Spatially explicit feature importance for building height estimation using research-access high-resolution SAR and optical sensors
Using geographically weighted random forest with TerraSAR-X, PlanetScope, and Sentinel-1 data, building height prediction RMSE is 5.34 meters in Porto Alegre.
Key Findings
Methodology
This study employs a geographically weighted random forest (GWRF) model integrating multi-source remote sensing data for building height estimation. Data sources include TerraSAR-X StripMap SAR, PlanetScope optical imagery, and Sentinel-1 SAR data. Features extracted encompass building footprint geometry, shadow length, spectral indices (NDVI, NDBI), SAR backscatter and texture, and InSAR-derived digital surface models (DSM). For each building, zonal statistics generate a 66-variable feature set. Recognizing the spatial autocorrelation of building heights, the model applies spatial weighting, fitting local RF models for each building by weighting nearby samples. Feature importance analysis reveals spatially varying contributions: geometric features dominate for low-rise buildings, shadow-derived height for taller, isolated structures, and spectral reflectance for the tallest buildings. Validation shows RMSE of 5.34 meters and R² of 0.756, outperforming non-spatial models. Spatial importance maps highlight the differential sensor contributions across urban contexts, providing interpretability and practical insights.
Key Results
- The combined GWRF model achieves RMSE=5.34 m and R²=0.756, significantly better than global RF models (RMSE≈5.76 m, R²≈0.716), demonstrating the advantage of spatially adaptive modeling.
- Feature importance analysis indicates that for buildings under 6 meters, geometry accounts for 32.4%; for 6-20 meters, shadow features increase in importance; for buildings over 35 meters, spectral reflectance becomes dominant, reflecting the changing predictive power of different sensors.
- Spatial distribution of predictor importance reveals that urban core areas favor shadow and spectral features, while suburban zones rely more on geometric attributes. This heterogeneity underscores the necessity of spatially sensitive models for accurate urban remote sensing.
Significance
This research addresses the critical gap in urban 3D data in resource-limited regions by leveraging openly accessible multi-source satellite data. The spatial interpretability of the GWRF model offers valuable insights into sensor contributions across different urban typologies, facilitating targeted data collection and model deployment. The approach enhances the feasibility of detailed urban monitoring without reliance on costly LiDAR, supporting urban planning, disaster management, and material stock assessments in the Global South. Moreover, the methodology demonstrates how combining SAR and optical data within a spatially explicit framework can unlock new levels of accuracy and interpretability, advancing the state-of-the-art in satellite-based urban height estimation.
Technical Contribution
This study introduces the innovative application of GWRF to multi-source remote sensing data for building height estimation, effectively capturing spatial heterogeneity. The model integrates diverse features—geometric, shadow, spectral, SAR backscatter, and InSAR—within a local regression framework, overcoming limitations of traditional global models. The feature importance analysis at the local level provides physical interpretability, revealing how different sensors contribute variably across urban contexts. This approach advances the field by combining spatial modeling with multi-modal data fusion, offering a high-resolution, interpretable alternative to deep learning methods, and setting a new benchmark for resource-constrained urban remote sensing.
Novelty
The key novelty lies in applying a geographically weighted random forest to fuse SAR, optical, and InSAR data for building height prediction, with explicit analysis of spatially varying feature importance. Unlike previous global models, this approach captures local differences in sensor contributions, revealing the heterogeneity of urban environments. The integration of shadow analysis, spectral indices, and SAR texture within a spatially adaptive framework is unprecedented, providing both high accuracy and interpretability. This work is among the first to systematically analyze the spatial distribution of predictor importance across different urban typologies, especially in resource-limited settings, offering new insights into multi-modal remote sensing fusion.
Limitations
- The model's accuracy diminishes in highly complex terrains or densely built-up areas where shadow and SAR signals saturate or become ambiguous, potentially leading to larger errors.
- Dependence on high-quality LiDAR reference data for training may limit applicability where such data are unavailable or unreliable.
- The study is validated only in Porto Alegre; its generalizability to other cities with different urban morphologies and sensor configurations remains to be tested.
- Prediction of very tall buildings (>50 meters) still faces challenges due to sensor saturation and limited feature sensitivity, requiring further methodological enhancements.
Future Work
Future research should explore deep learning architectures like CNNs for improved high-rise prediction, incorporate multi-temporal data for dynamic urban monitoring, and validate the approach across diverse urban environments globally. Enhancing sensor fusion strategies, including hyperspectral or LiDAR-like data, could further improve accuracy for complex or tall structures. Developing transfer learning frameworks to adapt models trained in one city to others will facilitate broader applicability. Additionally, integrating this methodology into operational urban management systems can support real-time disaster response and sustainable urban development, especially in regions with limited data resources.
AI Executive Summary
In the era of rapid urbanization, acquiring accurate three-dimensional building data is vital for urban planning, disaster response, and resource management. Traditional methods like airborne LiDAR provide high precision but are costly and limited in coverage, especially in developing regions. Satellite-based approaches have emerged as promising alternatives, yet many rely on high-cost commercial imagery or coarse-resolution data that cannot resolve individual building footprints. This gap in data availability hampers effective urban monitoring, particularly in the Global South.
Addressing this challenge, the current study introduces a novel framework that combines multiple freely accessible satellite datasets—TerraSAR-X SAR, PlanetScope optical imagery, and Sentinel-1 SAR—within a geographically weighted random forest (GWRF) model. This approach leverages the unique strengths of each sensor: SAR's structural information, optical spectral and shadow features, and InSAR's surface deformation signals. By systematically extracting 66 features related to building geometry, shadow length, spectral indices, SAR backscatter, and texture, the model captures diverse cues indicative of building height.
The core innovation lies in applying spatially adaptive modeling. Recognizing that urban environments are heterogeneous, the GWRF assigns local weights to training samples, fitting a separate RF model for each building based on its spatial neighborhood. This allows the model to account for local variations in sensor contribution and urban morphology, leading to more accurate and interpretable predictions. Validation in Porto Alegre demonstrates a RMSE of 5.34 meters and an R² of 0.756, outperforming traditional global models.
Feature importance analysis reveals that in low-rise areas, geometric attributes dominate, while shadow and spectral features become increasingly relevant for taller buildings. Spatial maps of predictor importance highlight how sensor contributions vary across different urban zones, providing valuable insights for targeted data collection and model refinement. The results confirm that multi-source, spatially explicit modeling can achieve detailed building height estimation without relying on costly LiDAR data.
This methodology offers a practical, scalable solution for urban authorities and researchers in resource-limited settings. It enables detailed urban analysis, supports disaster resilience planning, and facilitates material stock assessments. Future directions include integrating deep learning techniques, expanding to other cities, and developing real-time monitoring systems. Overall, this work advances the frontier of satellite-based urban 3D mapping, making high-resolution city modeling accessible and interpretable in diverse contexts.
Deep Analysis
Background
Urban building height data是城市遥感研究的重要组成部分。早期方法主要依赖激光雷达（LiDAR）和立体像对，具有高精度但成本高昂，难以大规模推广。随着遥感技术的发展，光学影像、合成孔径雷达（SAR）和InSAR技术逐渐成为替代方案。代表性研究如Frantz等（2021）结合Sentinel-1和Sentinel-2实现德国城市建筑高度映射，误差约6.07米。Yadav等（2025）利用深度学习架构将误差降至1.89米。然而，这些方法多依赖高分辨率数据，成本较高，限制了在资源有限地区的应用。近年来，学者们开始探索低成本、多源遥感数据融合的可能性，以实现更广泛的城市空间尺度下的建筑高度估算。本研究正是在此背景下，结合公开获取的TerraSAR-X、PlanetScope和Sentinel-1数据，提出空间加权模型，以提升建筑高度的空间分辨率和解释能力。
Core Problem
在全球南方地区，尤其是发展中国家，缺乏大规模、高精度的激光雷达（LiDAR）数据，严重制约城市三维信息的获取。传统方法依赖昂贵的商业高分辨率影像或激光雷达，成本高、数据获取难、更新频率低，难以满足快速发展的城市需求。此外，单一传感器在不同建筑类型和空间环境中的表现差异显著，缺乏对空间异质性的理解。如何利用低成本、公开获取的遥感数据，结合空间敏感的模型，实现高精度、细粒度的建筑高度估算，成为亟待解决的核心问题。
Innovation
本研究的创新点主要体现在以下几个方面：1）引入地理加权随机森林（GWRF）模型，有效处理空间自相关和异质性问题，提升预测精度；2）融合TerraSAR-X、PlanetScope和Sentinel-1多源数据，充分利用结构信息、材料反射和微变形特征，丰富特征空间；3）系统提取66个多模态特征，结合建筑轮廓、阴影、光谱、SAR背散射和纹理，实现多角度、多尺度的特征表达；4）通过空间局部特征重要性分析，揭示不同建筑类型和空间区域的特征贡献差异，为城市规划提供可解释的依据。这些创新共同推动了低成本、多源遥感建筑高度估算的技术发展。
Methodology
- �� 数据采集：整合TerraSAR-X StripMap SAR数据、PlanetScope光学影像和Sentinel-1 SAR数据，获得Porto Alegre市区的多源遥感影像。
- �� 特征提取：从光学影像中提取NDVI、NDBI、亮度等光谱指标及纹理特征；利用阴影指数和太阳角度计算阴影长度，估算建筑高度；通过InSAR差分生成数字表面模型（DSM）；提取SAR背散射强度和纹理特征；分析建筑轮廓几何属性（面积、周长、方向、延展性）及空间邻近关系。
- �� 数据预处理：对所有特征进行区域统计，确保每个建筑物的特征完整性，构建包含66个变量的特征集。
- �� 空间自相关分析：采用Moran's I检验建筑高度的空间聚集性，确认模型需要空间敏感策略。
- �� 模型构建：基于空间加权思想，采用GWRF模型，为每个建筑局部拟合随机森林，结合局部与全局预测。
- �� 特征重要性分析：在空间层面评估每个特征的贡献，识别不同空间和建筑类型的主导特征。
- �� 模型验证：采用10折交叉验证，评估RMSE和R²指标，比较空间加权与非空间模型性能。
Experiments
实验在Porto Alegre市进行，利用LiDAR数据作为参考，验证模型的预测能力。模型训练采用包含66个特征的全数据集，采用10折交叉验证，确保结果的稳健性。对比分析包括全局随机森林模型和空间加权模型的性能差异。特征重要性通过局部分析揭示不同建筑类型和空间区域的特征贡献。模型参数如带宽和空间权重比值通过空间自相关分析优化。实验还分析了不同建筑高度区间的特征贡献差异，验证模型在低层、中层和高层建筑中的适应性。最终，模型在验证集中实现了RMSE为5.34米，R²为0.756，充分展现了多源数据融合和空间加权策略的有效性。
Results
模型整体性能优异，RMSE为5.34米，R²达0.756，显著优于传统非空间模型（RMSE约5.76米，R²约0.716），验证了空间加权策略的有效性。特征重要性分析显示，低层建筑（<6米）主要由几何特征支配，占比32.4%；中高层建筑（6-20米）阴影特征占比逐步上升；超高层建筑（>35米）由光谱反射率主导，反映不同建筑类型的特征差异。空间分布分析揭示，不同城市区域的建筑高度预测依赖不同传感器组合。例如，市中心区域阴影和光谱特征占优势，而郊区则几何特征更重要。这种空间异质性为城市规划和灾后评估提供了有价值的参考。
Applications
该方法适用于城市基础数据的快速更新、灾害后重建评估和材料存量统计。城市规划部门可以利用模型提供的高精度建筑高度信息，优化土地利用和基础设施布局。灾害响应中，快速获得建筑损毁情况，辅助决策制定。研究还可推广至其他资源有限地区，推动低成本城市遥感监测体系的建立。未来结合动态多时相数据，有望实现城市变化的实时监测和管理，为智能城市建设提供技术支撑。
Limitations & Outlook
模型在极端复杂地形或密集城区中可能受到阴影和SAR信号饱和的影响，导致预测误差增加。参考LiDAR数据的质量直接影响模型训练效果，若数据偏差会带来误导。模型目前仅在Porto Alegre验证，泛化能力有限，需在不同城市和地理环境中验证其适用性。除此之外，高层建筑（>50米）预测仍存在困难，需引入更丰富的特征或深度学习技术以提升性能。
Plain Language Accessible to non-experts
想象你在一个工厂里工作，工厂里有许多不同高度的机器。有些机器很矮，有些很高。工厂的管理者想知道每台机器的高度，但他们不能逐一测量，因为工厂太大了，太费时间。于是，他们用了一些特殊的相机和传感器，从不同角度拍摄工厂的图片和视频。这些相机可以看到机器的结构、投下的影子、反射的光线。工程师们把这些信息变成数据，比如机器的轮廓、影子长度、反光程度。然后，他们用一种聪明的算法，把这些数据结合起来，建立一个模型，告诉他们每台机器大概有多高。
这个模型就像一个非常聪明的机器人，它可以根据不同的线索判断机器的高度。比如，矮的机器主要靠轮廓线判断，高的机器则靠影子和反光来估算。这个方法非常节省时间和成本，而且还能告诉管理者工厂里哪些机器很高，哪些很矮。这样，他们就能更好地安排工作，确保每台机器都在合理的位置上。这个过程就像用不同的观察角度和线索，拼凑出工厂里每台机器的高度图谱，非常有趣，也非常实用。
ELI14 Explained like you're 14
想象你在学校操场玩影子游戏。你用手挡住太阳，观察影子变长还是变短。你发现，影子越长，物体越高；影子越短，物体越矮。现在，假设你想知道远处建筑的高度，但不能直接测量。于是，你用一台特殊的相机拍摄建筑，得到建筑的影子长度和反光情况。你还用另一台相机看建筑的轮廓和形状。通过这些信息，你可以用一些数学方法，把影子长度和反光情况转化成建筑的高度。这个过程就像拼图游戏，把不同的线索拼在一起，帮你猜出建筑有多高。科学家们用类似的方法，结合遥感数据，建立模型，预测城市中每栋建筑的高度。这样，即使没有直接测量，也能得到详细的城市天际线信息。这对城市规划和灾害评估都非常有帮助，就像用影子游戏了解远处的建筑一样聪明又有趣！
Abstract
Accurate building height information at the individual footprint scale is essential for material stock accounting and post-disaster damage assessments yet remains difficult to obtain at city scale in the Global South where airborne LiDAR coverage is rare and commercial very high-resolution imagery is cost-prohibitive or unavailable. While recent works have demonstrated building height estimation using freely available Sentinel imagery, the resolution ceiling of resulting products is still coarse for material stock analysis. This study incorporates products derived from data freely accessible under scientific research licenses, TerraSAR-X StripMap and PlanetScope, alongside Sentinel-1 to predict building heights in a large city in Brazil. To account for the spatial autocorrelation in the training set, features from all sources are integrated in a geographically weighted random forest model, returning an RMSE of 5.34 m and R2 of 0.756 against a LiDAR reference dataset. Local feature importance showed predictor dominance to vary consistently across intra-urban contexts, with footprint geometry dominating for low-rise buildings, shadow-derived height for taller and more isolated structures, and spectral reflectance for the tallest buildings in the set. Sentinel-1 backscatter and InSAR occupy complementary spatial niches, with no single sensor uniformly preferable across the set. Results provide optioneering guidance and insight over satellite-derived products predictive relevance in distinct contexts, which global machine learning or neural network models cannot offer.
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