A Multiscale Pyramid Model of Cardinal Directions for Different Scenarios

ABSTRACT As a crucial spatial constraint, directional relationships play an essential role in advanced spatial queries, spatial reasoning, image analysis, spatial indexing, and a variety of other applications. This paper concentrates on spatial cognitive tendencies and multiscale formal frameworks of directional associations within diverse contexts. We develop a multiscale pyramid cardinal direction model to fulfill the expression requirements in various application scenarios. The pyramid model integrates and extends existing models, thereby constructing a multiscale directional model that is suitable for spatial objects of different geometric types and varying expression accuracy demands. Firstly, it extends the direction‐relation model of reference point by increasing the division from the basic directional tiles to segmentation directional tiles, thus enhancing the accuracy of qualitative directional description. Based on the reference point model, two layers of models for extended objects are further constructed, namely the nontopological overall matrix model and the topological local matrix model. The overall matrix model evolves the directional relations matrix to the segmentation directional matrix. It regards the reference line/polygon as a whole and constructs directional tiles with two levels of expressiveness. The local matrix model, based on topological references, conducts topological partitioning and directional tile partition for the minimum bounding rectangle region, addressing the expression of directional relations under complex topological relations. Simultaneously, the pyramid model constructs two types of models: qualitative and statistical matrices, catering to the needs of spatial similarity evaluation. Notably, the new model establishes flexible conversion channels between different scale models, enabling the model to enhance expression precision while ensuring computational speed and efficiency. The experimental results validate the higher accuracy of the new model and its feasibility across various scale application scenarios.