A training-free method for estimating the relative height of buildings

Abstract. Urbanization’s vertical shift underscores the need for accurate building height estimation to support sustainable planning. Existing methods, limited by low-resolution data and poor generalization, cannot resolve individual buildings. We propose a training-free approach leveraging the foundation model Depth Anything V2 for relative depth estimation from high-resolution remote sensing (RS) imagery. To address GPU memory constraints, RS images are cropped into overlapping patches, and their depth predictions are unified using a height-weighted graph optimization with Levenberg–Marquardt refinement, prioritizing building-related errors. A viewpoint bias filter, modeled as terrain variation, converts relative depth to height by subtracting a morphologically derived DEM. Experiments on Google satellite imagery with 0.5 m resolution over 20 km² in Wuhan, validated against airborne LiDAR, show an R² of 0.73 for building heights, significantly outperforming the state-of-the-art MLSBRN whose R² is only 0.25 and which underestimates tall buildings. Without annotation or training, our scalable method accurately estimates individual building heights, generalizes across complex urban morphologies, and provides a robust solution for 3D urban studies.