###### Abstract  
In the field of multi-view satellite photogrammetry, the neural radiance field (NeRF) method has received widespread attention due to its ability to provide continuous scene representation and realistic rendering effects. However, the satellite radiance field methods based on the NeRF are limited by the slow training speed of the original NeRF, and the scene reconstruction efficiency is low. Training for a single scene usually takes 8-10 h or even longer, which severely constrains the utilization and exploration of the NeRF approach within the domain of satellite photogrammetry. In response to the above problems, we propose an efficient neural radiance field method called SatelliteRF, which aims to quickly and efficiently reconstruct the earth's surface through multi-view satellite images. By introducing innovative multi-resolution hash coding, SatelliteRF enables the model to greatly increase the training speed while maintaining high reconstruction quality. This approach allows for smaller multi-layer perceptron (MLP) networks, reduces the computational cost of neural rendering, and accelerates the training process. Furthermore, to overcome the challenges of illumination changes and transient objects encountered when processing multi-date satellite images, we adopt an improved irradiance model and learn transient embeddings for each image. This not only increases the adaptability of the model to illumination variations but also improves its ability to handle changing objects. We also introduce a loss function based on stochastic structural similarity (SSIM) to provide structural information of the scene for model training, which further improves the quality and detailed performance of the reconstructed scene. Through extensive experiments on the DFC 2019 dataset, we demonstrate that SatelliteRF is not only able to significantly reduce the training time for the same region from the original 8-10 h to only 5-10 min but also achieves better performance in terms of rendering and the reconstruction quality. multi-view satellite photogrammetry; implicit representation and neural radiance fields; earth surface reconstruction +
Footnote †: journal: Applied  
0000-0001-990-22001-1999-2  
active sensor technologies such as lidar, 3D reconstruction methods based on multi-view satellite images are widely used in urban mapping [5; 6], environmental monitoring [7], navigation [8], and emergency rescue [9; 10] due to their advantages in terms of easily accessible data, high collection efficiency, and low cost. However, 3D reconstructions based on multi-view satellite images still face many challenges. Unlike stereo or tri-stereo images, which are acquired almost simultaneously, multi-view satellite images are usually obtained during multiple acquisitions at different times, which means that images from different viewpoints may vary due to illumination conditions, seasonal changes, and changes in the surface content [11]. In addition, the number of multi-view satellite images and the distribution of viewpoints are often sparse. These characteristics greatly increase the difficulty of the 3D reconstruction of satellite remote sensing. In traditional 3D reconstruction methods for satellite images, stereo matching methods like semiglobal matching (SGM) [12] are usually first used to generate depth maps, and then these depth maps are fused to build the digital surface model (DSM). The entire 3D reconstruction pipeline involves several steps such as stereo pair selection, dense stereo matching, triangulation, and depth map fusion [13]. When processing multi-view satellite images with appearance variations, this approach may struggle to extract effective visual features, resulting in holes or complete failure. Additionally, the selection of stereo pairs and the process of designing features often depend on manual design and expert knowledge. Deep-learning-based approaches improve the robustness of appearance changes in multi-view satellite images.