A continuous digital elevation representation model for DEM super-resolution

The surface of the Earth is continuous, and obtaining precise elevation data at arbitrary query positions is essential for many applications and analyses. However, existing digital elevation models suffer from a precision gap caused by discretization. Therefore, we develop a new continuous representation model (CDEM) that allows height values to be obtained at any arbitrary query position. Inspired by recent research on the implicit neural representation model, we train an encoder-decoder network to learn CDEM from discrete elevation data for DEM super-resolution tasks. The encoder targets generating latent codes from discrete elevation data, while the decoder composes these latent codes with query positions to predict corresponding elevation values. Such a learning pipeline is well-suited for DEM super-resolution tasks. To improve model accuracy, we also propose predicting the bias of elevation values between the query position and its closest known position. Real-world terrain surfaces exhibit inherent roughness with numerous small variations in localized regions, resulting in high-frequency targets that are difficult for neural networks to fit. In order to facilitate the network's ability to model data with high-frequency variations, we introduce positional encoding to map query positions into a higher-dimensional space. Compared to the Bicubic interpolation method and state-of-the-art TfaSR model, our method is demonstrated to obtain more accurate elevation values and preserve more details of terrain structure on the TFASR30, Pyrenees, and Tyrol datasets. Specifically, our EBCF-CDEM model demonstrates performance improvements over the TfaSR model, with reductions in the RMSE of elevation, slope, and aspect by 7.03%, 4.81%, and 3.07% respectively at x4 super-resolution scale on the TFASR30 dataset, by 9.92%, 7.06%, and 6.15% at x8 super-resolution scale on the Pyrenees dataset. Extensive experiments further validate the generalizability of our EBCF-CDEM, compared to the TfaSR model, our results in terms of RMSE of elevation, slope, and aspect are reduced by 14.78%, 12.12%, and 8.99% respectively at x8 super-resolution scale on the Tyrol dataset, and 26.92%, 7.14% and 5.36% on the TIFASR30to10 dataset. We release our source code (including the datasets) at https://github.com/AlcibiadesTophetScipio/EBCF-CDEM to reproduce our results and encourage future research.