Integrating physical model-based features and spatial contextual information to estimate building height in complex urban areas

Building height, as an essential measure of urban vertical structure, is key to understanding how urbanization is reshaping inner-city characteristics, particularly in developing countries. However, estimating building height in urban environments remains challenging. Building height estimation with physical model-based feature approaches and machine learning approaches are limited by a constrained large-scale application capability and the lack of physical significance, respectively. In this study, we proposed a two-step method to estimate building height in spatially heterogeneous urban areas by integrating the merits of machine learning approaches and physical model-based features, together with spatial contextual information. First, we trained a block-level machine learning model on Hangzhou block units to estimate average block-level building height as spatial contextual information. Second, we trained a building-level machine learning model to estimate the final building height of Hangzhou with the estimated spatial contextual information and additional physical model-based features, including radar look angle, building wall orientation, the length of the building, and dielectric constants of the building wall. Our results showed that the proposed method can largely improve the performance of building height estimation, with an overall R2 and RMSE of 0.76 and 6.64 m, respectively. Incorporating physical model-based features and spatial contextual information reduced model RMSE by 32 %. Compared with existing methods, our proposed model demonstrated a better accuracy performance and improved capability in addressing the prevailing overestimation of low-rise buildings and the underestimation of high-rise buildings in highly heterogeneous urban areas.