## 2 Related Work
### Geometric Information Content Measurement of Area Objects  
The geometric morphological characteristics of area objects are the main source of geometric information. Scholars have proposed a series of algorithms for measuring the geometric morphological information of area objects. In summary, the information content generated by the geometric morphology of area objects is related to the diversity of their geometric morphology. This diversity is determined by the degree of difference among the characteristics that represent the geometric morphology of area objects. The higher the degree of difference, the higher the degree of diversity in geometric morphology. Some scholars measure the diversity of geometric information by considering the closeness of area objects to related simple shapes, thereby expressing the geometric information content. For example, [PERSON] et al. measured the degree of diversity by considering the closeness of target objects to their convex hulls [17]. [PERSON] et al. used the proximity between target objects and its equivalent rectangles as a metric [13]. [PERSON] et al. (2003) expressed the degree of diversity by considering the closeness of target objects to reference triangles and ellipses [22]. The shortcoming of such methods lies in the lack of a clear standard for the reference shape. The reference shapes for different area objects may vary significantly; therefore, the measure obtained through this comparison lacks a unified standard, resulting in the incomparability of the measured information content. At the same time, map data contains a large number of natural features, which differ significantly from rectangles and convex polygons with rectangular features. Therefore, they are not suitable as reference shapes for natural features. Finally, there are many artificial structures with rectangular or convex polygon features in map data, which will cause the measurement values of such methods to approach zero or be consistent when dealing with artificial structures, leading to a decrease in discrimination power. [PERSON] et al. used the area proportion occupied by area objects on a map as a probability parameter to measure the geometric information content of the object [16]. This method has the advantages of simplicity and efficiency in calculation. However, a significant shortcoming is that it is susceptible to the limitations of the spatial scope of the map. For example, the comparison of spatial information between two maps is only valid within a fixed spatial scope, which restricts the application range of the spatial information content of the map. The studies expressed geometric information content in the form of a single indicator. However, it is evident that a single indicator often only considers one aspect of geometric information content and fails to take into account more comprehensive characteristics. To address this issue, scholars have considered combining various features that influence the geometric information of area objects to form a multi-parameter measurement model that considers multiple geometric characteristics. [PERSON] and [PERSON] employed two features, namely the global distance entropy of shape contours and the metric of shape randomness, to represent the global information of shapes, while using local angular entropy to characterize the local detail information of shapes [23]. They calculated the complexity of shape contours by decomposing them from global to local perspectives. [PERSON] et al. analyzed the overall complexity of shapes from three aspects: the complexity of shape boundaries, the solidity of convex hulls, and shape symmetry, comprehensively calculating the geometric information content of shapes [24]. [PERSON] and [PERSON] et al. used a weighted linear combination of multiple parameters to express various indicators of information content. However, in both methods, the weight parameters were determined based on human experience, which increased the subjectivity of the information measurement model [23; 24].