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AbstractIn order to improve the comparability between the geometric information content of vector area objects, this article proposes a method for measuring the geometric information content of area objects based on discrepancy degree of shape points. First, the method selects circles with unique geometric feature as the reference shape for extracting geometric features, and the geometric in-formation carried by each shape point of area objects is represented by the discrepancy degree between the area object and the reference circle at the point position. Second, the proposed method measures the geometric information content of area objects from both local and global perspectives. To avoid the subjectivity of assigning feature weights based on empirical experience, the article uses the relationships between the radii of three reference circles (MIC: Maximum Inscribed Circle, EAC: Equal-area circle, and MCC: Minimum Circumscribed Circle) as adaptive weight parameters for local and global structural geometric information. The amount of geometric information at each shape point is obtained by weighted summation, and the total geometric information content of an area object is the sum of the amount of geometric information of all shape points. To verify the effectiveness and rationality of the proposed method, this article designs a noise simulation dataset for simply building area objects and an empirical ranking dataset for evaluating the measurement performance of the proposed method. The experimental results show that the proposed method achieves a Kendall rank correlation coefficient of 0.88 on the empirical ranking dataset, which is higher than that of the nine existing representative methods. The proposed method is more consistent with human cognition and is highly correlated with the amount and intensity of noise information. Moreover, the proposed method achieves the comparability of geometric information content of area objects and the adaptive determination of geometric feature weights. The proposed method is an effective method for measuring the geometric information quantity of area objects.

Existing methods for measuring the spatial information of area maps fail to take into account the diversity of adjacency relations and the heterogeneity of adjacency distances among area objects, resulting in insufficient measurement information. This article proposes a method for measuring area map information that considers the diversity of the node–edge and Gestalt principles. Firstly, this method utilizes the adjacency relations between the Voronoi diagram of area objects to construct an adjacency graph that characterizes the spatial distribution of area objects in area maps. This adjacency graph serves as the information representation of area maps. Secondly, the method selects four characteristic indicators, namely geometric information, node degree, adjacency distance, and adjacency strength, to represent the diversity of nodes and edges in the graph that affect spatial information. Finally, nodes in the adjacency graph are taken as the basic units, and the spatial information of area maps is comprehensively calculated by integrating the four characteristics that represent spatial information. To verify the validity and rationality of the proposed method, a dataset of continuously simplified area maps and a dataset of artificially simulated degrees of randomness were designed to evaluate the performance of the existing method and the method proposed in this paper. The results indicate that the correlation between the measurement results obtained by the method proposed in this paper and the degree of disorder is as high as 0.94, outperforming the existing representative methods. Additionally, the correlation between the measurement results of this method and the degree of simplification reaches 1, indicating that the variation range of the measured values is more consistent with the cognitive assumptions based on artificial simulations compared to the existing methods. The experimental results show that the method proposed in this paper is an effective metric approach for representing spatial information in area maps. [ABSTRACT FROM AUTHOR]

Three-dimensional topological relationships serve as a theoretical foundation for quality control, update processing, and spatial analysis of three-dimensional spatial data in real-world three-dimensional GIS. The existing 3D topological relationship models are all basic relationship models that cannot distinguish the refined topological relationship between the line and the body with multiple intersections. In this study, we develop a 3D refined topological relationship description framework that draws from the two-dimensional refined topological relationship model, defines the unit intersection between the line and the body based on manifold topology, and proposes a method for describing the unit intersections between the line and the body considering Euler numbers and adjacency types. In total, 23 basic types between the line and the body are deduced. An example is provided to illustrate the distinguished refined topological relationship between the line and the body with multiple intersections. Subsequently, an algorithm for determining the basic type of line/body is developed. Finally, a line/body refined topological relationship computation prototype system is developed using the Nef polyhedron model, C++ language, and an open-source geometric algorithm library, and the effectiveness of our method is verified using actual building and pedestrian data. [ABSTRACT FROM AUTHOR]

Quantifying the information content of remote sensing images is considered to be a fundamental task in quantitative remote sensing. Traditionally, the grayscale entropy designed by Shannon’s information theory cannot capture the spatial structure of images, which has prompted successive proposals of a series of neighborhood-based improvement schemes. However, grayscale or neighborhood-based spatial structure is only a basic feature of the image, and the spatial structure should be divided into the overall structure and the local structure and separately characterized. For this purpose, a multi-feature quantification framework for image information content is proposed. Firstly, the information content of optical remote sensing images is measured based on grayscale, contrast, neighborhood-based topology, and spatial distribution features instead of simple grayscale or spatial structure. Secondly, the entropy metrics of the different features are designed to quantify the uncertainty of images in terms of both pixel and spatial structure. Finally, a weighted model is used to calculate the comprehensive information content of the image. The experimental results confirm that the proposed method can effectively measure the multi-feature information content, including the overall and local spatial structure. Compared with state-of-the-art entropy models, our approach is the first study to systematically consider the multiple features of image information content based on Shannon entropy. It is comparable to existing models in terms of thermodynamic consistency. This work demonstrates the effectiveness of information theory methods in measuring the information content of optical remote sensing images.