# ImplicitTerrainV2: Wavelet-Guided Spatially Adaptive Neural Terrain Representation

arXiv: https://arxiv.org/abs/2605.22556 · HTML: https://mlsanity.com/paper/2605.22556/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 24 of its 65 references that are in the map.
- First posted on arXiv 21 May 2026.

## Builds on (most cited first, 24 of 24)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Instant Neural Graphics Primitives with a Multiresolution Hash Encoding](https://mlsanity.com/paper/2201.05989/) (2022)
- [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)
- [On the Spectral Bias of Neural Networks](https://mlsanity.com/paper/1806.08734/) (2018)
- [Mixed Precision Training](https://mlsanity.com/paper/1710.03740/) (2017)
- [Implicit Geometric Regularization for Learning Shapes](https://mlsanity.com/paper/2002.10099/) (2020)
- [COIN: COmpression with Implicit Neural representations](https://mlsanity.com/paper/2103.03123/) (2021)
- [Sobolev Training for Neural Networks](https://mlsanity.com/paper/1706.04859/) (2017)
- [BACON: Band-limited Coordinate Networks for Multiscale Scene Representation](https://mlsanity.com/paper/2112.04645/) (2021)
- [Frequency Bias in Neural Networks for Input of Non-Uniform Density](https://mlsanity.com/paper/2003.04560/) (2020)
- [SAPE: Spatially-Adaptive Progressive Encoding for Neural Optimization](https://mlsanity.com/paper/2104.09125/) (2021)
- [COOL-CHIC: Coordinate-based Low Complexity Hierarchical Image Codec](https://mlsanity.com/paper/2212.05458/) (2022)
- [Where Do We Stand with Implicit Neural Representations? A Technical and Performance Survey](https://mlsanity.com/paper/2411.03688/) (2024)
- [Improved Implicit Neural Representation with Fourier Reparameterized Training](https://mlsanity.com/paper/2401.07402/) (2024)
- [INCODE: Implicit Neural Conditioning with Prior Knowledge Embeddings](https://mlsanity.com/paper/2310.18846/) (2023)
- [Exploring Differential Geometry in Neural Implicits](https://mlsanity.com/paper/2201.09263/) (2022)
- [Tuning the Frequencies: Robust Training for Sinusoidal Neural Networks](https://mlsanity.com/paper/2407.21121/) (2024)
- [High-performance Effective Scientific Error-bounded Lossy Compression with Auto-tuned Multi-component Interpolation](https://mlsanity.com/paper/2311.12133/) (2023)
- [Sobolev Training for Implicit Neural Representations with Approximated Image Derivatives](https://mlsanity.com/paper/2207.10395/) (2022)
- [Critical Features Tracking on Triangulated Irregular Networks by a Scale-Space Method](https://mlsanity.com/paper/2409.06638/) (2024)
- [A Unified Theory of Sinusoidal Activation Families for Implicit Neural Representations](https://mlsanity.com/paper/2502.00869/) (2025)
- [ImplicitTerrain: a Continuous Surface Model for Terrain Data Analysis](https://mlsanity.com/paper/2406.00227/) (2024)
- [Spatially-Adaptive Hash Encodings For Neural Surface Reconstruction](https://mlsanity.com/paper/2412.05179/) (2024)

## Abstract (arXiv)

Digital elevation models (DEMs) underpin terrain analysis in Geographic Information Systems (GIS), but commonly as raster representation, they rely on interpolation for off-grid sampling and finite-difference operators for derivative-based analysis. Implicit neural representations (INRs) offer a continuous alternative, but prior terrain INRs lack explicit frequency control, neglect the gradient structure of terrain, and remain too large and costly to train for practical deployment. We present ImplicitTerrainV2, which advances terrain INRs toward a compact, efficient neural terrain data format by combining a spectral control mechanism with wavelet-guided spatial adaptivity, derivative-aware supervision, and post-training model compression. At its core, a wavelet complexity field (WCF) derives spatially-adaptive frequency masks from analytically computed wavelet coefficients, localizing high-frequency capacity to complex terrain regions. The same field guides complexity-aware adaptive sampling that concentrates training in high-complexity regions, while gradient matching applies extra supervision to enforce the smooth manifold structure of terrain DEMs for improved derivative fidelity. Post-training mixed-precision quantization and entropy coding reduce storage to 1.23 bpp with a 0.28 dB PSNR drop. On 50 morphologically diverse Swiss terrain tiles, ImplicitTerrainV2 reaches 66.25 dB end-to-end PSNR, improving over the prior work by 5.70 dB while using 3.2x fewer parameters and training in 55 s per tile on a single GPU. Our compressed neural format is competitive with several established DEM codecs in rate-distortion performance, while additionally supporting off-grid point queries, closed-form derivative evaluation, and resolution-independent reconstruction, which may benefit many downstream GIS applications.