# Height estimation from single aerial images using a deep ordinal regression network

arXiv: https://arxiv.org/abs/2006.02801 · HTML: https://mlsanity.com/paper/2006.02801/

## Key facts

- Cited by 14 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 4 Jun 2020.

## Built on by (most cited first, 14 of 14)

- [Elevation Estimation-Driven Building 3D Reconstruction from Single-View Remote Sensing Imagery](https://mlsanity.com/paper/2301.04581/) (2023)
- [RingMoE: Mixture-of-Modality-Experts Multi-Modal Foundation Models for Universal Remote Sensing Image Interpretation](https://mlsanity.com/paper/2504.03166/) (2025)
- [Sub-Meter Tree Height Mapping of California using Aerial Images and LiDAR-Informed U-Net Model](https://mlsanity.com/paper/2306.01936/) (2023)
- [Remote Sensing Novel View Synthesis with Implicit Multiplane Representations](https://mlsanity.com/paper/2205.08908/) (2022)
- [SynRS3D: A Synthetic Dataset for Global 3D Semantic Understanding from Monocular Remote Sensing Imagery](https://mlsanity.com/paper/2406.18151/) (2024)
- [THE Benchmark: Transferable Representation Learning for Monocular Height Estimation](https://mlsanity.com/paper/2112.14985/) (2021)
- [HTC-DC Net: Monocular Height Estimation from Single Remote Sensing Images](https://mlsanity.com/paper/2309.16486/) (2023)
- [High Resolution Tree Height Mapping of the Amazon Forest using Planet NICFI Images and LiDAR-Informed U-Net Model](https://mlsanity.com/paper/2501.10600/) (2025)
- [Enhancing Monocular Height Estimation via Sparse LiDAR-Guided Correction](https://mlsanity.com/paper/2505.06905/) (2025)
- [HeightFormer: A Multilevel Interaction and Image-adaptive Classification-regression Network for Monocular Height Estimation with Aerial Images](https://mlsanity.com/paper/2310.07995/) (2023)
- [SC-Lane: Slope-aware and Consistent Road Height Estimation Framework for 3D Lane Detection](https://mlsanity.com/paper/2508.10411/) (2025)
- [TSE-Net: Semi-supervised Monocular Height Estimation from Single Remote Sensing Images](https://mlsanity.com/paper/2511.13552/) (2025)
- [ZRG: A Dataset for Multimodal 3D Residential Rooftop Understanding](https://mlsanity.com/paper/2304.13219/) (2023)
- [The First Assessment of PhiSat-2 Imagery for Monocular Building Height Estimation](https://mlsanity.com/paper/2603.29245/) (2026)

## Abstract (arXiv)

Understanding the 3D geometric structure of the Earth's surface has been an active research topic in photogrammetry and remote sensing community for decades, serving as an essential building block for various applications such as 3D digital city modeling, change detection, and city management. Previous researches have extensively studied the problem of height estimation from aerial images based on stereo or multi-view image matching. These methods require two or more images from different perspectives to reconstruct 3D coordinates with camera information provided. In this paper, we deal with the ambiguous and unsolved problem of height estimation from a single aerial image. Driven by the great success of deep learning, especially deep convolution neural networks (CNNs), some researches have proposed to estimate height information from a single aerial image by training a deep CNN model with large-scale annotated datasets. These methods treat height estimation as a regression problem and directly use an encoder-decoder network to regress the height values. In this paper, we proposed to divide height values into spacing-increasing intervals and transform the regression problem into an ordinal regression problem, using an ordinal loss for network training. To enable multi-scale feature extraction, we further incorporate an Atrous Spatial Pyramid Pooling (ASPP) module to extract features from multiple dilated convolution layers. After that, a post-processing technique is designed to transform the predicted height map of each patch into a seamless height map. Finally, we conduct extensive experiments on ISPRS Vaihingen and Potsdam datasets. Experimental results demonstrate significantly better performance of our method compared to the state-of-the-art methods.