# Geometric Similarity Measurement Method for Micro Scene Generalization
## 1 Introduction  
Matching and analyzing geometric similarities play important roles in the field of GIS, and these tasks have garnered considerable research attention [1, 2, 3]. Geometric similarities can also be applied in map quality evaluation [4, 5], spatial transmission [6, 7], map updating [8, 9], cartographic generalization [10, 11, 12], and others. Spatial group objects manifest on two-dimensional (2D) maps as point groups, line groups, and polygon groups. The point group is composed of point features, which can be bus stops, commercial outlets, and point-of-interest (POI) data. The line group is considered the greater set of elements in a cartographic database, and it constitutes the primary information presented in a map [13]; the line group may be used to represent geographic vector data, which consist of the following three groups: road networks, river networks, and contour clusters. The polygon group is an important entity of geographical space distribution [14], which includes the building group, island group, and lake group. In the field of cartography, line groups and polygon groups often exist in the form of composite features, such as complex river sections that are composed of islands and riverbanks, as well as blocks that are composed of roads and buildings. Traditional studies mostly divided the above-mentioned composite features into line groups and polygon groups for separate research [15; 16; 17], thereby splitting the overall connection between the elements. In this study, we addressed a spatial scene composed of a line group and a polygon group as a micro scene (Figure 1). These micro scenes were derived from roads, rivers, islands, lakes, and buildings in the real world, such as a block composed of roads and buildings (scene a), an urban waterfront composed of buildings and rivers (scene b), and the river system formed by rivers and lakes (scene c). In practical applications, micro scenes are the basis for hand-drawn scene navigation, fragment scene positioning, and criminal investigation analysis. Numerous studies have attempted to compare scenes based on geometric similarities [18; 19]. However, the definition and representation of similarity are complex, and human expression and cognition relative to space are hierarchical [20; 21; 22]. Almost all of the existing geometric similarity theories, methods, and models are imperfect. The central question of micro scene comparisons is how to associate objects and relationships in one scene to corresponding objects and relationships in another scene. Therefore, it is important to identify what factors should guide the correspondence amongst them. Our purpose in this study was to research the preservation of micro scenes' geometric similarity in generalization, and to apply the geometric similarity to evaluate the quality of cartography. Therefore, we chose the three basic geometric characteristics of shape, direction, and position [23], upon which geometric similarity or matching is often based [24]. Complex structures exist in the spatial objects of micro scenes. In the process of calculating similarity, it is necessary to comprehensively calculate the overall shape similarity and the direction similarity, and the position similarity of the objects should also be considered. Thus, we constructed a method for measuring the geometric similarities of micro scene generalizations, which considers the transformations in shape, direction, and position. The improvements mainly include: (1) a proposed method for accounting the relationships amongst the geometrical shape, direction, and a position of a micro scene during cartographic generalization; and (2) a method that is able to quantitatively evaluate the preservation of geometric features between original micro scenes and their generalized counterparts.