A Novel Method for Comparing Building Height Hierarchies

Understanding the hierarchical patterns of building heights is essential for sustainable urban development and planning. This study presents a novel approach for detecting and comparing building height hierarchies in four major bay areas: the San Francisco Bay Area, the New York Bay Area in the United States, the Tokyo Bay Area in Japan, and the Guangdong-Hong Kong-Macau Greater Bay Area in China. Kernel density estimation was first used to create continuous spatial distributions of building heights, forming the basis for our analysis. The approach then uses the contour tree algorithm to abstract and visualize these hierarchies. A structural similarity index is proposed to compare the hierarchies by identifying the maximum common sub-contour tree across the different contour trees. The results reveal that all four bay areas exhibit a multi-core hierarchical structure, with the greater bay area exhibiting the most complex pattern. Quantitative comparison reveals that the building height hierarchies of the New York Bay Area and Tokyo Bay Area are most similar (similarity index = 0.74), while those of the San Francisco Bay Area and Greater Bay Area are the least similar (similarity index = 0.17). Our approach provides a practical tool for understanding building height hierarchies and can be readily applied to analyze diverse spatial patterns.