# Rational Polynomial Camera Model Warping for Deep Learning Based Satellite Multi-View Stereo Matching

arXiv: https://arxiv.org/abs/2109.11121 · HTML: https://mlsanity.com/paper/2109.11121/

## Key facts

- Cited by 14 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 33 references that are in the map.
- First posted on arXiv 23 Sep 2021.

## Builds on (most cited first, 15 of 15)

- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Feature Pyramid Networks for Object Detection](https://mlsanity.com/paper/1612.03144/) (2016)
- [A Large Dataset to Train Convolutional Networks for Disparity, Optical Flow, and Scene Flow Estimation](https://mlsanity.com/paper/1512.02134/) (2015)
- [MVSNet: Depth Inference for Unstructured Multi-view Stereo](https://mlsanity.com/paper/1804.02505/) (2018)
- [Cascade Cost Volume for High-Resolution Multi-View Stereo and Stereo Matching](https://mlsanity.com/paper/1912.06378/) (2019)
- [End-to-End Learning of Geometry and Context for Deep Stereo Regression](https://mlsanity.com/paper/1703.04309/) (2017)
- [DeepMVS: Learning Multi-view Stereopsis](https://mlsanity.com/paper/1804.00650/) (2018)
- [Recurrent MVSNet for High-resolution Multi-view Stereo Depth Inference](https://mlsanity.com/paper/1902.10556/) (2019)
- [Cost Volume Pyramid Based Depth Inference for Multi-View Stereo](https://mlsanity.com/paper/1912.08329/) (2019)
- [Deep Stereo using Adaptive Thin Volume Representation with Uncertainty Awareness](https://mlsanity.com/paper/1911.12012/) (2019)
- [SurfaceNet: An End-to-end 3D Neural Network for Multiview Stereopsis](https://mlsanity.com/paper/1708.01749/) (2017)
- [Semantic Stereo for Incidental Satellite Images](https://mlsanity.com/paper/1811.08739/) (2018)
- [A Novel Recurrent Encoder-Decoder Structure for Large-Scale Multi-view Stereo Reconstruction from An Open Aerial Dataset](https://mlsanity.com/paper/2003.00637/) (2020)
- [Learned Multi-Patch Similarity](https://mlsanity.com/paper/1703.08836/) (2017)
- [Leveraging Vision Reconstruction Pipelines for Satellite Imagery](https://mlsanity.com/paper/1910.02989/) (2019)

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

- [Sat-NeRF: Learning Multi-View Satellite Photogrammetry With Transient Objects and Shadow Modeling Using RPC Cameras](https://mlsanity.com/paper/2203.08896/) (2022)
- [EarthNets: Empowering AI in Earth Observation](https://mlsanity.com/paper/2210.04936/) (2022)
- [SparseSat-NeRF: Dense Depth Supervised Neural Radiance Fields for Sparse Satellite Images](https://mlsanity.com/paper/2309.00277/) (2023)
- [Skyfall-GS: Synthesizing Immersive 3D Urban Scenes from Satellite Imagery](https://mlsanity.com/paper/2510.15869/) (2025)
- [SkySplat: Generalizable 3D Gaussian Splatting from Multi-Temporal Sparse Satellite Images](https://mlsanity.com/paper/2508.09479/) (2025)
- [SUNDIAL: 3D Satellite Understanding through Direct, Ambient, and Complex Lighting Decomposition](https://mlsanity.com/paper/2312.16215/) (2023)
- [From Orbit to Ground: Generative City Photogrammetry from Extreme Off-Nadir Satellite Images](https://mlsanity.com/paper/2512.07527/) (2025)
- [Sat3DGen: Comprehensive Street-Level 3D Scene Generation from Single Satellite Image](https://mlsanity.com/paper/2605.14984/) (2026)
- [Pursuing 3D Scene Structures with Optical Satellite Images from Affine Reconstruction to Euclidean Reconstruction](https://mlsanity.com/paper/2201.06037/) (2022)
- [RPC-GS: Gaussian Splatting with native RPC Rendering for Satellite Imagery](https://mlsanity.com/paper/2606.06690/) (2026)
- [EO-VGGT: Orbital Ray-Conditioned 3D Foundation Models for Satellite Multi-View Reconstruction](https://mlsanity.com/paper/2607.00417/) (2026)
- [Refined Equivalent Pinhole Model for Large-scale 3D Reconstruction from Spaceborne CCD Imagery](https://mlsanity.com/paper/2310.20117/) (2023)
- [Multi-view dense image matching with similarity learning and geometry priors](https://mlsanity.com/paper/2505.11264/) (2025)
- [GeoRay: Gauge-Aware Feed-Forward Satellite 3D Reconstruction in the Geodetic Frame](https://mlsanity.com/paper/2608.29680/) (2026)

## Abstract (arXiv)

Satellite multi-view stereo (MVS) imagery is particularly suited for large-scale Earth surface reconstruction. Differing from the perspective camera model (pin-hole model) that is commonly used for close-range and aerial cameras, the cubic rational polynomial camera (RPC) model is the mainstream model for push-broom linear-array satellite cameras. However, the homography warping used in the prevailing learning based MVS methods is only applicable to pin-hole cameras. In order to apply the SOTA learning based MVS technology to the satellite MVS task for large-scale Earth surface reconstruction, RPC warping should be considered. In this work, we propose, for the first time, a rigorous RPC warping module. The rational polynomial coefficients are recorded as a tensor, and the RPC warping is formulated as a series of tensor transformations. Based on the RPC warping, we propose the deep learning based satellite MVS (SatMVS) framework for large-scale and wide depth range Earth surface reconstruction. We also introduce a large-scale satellite image dataset consisting of 519 5120×5120 images, which we call the TLC SatMVS dataset. The satellite images were acquired from a three-line camera (TLC) that catches triple-view images simultaneously, forming a valuable supplement to the existing open-source WorldView-3 datasets with single-scanline images. Experiments show that the proposed RPC warping module and the SatMVS framework can achieve a superior reconstruction accuracy compared to the pin-hole fitting method and conventional MVS methods. Code and data are available at https://github.com/WHU-GPCV/SatMVS.