A Model for Quantitatively Calculating and Qualitatively Describing Direction Relationships Between Object Groups

Objectives: The modeling of direction relationships between object groups is one of the important research topics in the theory of spatial relationships. However, the existing models fail to reasonably classify the direction relationships between object groups, and ignore the impacts of the distribution shapes of object groups and the distribution density of their sub-objects on direction relationships, making it difficult to accurately determine direction relationships. Methods: To solve the problem, this paper classified the direction relationships between object groups into three categories in the light of the different visual cognitive outcomes of object groups; and it was found that the adjacent regions between object groups can reflect the impacts of the distribution shapes of object groups and the distribution density of their sub-objects on direction relationships. Based on this, a model for quantitatively calculating and qualitatively describing direction relationships between object groups was proposed. It consists of the following steps: firstly, using Delaunay triangulation to construct the adjacent region between object groups; then, distinguishing different types of direction relationships by preprocessing the triangles in the adjacent region; after this, separating the quantitative direction relationships between object groups into the ones between the vertices and the edges of the triangles (i.e. the local quantitative direction relationships) for calculation; and finally, transforming and fusing the local quantitative direction relationships into the qualitative direction relationships between object groups. Results: The experimental results show that:(1) The proposed model can reasonably classify the direction relationships between object groups, and accurately distinguish and describe the direction relationships in some complex situations. (2) It can fully consider the impacts of the distribution shapes of object groups and the distribution density of their sub-objects on direction relationships, and effectively determine the direction relationships between different geometric types of object groups in map space. Conclusions: The proposed model has good applicability and feasibility, which can overcome the disadvantages of the existing models, and improve the accuracy of determining the direction relationships between object groups.