are divided into three types, crisp entity and crisp entity (CC), rough entity and crisp entity (RC), and rough entity and rough entity (RR). A universal intersected equation is further proposed. Finally, the maximum and minimum maps of river thematic classification are generated via rough membership function and rough relationships in our case study.

Spatio-temporal predicates

Investigates temporal changes of topological relationships and thereby integrates two important research areas: first, 2D topological relationships that have been investigated quite intensively, and second, the change of spatial information over time. We investigate spatio-temporal predicates, which describe developments of well-known spatial topological relationships. A framework is developed in which spatio-temporal predicates can be obtained by temporal aggregation of elementary spatial predicates and sequential composition. We compare our framework with two other possible approaches: one is based on the observation that spatio-temporal objects correspond to 3D spatial objects for which existing topological predicates can be exploited. The other approach is to consider possible transitions between spatial configurations. These considerations help to identify a canonical set of spatio-temporal predicates.

Dealing with spatial relations for spatial objects with randomness in GIS

To design retrieval algorithm of spatial relations for spatial objects with randomness in GIS, this paper builds up the membership functions based on set theory idea, used for determination of topological spatial relations between random objects, such as between point and point, point and line or polygon, which provides theoretical basis for retrieving spatial relations between certain and random objects. Finally, this paper interprets detailed methods and steps of realizing them by means of some simple examples under the GIS's environment.

Metric details for natural-language spatial relations

Spatial relations often are desired answers that a geographic information system (GIS) should generate in response to a user's query. Current GIS's provide only rudimentary support for processing and interpreting natural-language-like spatial relations, because their models and representations are primarily quantitative, while natural-language spatial relations are usually dominated by qualitative properties. Studies of the use of spatial relations in natural language showed that topology accounts for a significant portion of the geometric properties. This article develops a formal model that captures metric details for the description of natural-language spatial relations. The metric details are expressed as refinements of the categories identified by the 9-intersection, a model for topological spatial relations, and provide a more precise measure than does topology alone as to whether a geometric configuration matches with a spatial term or not. Similarly, these measures help in identifying the spatial term that describes a particular configuration. Two groups of metric details are derived: splitting ratios as the normalized values of lengths and areas of intersections; and closeness measures as the normalized distances between disjoint object parts. The resulting model of topological and metric properties was calibrated for 64 spatial terms in English, providing values for the best fit as well as value ranges for the significant parameters of each term. Three examples demonstrate how the framework and its calibrated values are used to determine the best spatial term for a relationship between two geometric objects.

Approximate analysis of binary topological relations between geographic regions with indeterminate boundaries

The development of formal models of spatial relations is a topic of great importance in spatial reasoning, geographic information systems (GIS) and computer vision, and has gained much attention from researchers across these research areas during the past two decades. In recent years significant achievements have been made on the development of models of spatial relations between spatial objects with precisely defined boundaries. However, these models cannot be directly applied to spatial objects with indeterminate boundaries which are found in many applications in geographic analysis and image understanding. This article develops a method for approximately analyzing binary topological relations between geographic regions with indeterminate boundaries based upon previous work on topological spatial relations and fuzzy sets. In addition, examples are given to demonstrate the method and related concepts. It is shown that the eight binary topological relations between regions in a two-dimensional space can be easily determined by the method.

Point-set topological spatial relations

Abstract Practical needs in geographic information systems (GIS) have led to the investigation of formal and sound methods of describing spatial relations. After an introduction to the basic ideas and notions of topology, a novel theory of topological spatial relations between sets is developed in which the relations are defined in terms of the intersections of the boundaries and interiors of two sets. By considering empty and non-empty as the values of the intersections, a total of sixteen topological spatial relations is described, each of which can be realized in R 2. This set is reduced to nine relations if the sets are restricted to spatial regions, a fairly broad class of subsets of a connected topological space with an application to GIS. It is shown that these relations correspond to some of the standard set theoretical and topological spatial relations between sets such as equality, disjointness and containment in the interior.