ImplicitTerrainV2: Wavelet-Guided Spatially Adaptive Neural Terrain Representation

Haoan Feng, Xin Xu, Leila De Floriani · University of Maryland, College Park

ACM SIGSPATIAL 2026

Project page · Paper (arXiv) · Earlier work: ImplicitTerrain

Overview of the ImplicitTerrainV2 pipeline. A terrain DEM is decomposed into a smooth shape model with gradient matching and a residual geometry model with WCF-guided spatial adaptivity. The combined representation supports topological and topographical analysis via analytical gradients, and model compression yields a compact neural terrain data format.

Summary

ImplicitTerrainV2 encodes a terrain tile as a cascade of two frequency-controlled SIREN networks: a smooth shape model trained with gradient supervision, and a residual geometry model whose high-frequency capacity is gated in space by a wavelet complexity field computed analytically from the input. On 50 morphologically diverse swissALTI3D tiles it reaches 66.25 dB end-to-end PSNR at 124K parameters, improving over ImplicitTerrain by +5.70 dB with 3.2× fewer parameters and 55 s of training per tile. Mixed-precision quantization and entropy coding compress the stored model to 1.23 bpp at a 0.28 dB cost, and the resulting format answers off-grid queries, returns closed-form derivatives, and reconstructs at arbitrary resolution.

Code

The reference implementation is in code/: the cascaded model, the two-stage training pipeline, end-to-end evaluation, and topographic analysis from analytical derivatives. To verify an install, run the smoke test, which fits a synthetic tile on CPU and needs no data:

cd code
python scripts/fit_tile.py --tile synthetic --max_side 128 --iters 60 --device cpu

See code/README.md for usage and configuration.

Related projects

• ImplicitTerrain (CVPR 2024 Workshop INRV) · code — the predecessor. ImplicitTerrainV2 keeps its cascade of a smooth surface model and a residual geometry model, and is benchmarked against it.
• SASNet (CVPR 2026) · code — the band-wise frequency masking in the geometry model is adopted from SASNet. ImplicitTerrainV2 derives the masks from the wavelet complexity field instead of training a hash-grid branch jointly with the network.
• Rethinking Amortized Neural Representations for Terrain (ACM SIGSPATIAL 2026, poster) · code — the companion paper on swisstopo terrain, from the amortized side: one shared model maps each tile to a compact token, where ImplicitTerrainV2 fits a network per tile.

Citation

@inproceedings{feng2026implicitterrainv2,
  title     = {ImplicitTerrainV2: Wavelet-Guided Spatially Adaptive Neural Terrain Representation},
  author    = {Feng, Haoan and Xu, Xin and De Floriani, Leila},
  booktitle = {Proceedings of the 34th ACM International Conference on Advances in Geographic Information Systems (SIGSPATIAL '26)},
  year      = {2026},
  eprint    = {2605.22556},
  archivePrefix = {arXiv},
  primaryClass  = {cs.LG}
}

License

Four different terms apply to the contents of this repository:

• Site code (index.html, static/css/index.css): MIT, see LICENSE.
• Reference implementation (code/): MIT, see code/LICENSE.
• Page template: adapted from the Nerfies project page, released under CC BY-SA 4.0.
• Paper figures (static/images/*): © 2026 the authors; publication rights licensed to ACM. Not covered by the MIT license above — reuse is governed by the ACM copyright notice in the published paper.