Measuring the similarity of building patterns using Graph Fourier transform

Building patterns analysis is critical for landscape evaluation, social analysis, and urban planning. Quantitative evaluation of building patterns is a challenging task because both the complex morphological properties and the spatial similarity relations/degree of the building groups must be considered on a global scale. The existing methods focus on the building pattern indicators (e.g., density) in the spatial domain that can hardly measure all of the features of the building pattern with different group alignments and individual properties. To measure the similarity between two building patterns, it is necessary to first identify their consistent characteristics and then calculate their relative deviation from each other in terms of the extracted characteristics. In this process, we need to use the graph model, and in terms of the effect of the existing graph model measurement methods, the performance of the measurement methods in the frequency domain is obviously better than that in the spatial domain, and therefore, Our research builds a bridge between the spatial domain and the frequency domain and measures the similarity of the building patterns in the corresponding frequency domain. The proposed Graph Fourier transform (GFT)-based method first constructs a Delaunay triangulation graph to represent the building groups in the map space. The spatial similarity relations/degrees and morphological properties of building objects are used in the graph to model the nodes and edges with weights. Then, we apply the GFT to transform the graph from the spatial domain into the frequency domain. Thus, the similarity between the building patterns is equivalent to their deviation from each other with respect to the frequency domain features. The whole measuring process combines the geometric features and pattern-related variables (e.g., area and orientation). Using experiments on building pattern analysis and spatial retrieval, we show that the GFT-based results are consistent with those of human cognition.