A scale-explicit model for checking directional consistency in multi-resolution spatial data

Multi-resolution spatial data always contain the inconsistencies of topological, directional, and metric relations due to measurement methods, data acquisition approaches, and map generalization algorithms. Therefore, checking these inconsistencies is critical for maintaining the integrity of multi-resolution or multi-source spatial data. To date, research has focused on the topological consistency, while the directional consistency at different resolutions has been largely overlooked. In this study we developed computation methods to derive the direction relations between coarse spatial objects from the relations between detailed objects. Then, the consistency of direction relations at different resolutions can be evaluated by checking whether the derived relations are compatible with the relations computed from the coarse objects in multi-resolution spatial data. The methods in this study modeled explicitly the scale effects of direction relations induced by the map generalization operator – merging, thus they are efficient for evaluating consistency. The directional consistency is an essential complement to topological and object-based consistencies.     

拓扑关系和方向关系的定性组合描述

空间关系理论研究是当前GIS界重点研究的前沿课题之一,但就目前研究成果看,空间关系理论中的拓扑关系和方向关系的理论研究多采用独立的描述模型,影响了空间推理和空间表达的精度。该文在分析拓扑关系和方向关系描述模型的基础上,提出将拓扑关系和方向关系定性表示相结合的TD模型,并用实例说明该模型能较全面地描述空间对象的空间关系。     

Integrative representation and inference of qualitative locations about points,lines, and polygons

Qualitative knowledge representation of spatial locations and relations is popular in many text-based media, for example, postings on social networks, news reports, and encyclopedia, as representing qualitative spatial locations is indispensable to infer spatial knowledge from them. However, an integrative model capable of handling direction-based locations of various spatial objects is missing. This study presents an integrative representation and inference framework about direction-based qualitative locations for points, lines, and polygons. In the framework, direction partitions of different types of reference objects are first unified to create a partition consisting of cells, segments, and corners. They serve as a frame of reference to locate spatial objects (e.g., points, lines, and polygons). Qualitative relations are then defined to relate spatial objects to the elements in a cell partition, and to form the model of qualitative locations. Last, based on the integrative representation, location-based reasoning mechanism is presented to derive topological relations between objects from their locations, such as point–point, line–line, point–line, point–polygon, line–polygon, and polygon–polygon relations. The presented model can locate any type of spatial objects in a frame of reference composed of points, lines, and polygons, and derive topological relations between any pairs of objects from the locations in a unified method.     

地理空间意像模式的Voronoi模型

提出用Voronoi空间模型来表达意像模式，Voronoi模型无岐义空间邻近关系，构建能封装对象间空间关系的拓扑网络，使用该模型将各种空间介词映射为不同的拓扑结构，GIS采用该模型，可按自然语言中空间介词描述的定性空间关系查询检索模糊地理信息。     

Topology revisited: representing spatial relations

Topology is a central, defining feature of geographical information systems (GIS). The advantages of topological data structures are that data storage for polygons is reduced because boundaries between adjacent polygons are not stored twice, explicit adjacency relations are maintained, and data entry and map production is improved by providing a rigorous, automated method to handle artifacts of digitizing. However, what explains the resurgence of non-topological data structures and why do contemporary desktop GIS packages support them? The historical development of geographical data structures is examined to provide a context for identifying the advantages and disadvantages of topological and non-topological data structures. Although explicit storage of adjacent features increases performance of adjacency analyses, it is not required to conduct these operations. Non-topological data structures can represent features that conform to planar graph theory (i.e. non-overlapping, space-filling polygons). A data structure that can represent proximal and directional spatial relations, in addition to topological relationships is described. This extension allows a broader set of functional relationships and connections between geographical features to be explicitly represented.     

A Euler number-based topological computation model for land parcel database updating

Intersection relations are important topological considerations in database update processes. The differentiation and identification of non-empty intersection relations between new updates and existing objects is one of the first steps in the automatic incremental update process for a land parcel database. The basic non-empty intersection relations are meet, overlap, cover, equal and inside, but these basic relationships cannot reflect the complex and detailed non-empty relations between a new update and the existing objects. It is therefore necessary to refine the basic non-empty topological relations to support and trigger the relevant update operations. Such relations have been refined by several researchers using topological invariants (e.g., dimension, type and sequence) to represent the intersection components. However, the intersection components often include only points and lines, and the refined types of 2-dimensional intersection components that occur between land parcels have not been defined. This study examines the refinement of non-empty relations among 2-dimensional land parcels and proposes a computation model. In this model, an entire spatial object is directly used as the operand, and two set operations (i.e., intersection (∩) and difference (\)) are applied to form the basic topological computation model. The Euler number is introduced to refine the relations with a single 2-dimensional intersection (i.e., cover, inside and overlap) and to distinguish the refined types of 2-dimensional intersection components for the relations with multiple intersections. In this study, the cover and overlap relations with single intersections between regions are refined into seven cases, and nine basic types of 2-dimensional intersection components are distinguished. A composite computation model is formed with both Euler number values and dimensional differences. In this model, the topological relations with single intersections are differentiated by the value of the dimension and the Euler number of the resulting set of the whole-object intersection and differences, whereas the relations with multiple intersections are discriminated by the value of the resulting set at a coarse level and are further differentiated by the type and sequence of the whole-object intersection component in a hierarchical manner. Based on the refined topological relations, an improved method for automatic and incremental updating of the land parcel database is presented. The effectiveness of the models and algorithms was verified by the incremental update of a land cover database. The results of this study represent a new avenue for automatic spatial data handling in incremental update processes.     

A vector field model to handle the displacement of multiple conflicts in building generalization

In map generalization, the displacement operation attempts to resolve proximity conflicts to guarantee map legibility. Owing to the limited representation space, conflicts may occur between both the same and different features under different contexts. A successful displacement should settle multiple conflicts, suppress the generation of secondary conflicts after moving some objects, and preserve the distribution patterns. The effect of displacement can be understood as a force that pushes related objects away with properties of propagation and distance decay. This study borrows the idea of vector fields from physics discipline and establishes a vector field model to handle the displacement of multiple conflicts in building generalization. A scalar field is first constructed based on a Delaunay triangulation skeleton to partition the buildings being examined (e.g., a street block). Then, we build a vector field to conduct displacement measurements through the detection of conflicts from multiple sources. The direction and magnitude of the displacement force are computed based on an iso-line model of vector field. The experiment shows that this global method can settle multiple conflicts and preserve the spatial relations and important building patterns.     

Multidimensional-unified topological relations computation: a hierarchical geometric algebra-based approach

This article presents a geometric algebra-based model for topological relation computation. This computational model is composed of three major components: the Grassmann structure preserving hierarchical multivector-tree representation (MVTree), multidimensional unified operators for intersection relation computation, and the judgement rules for assembling the intersections into topological relations. With this model, the intersection relations between the different dimensional objects (nodes at different levels) are computed using the Tree Meet operator. The meet operation between two arbitrary objects is accomplished by transforming the computation into the meet product between each pair of MVTree nodes, which produces a series of intersection relations in the form of MVTree. This intersection tree is then processed through a set of judgement rules to determine the topological relations between two objects in the hierarchy. Case studies of topological relations between two triangles in 3D space are employed to illustrate the model. The results show that with the new model, the topological relations can be computed in a simple way without referring to dimension. This dimensionless way of computing topological relations from geographic data is significant given the increased dimensionality of geographic information in the digital era.     

Quantification of spatial gradation of slope positions

Transition between slope positions (e.g., ridge, shoulder slope, back slope, foot slope, and valley) is often gradual. Quantification of spatial transitions or spatial gradations between slope positions can increase the accuracy of terrain parameterization for geographical or ecological modeling, especially for digital soil mapping at a fine scale. Current models for characterizing the spatial gradation of slope positions based on a gridded DEM either focus solely on the parameter space or depend on too many rules defined by topographic attributes, which makes such approaches impractical. The typical locations of a slope position contain the characteristics of the slope position in both parameter space and spatial context. Thus, the spatial gradation of slope positions can be quantified by comparing terrain characteristics (spatial and parametrical) of given locations to those at typical locations. Based on this idea, this paper proposes an approach to quantifying the spatial gradation of slope positions by using typical locations as prototypes. This approach includes two parts: the first is to extract the typical locations of each slope position and treat them as the prototypes of this position; and the second is to compute the similarity between a given location and the prototypes based on both local topographic attributes and spatial context. The new approach characterizes slope position gradation in both the attribute domain (i.e., parameter space) and the spatial domain (i.e., geographic space) in an easy and practicable way. Applications show that the new approach can quantitatively describe spatial gradations among a set of slope positions. Comparison of spatial gradation of A-horizon sand percentages with the quantified spatial gradation of slope positions indicates that the latter reflects slope processes, confirming the effectiveness of the approach. The comparison of a soil subgroup map of the study area with the maximum similarity map derived from the approach also suggests that the quantified spatial gradation of slope position can be used to aid geographical modeling such as digital soil mapping.     

Algebraic approach to spatial reasoning

Abstract

A simple, exemplary system is described that performs reasoning about the spatial relationships between members of a set of spatial objects. The main problem of interest is to make sound and complete inferences about the set of all spatial relationships that hold between the objects, given prior information about a subset of the relationships. The spatial inferences are formalized within the framework of relation algebra and procedurally implemented in terms of constraint satisfaction procedures. Although the approach is general, the particular example employs a new ‘complete’ set of topological relationships that have been published elsewhere. In particular, a relation algebra for these topological relations is developed and a computational implementation of this algebra is described. Systems with such reasoning capabilities have many applications in geographical analysis and could be usefully incorporated into geographical information systems and related systems.     

Modeling the scale dependences of topological relations between lines and regions induced by reduction of attributes

The scale dependences of topological relations are caused by the changes of spatial objects at different scales, which are induced by the reduction of attributes. Generally, the detailed partitions and multi-scale attributes are stored in spatial databases, while the coarse partitions are not. Consequently, the detailed topological relations can be computed and regarded as known information, while the coarse relations stay unknown. However, many applications (e.g., multi-scale spatial data query) need to deal with the topological relations at multiple scales. In this study new methods are proposed to model and derive the scale dependences of topological relations between lines and multi-scale region partitions. The scale dependences of topological relations are modeled and used to derive the relations between lines and coarse partitions from the relations about the detailed partitions. The derivation can be performed in two steps. At the first step, the topological dependences between a line and two meeting, covered and contained regions are computed and stored into composition tables, respectively. At the second step, a graph is used to represent the neighboring relations among the regions in a detailed partition. The scale dependences and detailed relations are then used to derive topological relations at the coarse level. Our methods can also be extended to handle the scale dependences of relations about disconnected regions, or the combinations of connected and disconnected regions. Because our methods use the scale dependences to derive relations at the coarse level, rather than generating coarse partition and computing the relations with geometric information, they are more efficient to support scale-dependent applications.     

Quality assessment of linear data

This paper presents methods to evaluate the geometric quality of spatial data. Firstly, a point‐based method is presented, adapting conventional assessment methods whereby common points between datasets are compared. In our approach, initial matches are established automatically and refined further through interactive editing. Second, a line‐based method which uses correspondences between line segments is proposed. Here, the geometry of line segments in vector is transformed into a set of rasterized values so that their combination at each pixel can restore their original vector geometry. Matching is performed on rasterized line segments and their matching lengths and displacements are measured. Experimental results show that the line‐based approach proposed is efficient to evaluate the geometric quality of spatial data without requirements of topological relationships among line features.     

Development of Voronoi-based cellular automata -an integrated dynamic model for Geographical Information Systems

This paper presents a development of the extended Cellular Automata (CA), a Voronoi-based CA, to model dynamic interactions among spatial objects. Cellular automata are efficient models for representing dynamic spatial interactions. A complex global spatial pattern is generated by a set of simple local transition rules. However, its original definition for a two-dimensional array limits its application to raster spatial data only. This paper presents a newly developed Voronoi-based CA in which the CA is extended by using the Voronoi spatial model as its spatial framework. The Voronoi spatial model offers a ready solution to handling neighbourhood relations among spatial objects dynamically. By implementing this model, we have demonstrated that the Voronoi-based CA can model local interactions among spatial objects to generate complex global patterns. The Voronoi-based CA can further model interactions among point, line and polygon objects with irregular shapes and sizes in a dynamic system. Each of these objects possesses its own set of attributes, transition rules and neighbourhood relationships. The Voronoi-based CA models spatial interactions among real entities, such as shops, residential areas, industries and cities. Compared to the original CA, the Voronoi-based CA is a more natural and efficient representation of human knowledge over space.     

天目山阔叶林的TM影像及其地形的分维相关分析

在RS、GIS技术支持下,对天目山地区的TM影像进行处理与分类,得到研究区的阔叶林空间分布图。运用GIS空间分析与SPSS统计功能,对阔叶林的TM影像及其所处的地形进行分维估算,研究其分维的空间分布规律。阔叶林的TM影像分维在高程、坡度和坡向3个方面有分布规律:随海拔的升高、坡度的增加, TM影像分维呈增加的趋势;阳坡、半阴半阳坡比阴坡的影像分维大。阔叶林的地形分维在高程和坡向2个方面有分布规律:随海拔的升高,地形分维呈减小的趋势;阴坡比阳坡、半阴半阳坡的分维大;地形分维与坡度没有关系。阔叶林TM影像与其地形的分维之间存在正相关。     

A complete classification of spatial relations using the Voronoi-based nine-intersection model

In this article we show that the Voronoi-based nine-intersection (V9I) model proposed by Chen et al. (2001, A Voronoi-based 9-intersection model for spatial relations. International Journal of Geographical Information Science, 15 (3), 201–220) is more expressive than what has been believed before. Given any two spatial entities A and B, the V9I relation between A and B is represented as a 3 × 3 Boolean matrix. For each pair of types of spatial entities that is, points, lines, and regions, we first show that most Boolean matrices do not represent a V9I relation by using topological constraints and the definition of Voronoi regions. Then, we provide illustrations for all the remaining matrices. This guarantees that our method is sound and complete. In particular, we show that there are 18 V9I relations between two areas with connected interior, while there are only nine four-intersection relations. Our investigations also show that, unlike many other spatial relation models, V9I relations are context or shape sensitive. That is, the existence of other entities or the shape of the entities may affect the validity of certain relations.     

地缘体概念内涵及特征研究

地缘理论是在地缘政治、地缘经济、地缘文化、地缘科技等研究领域基础上构建的基础理论。地缘体是地缘问题的研究对象,是地缘理论研究的核心内容。论文在综合分析各地缘研究领域基础上,提出并明确了地缘体的概念与内涵,初步建立了地缘体类型体系,分析了地缘体空间、属性和时间等特征,并对地缘体的空间拓扑关系进行了简要描述,为地缘理论的建立奠定了基础。     

基于GIS的二维非结构化剖分网格优化

非结构化网格剖分是数值模拟的关键技术之一,网格质量直接影响到计算的收敛性和精确度。在GIS辅助建立非结构化网格空间拓扑关系的基础上,针对GIS和实际研究问题给出Spring-Laplace方法——一种新的单元尺度函数定义,在GIS空间算法下利用该方法优化节点位置,并基于推进阵面算法的思想,结合空间邻近拓扑关系实现了三角剖分节点和网格的重新编号算法,方便了开边界条件的赋值,提高了计算效率。实例表明,该方法大大提高了网格生成质量,能适应FVCOM数值模型对非结构化网格剖分的要求,其收敛速度快,具有较高的运算效率。     

A bottom‐up approach to discover transition rules of cellular automata using ant intelligence

This paper presents a new method to discover transition rules of geographical cellular automata (CA) based on a bottom‐up approach, ant colony optimization (ACO). CA are capable of simulating the evolution of complex geographical phenomena. The core of a CA model is how to define transition rules so that realistic patterns can be simulated using empirical data. Transition rules are often defined by using mathematical equations, which do not provide easily understandable explicit forms. Furthermore, it is very difficult, if not impossible, to specify equation‐based transition rules for reflecting complex geographical processes. This paper presents a method of using ant intelligence to discover explicit transition rules of urban CA to overcome these limitations. This ‘bottom‐up’ ACO approach for achieving complex task through cooperation and interaction of ants is effective for capturing complex relationships between spatial variables and urban dynamics. A discretization technique is proposed to deal with continuous spatial variables for discovering transition rules hidden in large datasets. The ACO–CA model has been used to simulate rural–urban land conversions in Guangzhou, Guangdong, China. Preliminary results suggest that this ACO–CA method can have a better performance than the decision‐tree CA method.     

基于无人机摄影测量的地形变化检测方法与小流域输沙模型研究

流域输沙过程是地貌学和地表动力学的重要研究内容,但传统的输沙过程监测方法仅能得到某个区域的总输沙率,无法推算其空间分布。论文以黄土高原绥德县窑家湾小流域为例,利用无人机摄影测量技术得到其2006年和2019年2期数字高程模型(DEM)并计算地形变化量;然后,根据质量守恒原理和多流向算法建立泥沙在空间上的输送模型,进而计算小流域输沙率的空间分布。实验结果表明,该模型能有效模拟泥沙在空间上的输送情况,输沙率出现质量不守恒的区域面积占比小于4%,且不守恒区域多为人类活动影响区。同时,论文讨论了DEM的选择和不同地形变化检测水平对模型结果的影响。当使用第一期DEM进行泥沙搬运路径推算时,质量不守恒区域的面积显著降低。使用误差空间分布图进行地形变化检测得到的输沙率结果鲁棒性更强。使用中误差进行地形检测得到的结果在不同置信度下变化较大。基于无人机地形变化检测的空间输沙模型能方便、快捷地提供详尽的输沙率空间分布,为地表过程研究带来了新的机遇。