# ImplicitTerrain: a Continuous Surface Model for Terrain Data Analysis

arXiv: https://arxiv.org/abs/2406.00227 · HTML: https://mlsanity.com/paper/2406.00227/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 45 of its 80 references that are in the map.
- First posted on arXiv 31 May 2024.

## Builds on (most cited first, 30 of 45)

- [Instant Neural Graphics Primitives with a Multiresolution Hash Encoding](https://mlsanity.com/paper/2201.05989/) (2022)
- [DeepSDF: Learning Continuous Signed Distance Functions for Shape Representation](https://mlsanity.com/paper/1901.05103/) (2019)
- [Implicit Neural Representations with Periodic Activation Functions](https://mlsanity.com/paper/2006.09661/) (2020)
- [Fourier Features Let Networks Learn High Frequency Functions in Low Dimensional Domains](https://mlsanity.com/paper/2006.10739/) (2020)
- [Occupancy Networks: Learning 3D Reconstruction in Function Space](https://mlsanity.com/paper/1812.03828/) (2018)
- [NeuS: Learning Neural Implicit Surfaces by Volume Rendering for Multi-view Reconstruction](https://mlsanity.com/paper/2106.10689/) (2021)
- [On the Spectral Bias of Neural Networks](https://mlsanity.com/paper/1806.08734/) (2018)
- [Learning Implicit Fields for Generative Shape Modeling](https://mlsanity.com/paper/1812.02822/) (2018)
- [Volume Rendering of Neural Implicit Surfaces](https://mlsanity.com/paper/2106.12052/) (2021)
- [Scene Representation Networks: Continuous 3D-Structure-Aware Neural Scene Representations](https://mlsanity.com/paper/1906.01618/) (2019)
- [PIFu: Pixel-Aligned Implicit Function for High-Resolution Clothed Human Digitization](https://mlsanity.com/paper/1905.05172/) (2019)
- [GIRAFFE: Representing Scenes as Compositional Generative Neural Feature Fields](https://mlsanity.com/paper/2011.12100/) (2020)
- [Convolutional Occupancy Networks](https://mlsanity.com/paper/2003.04618/) (2020)
- [Implicit Geometric Regularization for Learning Shapes](https://mlsanity.com/paper/2002.10099/) (2020)
- [Differentiable Volumetric Rendering: Learning Implicit 3D Representations without 3D Supervision](https://mlsanity.com/paper/1912.07372/) (2019)
- [Scientific Machine Learning through Physics-Informed Neural Networks: Where we are and What's next](https://mlsanity.com/paper/2201.05624/) (2022)
- [Learning Continuous Image Representation with Local Implicit Image Function](https://mlsanity.com/paper/2012.09161/) (2020)
- [Neural Fields in Visual Computing and Beyond](https://mlsanity.com/paper/2111.11426/) (2021)
- [SAL: Sign Agnostic Learning of Shapes from Raw Data](https://mlsanity.com/paper/1911.10414/) (2019)
- [Local Implicit Grid Representations for 3D Scenes](https://mlsanity.com/paper/2003.08981/) (2020)
- [Implicit Functions in Feature Space for 3D Shape Reconstruction and Completion](https://mlsanity.com/paper/2003.01456/) (2020)
- [DISN: Deep Implicit Surface Network for High-quality Single-view 3D Reconstruction](https://mlsanity.com/paper/1905.10711/) (2019)
- [Deep Local Shapes: Learning Local SDF Priors for Detailed 3D Reconstruction](https://mlsanity.com/paper/2003.10983/) (2020)
- [Neural Radiance Flow for 4D View Synthesis and Video Processing](https://mlsanity.com/paper/2012.09790/) (2020)
- [Neural Unsigned Distance Fields for Implicit Function Learning](https://mlsanity.com/paper/2010.13938/) (2020)
- [NeRV: Neural Representations for Videos](https://mlsanity.com/paper/2110.13903/) (2021)
- [COIN: COmpression with Implicit Neural representations](https://mlsanity.com/paper/2103.03123/) (2021)
- [BungeeNeRF: Progressive Neural Radiance Field for Extreme Multi-scale Scene Rendering](https://mlsanity.com/paper/2112.05504/) (2021)
- [Texture Fields: Learning Texture Representations in Function Space](https://mlsanity.com/paper/1905.07259/) (2019)
- [Implicit Neural Representations for Image Compression](https://mlsanity.com/paper/2112.04267/) (2021)

## Built on by (most cited first, 3 of 3)

- [SASNet: Spatially-Adaptive Sinusoidal Networks for INRs](https://mlsanity.com/paper/2503.09750/) (2025)
- [ImplicitTerrainV2: Wavelet-Guided Spatially Adaptive Neural Terrain Representation](https://mlsanity.com/paper/2605.22556/) (2026)
- [Rethinking Amortized Neural Representations for High-Resolution Terrain Elevation Data](https://mlsanity.com/paper/2606.00404/) (2026)

## Abstract (arXiv)

Digital terrain models (DTMs) are pivotal in remote sensing, cartography, and landscape management, requiring accurate surface representation and topological information restoration. While topology analysis traditionally relies on smooth manifolds, the absence of an easy-to-use continuous surface model for a large terrain results in a preference for discrete meshes. Structural representation based on topology provides a succinct surface description, laying the foundation for many terrain analysis applications. However, on discrete meshes, numerical issues emerge, and complex algorithms are designed to handle them. This paper brings the context of terrain data analysis back to the continuous world and introduces ImplicitTerrain (Project homepage available at https://fengyee.github.io/implicit-terrain/), an implicit neural representation (INR) approach for modeling high-resolution terrain continuously and differentiably. Our comprehensive experiments demonstrate superior surface fitting accuracy, effective topological feature retrieval, and various topographical feature extraction that are implemented over this compact representation in parallel. To our knowledge, ImplicitTerrain pioneers a feasible continuous terrain surface modeling pipeline that provides a new research avenue for our community.