空间群（组）目标相似关系及计算模型研究
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摘要
空间关系是空间物体之间由空间物体的几何特性(位置、形状)所决定的关系,包括距离关系、拓扑关系、方向关系和相似关系,是空间信息科学(GeoSciences)的理论基础之一,一直是空间信息科学理论研究的“重中之重”.作为空间关系的一种,对空间相似关系进行研究,可以完善空间关系理论,提升地理空间认知,促进地理空间信息的应用,以及为地图制图综合提供支持等重要意义和作用。但在对空间关系的研究中,一方面由于空间相似关系的可计算性差,且研究相似关系的目的是揭示较深层次上的信息,需要复杂分析,另一方面,由于地理空间的复杂性,导致空间相似关系的计算要考虑的因素很多,比如空间关系、空间分布、几何特征、语义特征等,从而导致空间相似关系的研究一直以来被人们关注的较少。针对这一现状,论文以空间群(组)目标为研究对象,对空间群(组)目标之间的相似关系及其计算模型进行了探讨,具体研究内容包括：
(1)空间相似关系的基本理论。对空间相似关系理论的一些理论基础进行了阐述,如空间认知科学理论和格式塔心理学。同时论述了空间相似关系的定义、性质、分类,以及影响空间群(组)目标之间相似关系及相似度的主要因子等。引用前人的研究成果,采用集合学的方法对空间相似关系进行了定义；结合空间数据本身的特点和相关研究,定义了空间群(组)目标相似特征集合元素及本文研究的重点元素{空间关系集合,几何特征集合},构成了论文研究和论述的基础；从不同角度对空间相似关系进行了分类,并对空间相似关系的相关性质进行了简单描述。
(2)对空间点群目标相似关系进行了研究。顾及到视觉认知的Gestalt原则,论文提出一种综合考虑到点群的空间关系、空间分布和几何特征,注重空间点群的整体描述的相似度计算模型。利用点的拓扑邻居,定义了点群的拓扑关系及相似度计算模型；引入标准差椭圆,利用点群的标准差椭圆的长轴与x轴的夹角及标准差椭圆的短长轴之比分别定义了点群的方向和距离关系及相似度计算公式；利用“剥皮法”生成点群的分布范围,利用范围多边形的相似度定义了点群的分布范围相似度；生成点群的加权Voronoi图,将点的密度定义为该点所生成的V图的面积的倒数,建立点密度与灰度的线性关系,生成点密度分布的灰度图像,利用图像相似度定义了点密度相似度。最后结合点群的空间关系相似度和几何特征相似度,对空间点群的相似度进行了整体度量。
(3)对空间线群目标相似关系进行了研究。以线群目标的空间统计特征为基础,对线群目标的空间关系和几何特征进行了描述。利用拓扑关系概念领域图及对应的概念领域差异矩阵定义了线群目标之间的拓扑相似关系及计算模型,利用方向均值定义了线群目标之间的方向相似关系及计算模型,利用“环形方差”定义了线群目标之间的距离相似关系及计算模型,结合线群目标的长度和平均长度、线群密度及线群曲折度,建立了线群目标总体相似度计算模型,对线群目标相似度进行整体度量。
(4)对空间面群目标相似关系进行了研究。利用改进了的拓扑关系概念领域图及概念领域差异矩阵,定义了面群目标的拓扑相似关系及计算模型；针对不同的面群目标采用不同的“降维”技术(规则的面群目标采用其最小面积MBR的最长边代替描述原面状目标,不规则的面状目标采用其“骨架线”来代替描述原面状目标),将二维的面状目标“降维”为一维的线状目标,利用已经讨论过的线群目标的方向相似关系和距离相似关系计算方法来处理和描述面状目标的方向相似及距离相似关系；结合前人研究文献,给出了面状目标的几何特征描述参数及几何相似度计算模型。最后综合考虑面状目标的空间关系和几何特征,对空间面群目标的相似度进行了整体度量。
(5)对于空间场景之间的相似关系及相似度计算,主要借鉴了Bruns-Egenhofer模型和Li-Fonseca提出的TDD模型,并做了一些改进。利用改进了的拓扑关系概念领域图来计算空间场景之间的拓扑关系相似度,利用方向关系概念领域图来计算空间场景之间的方向关系相似度,利用距离关系概念领域图来计算空间场景之间的距离关系相似度,最后结合三种空间关系相似度,对空间场景之间的相似度进行了整体度量。
(6)实验部分,以地理学第一定律为基础,分别将地理学第一定律中的“距离”理解为“尺度距离”、“空间邻近度”和“时间邻近度”,从而得到多尺度空间下、不同空间邻近度环境下和不同时间分布的情况下,空间群(组)目标相似关系的不同表现,并分别以多尺度下的点群目标实验、基于空间邻近度的线群目标实验和基于时间邻近度的面群目标实验,利用论文所提算法模型进行了计算和检验,并指出空间相似关系及其计算模型潜在的应用方向。
Spatial relationship is the relationship which determined by the geometric properties (location, shape, etc) between spatial objects, includs topological relationship, directional relationship, distance relationship and similarity relationship. As one of the basis theory of Geosciences, Spatial relationship has been pay highly attention by scholars. As one kind of spatial relationship, spatial similarity relationship plays a very important role. Do research on spatial similarity relationship is a complement to spatial relationship theory, can promote the spatial cognition, can help boost the application of spatial information, and can serve for the map generalization etc. However, in current researches, for one reason the similarity between spatial objects is difficult to assess due to the purpose of research on spatial similarity relationship is to reveal the deep-seated information and require complex analysis; for another, there are many factors need to be take into account in the assessment of similarity between spatial objects because of the complexity of the Geo-space, such as spatial relationship, spatial distribution, geometric features, semantic features and so on, result in very few researches on spatial similarity relationship. In response to this situation, take the spatial group objects as study targets, the spatial similarity relationship and the assess model between spatial group objects were studied in this paper, the specific studies include:
(1) The basic theories of spatial similarity relationship were studied, include its definition, its characteristics, its classifications, and the factors which influence the spatial similarity relationship and similarity degree between spatial group objects. Based on related researches, the set theory was used to define the spatial similarity relationship; Combined with the characteristics of spatial data, the elements of spatial similarity feature sets and the key elements of this paper {spatial relationship sets, geometric feature sets} were defined, constituted the basis of this paper. Also the spatial similarity relationship's classification was described from different aspects; some related characters of the spatial similarity relationship were also described.
(2) The spatial similarity relationship of spatial point cluster was researched. Point cluster object contains much structured information in spatial distribution, which is interested for the research of spatial analysis. With the consideration of Gestalt principles in visual cognition, this paper proposed a similarity assessment model which has a comprehensive consideration of point cluster's spatial relationships, spatial distribution and geometry attributes. The topology relationship of point cluster was defined using point cluster's topology neighbour, the direction relationship and distance relationship was defined using point cluster's standard deviation ellipse, and then the computation method of point cluster's topology, direction and distance similarity assessment was given out on this basis. Also the distribution range and the distribution density of point cluster and their similarity assessment method was put forward. Finally the formal five factors were combined to do a whole assessment of point clusters similarity.
(3) The spatial similarity relationship of spatial line group was researched. Based on Spatial statistical characters, the spatial relationships and geometry features of line group were described. The conceptual neighborhood network of topological relationships between lines was used to define topology similarity between line groups, the directional mean was used to define direction similarity between line groups, their circular variance was used to define distance similarity between line groups; Combined with the length, average length, density and tortuosity of line group, a computation model for similarity assessment between line groups was established. The factors mentioned earlier were combined to do a whole assessment of line group similarity.
(4) The spatial similarity relationship of spatial polygon group was researched. The conceptual neighborhood network of topological relations between polygons was used to define topology similarity between polygon groups; A proper "dimensionality reduction" treatment was used for polygons of different types to change polygon groups to line groups, then the directional mean was used to define direction relations between line groups namely direction similarity of polygon groups, their circular variance was used to define distance relations between line groups namely distance similarity of polygon groups; Combined with the length, average length, area, average area, density and compactness of polygon group, a computation model for similarity assessment between polygon groups was established.
(5) The spatial similarity relationship of spatial scene was researched. Some improvements were made based on Bruns-Egehnoefr Model and Li-Fonseca (TDD) Model. An improved Conceptual neighborhood of topological relations was used to compute the topological similarity between spatial scenes, the conceptual neighborhoods of directional relations was used to compute the directional similarity between spatial scenes, the conceptual neighborhoods of distance relations was used to compute the distance similarity between spatial scenes, finally the 3 factors were combined together to do a whole assessment of spatial scenes.
(6) In the experiment section, based on the first law of geography, the "distance" was interpreted as "scale distance" "spatial proximity" and "temporal proximity" respectively, we can get the different performance of spatial group objects in different scale, different spatial proximity and different temporal proximity. The experiments of point cluster in multi-scale, line group in different space proximity and polygon group in different temporal proximity were carried out to verify the similarity assessment model proposed by this paper, and the potential application was also proposed.
(1)空间相似关系的基本理论。对空间相似关系理论的一些理论基础进行了阐述,如空间认知科学理论和格式塔心理学。同时论述了空间相似关系的定义、性质、分类,以及影响空间群(组)目标之间相似关系及相似度的主要因子等。引用前人的研究成果,采用集合学的方法对空间相似关系进行了定义；结合空间数据本身的特点和相关研究,定义了空间群(组)目标相似特征集合元素及本文研究的重点元素{空间关系集合,几何特征集合},构成了论文研究和论述的基础；从不同角度对空间相似关系进行了分类,并对空间相似关系的相关性质进行了简单描述。
(2)对空间点群目标相似关系进行了研究。顾及到视觉认知的Gestalt原则,论文提出一种综合考虑到点群的空间关系、空间分布和几何特征,注重空间点群的整体描述的相似度计算模型。利用点的拓扑邻居,定义了点群的拓扑关系及相似度计算模型；引入标准差椭圆,利用点群的标准差椭圆的长轴与x轴的夹角及标准差椭圆的短长轴之比分别定义了点群的方向和距离关系及相似度计算公式；利用“剥皮法”生成点群的分布范围,利用范围多边形的相似度定义了点群的分布范围相似度；生成点群的加权Voronoi图,将点的密度定义为该点所生成的V图的面积的倒数,建立点密度与灰度的线性关系,生成点密度分布的灰度图像,利用图像相似度定义了点密度相似度。最后结合点群的空间关系相似度和几何特征相似度,对空间点群的相似度进行了整体度量。
(3)对空间线群目标相似关系进行了研究。以线群目标的空间统计特征为基础,对线群目标的空间关系和几何特征进行了描述。利用拓扑关系概念领域图及对应的概念领域差异矩阵定义了线群目标之间的拓扑相似关系及计算模型,利用方向均值定义了线群目标之间的方向相似关系及计算模型,利用“环形方差”定义了线群目标之间的距离相似关系及计算模型,结合线群目标的长度和平均长度、线群密度及线群曲折度,建立了线群目标总体相似度计算模型,对线群目标相似度进行整体度量。
(4)对空间面群目标相似关系进行了研究。利用改进了的拓扑关系概念领域图及概念领域差异矩阵,定义了面群目标的拓扑相似关系及计算模型；针对不同的面群目标采用不同的“降维”技术(规则的面群目标采用其最小面积MBR的最长边代替描述原面状目标,不规则的面状目标采用其“骨架线”来代替描述原面状目标),将二维的面状目标“降维”为一维的线状目标,利用已经讨论过的线群目标的方向相似关系和距离相似关系计算方法来处理和描述面状目标的方向相似及距离相似关系；结合前人研究文献,给出了面状目标的几何特征描述参数及几何相似度计算模型。最后综合考虑面状目标的空间关系和几何特征,对空间面群目标的相似度进行了整体度量。
(5)对于空间场景之间的相似关系及相似度计算,主要借鉴了Bruns-Egenhofer模型和Li-Fonseca提出的TDD模型,并做了一些改进。利用改进了的拓扑关系概念领域图来计算空间场景之间的拓扑关系相似度,利用方向关系概念领域图来计算空间场景之间的方向关系相似度,利用距离关系概念领域图来计算空间场景之间的距离关系相似度,最后结合三种空间关系相似度,对空间场景之间的相似度进行了整体度量。
(6)实验部分,以地理学第一定律为基础,分别将地理学第一定律中的“距离”理解为“尺度距离”、“空间邻近度”和“时间邻近度”,从而得到多尺度空间下、不同空间邻近度环境下和不同时间分布的情况下,空间群(组)目标相似关系的不同表现,并分别以多尺度下的点群目标实验、基于空间邻近度的线群目标实验和基于时间邻近度的面群目标实验,利用论文所提算法模型进行了计算和检验,并指出空间相似关系及其计算模型潜在的应用方向。
Spatial relationship is the relationship which determined by the geometric properties (location, shape, etc) between spatial objects, includs topological relationship, directional relationship, distance relationship and similarity relationship. As one of the basis theory of Geosciences, Spatial relationship has been pay highly attention by scholars. As one kind of spatial relationship, spatial similarity relationship plays a very important role. Do research on spatial similarity relationship is a complement to spatial relationship theory, can promote the spatial cognition, can help boost the application of spatial information, and can serve for the map generalization etc. However, in current researches, for one reason the similarity between spatial objects is difficult to assess due to the purpose of research on spatial similarity relationship is to reveal the deep-seated information and require complex analysis; for another, there are many factors need to be take into account in the assessment of similarity between spatial objects because of the complexity of the Geo-space, such as spatial relationship, spatial distribution, geometric features, semantic features and so on, result in very few researches on spatial similarity relationship. In response to this situation, take the spatial group objects as study targets, the spatial similarity relationship and the assess model between spatial group objects were studied in this paper, the specific studies include:
(1) The basic theories of spatial similarity relationship were studied, include its definition, its characteristics, its classifications, and the factors which influence the spatial similarity relationship and similarity degree between spatial group objects. Based on related researches, the set theory was used to define the spatial similarity relationship; Combined with the characteristics of spatial data, the elements of spatial similarity feature sets and the key elements of this paper {spatial relationship sets, geometric feature sets} were defined, constituted the basis of this paper. Also the spatial similarity relationship's classification was described from different aspects; some related characters of the spatial similarity relationship were also described.
(2) The spatial similarity relationship of spatial point cluster was researched. Point cluster object contains much structured information in spatial distribution, which is interested for the research of spatial analysis. With the consideration of Gestalt principles in visual cognition, this paper proposed a similarity assessment model which has a comprehensive consideration of point cluster's spatial relationships, spatial distribution and geometry attributes. The topology relationship of point cluster was defined using point cluster's topology neighbour, the direction relationship and distance relationship was defined using point cluster's standard deviation ellipse, and then the computation method of point cluster's topology, direction and distance similarity assessment was given out on this basis. Also the distribution range and the distribution density of point cluster and their similarity assessment method was put forward. Finally the formal five factors were combined to do a whole assessment of point clusters similarity.
(3) The spatial similarity relationship of spatial line group was researched. Based on Spatial statistical characters, the spatial relationships and geometry features of line group were described. The conceptual neighborhood network of topological relationships between lines was used to define topology similarity between line groups, the directional mean was used to define direction similarity between line groups, their circular variance was used to define distance similarity between line groups; Combined with the length, average length, density and tortuosity of line group, a computation model for similarity assessment between line groups was established. The factors mentioned earlier were combined to do a whole assessment of line group similarity.
(4) The spatial similarity relationship of spatial polygon group was researched. The conceptual neighborhood network of topological relations between polygons was used to define topology similarity between polygon groups; A proper "dimensionality reduction" treatment was used for polygons of different types to change polygon groups to line groups, then the directional mean was used to define direction relations between line groups namely direction similarity of polygon groups, their circular variance was used to define distance relations between line groups namely distance similarity of polygon groups; Combined with the length, average length, area, average area, density and compactness of polygon group, a computation model for similarity assessment between polygon groups was established.
(5) The spatial similarity relationship of spatial scene was researched. Some improvements were made based on Bruns-Egehnoefr Model and Li-Fonseca (TDD) Model. An improved Conceptual neighborhood of topological relations was used to compute the topological similarity between spatial scenes, the conceptual neighborhoods of directional relations was used to compute the directional similarity between spatial scenes, the conceptual neighborhoods of distance relations was used to compute the distance similarity between spatial scenes, finally the 3 factors were combined together to do a whole assessment of spatial scenes.
(6) In the experiment section, based on the first law of geography, the "distance" was interpreted as "scale distance" "spatial proximity" and "temporal proximity" respectively, we can get the different performance of spatial group objects in different scale, different spatial proximity and different temporal proximity. The experiments of point cluster in multi-scale, line group in different space proximity and polygon group in different temporal proximity were carried out to verify the similarity assessment model proposed by this paper, and the potential application was also proposed.
引文
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