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ImplicitTerrainV2: Wavelet-Guided Spatially Adaptive Neural Terrain Representation

arXiv 2605.22556 ↗First posted 21 May 2026cs.LGcited by 0

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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.

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.

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24 of 65 references.

References · 24

  1. 2014Adam: A Method for Stochastic Optimizationcited by 37,240
  2. 2022Instant Neural Graphics Primitives with a Multiresolution Hash Encodingcited by 3,723
  3. 2020Implicit Neural Representations with Periodic Activation Functionscited by 2,238
  4. 2020Fourier Features Let Networks Learn High Frequency Functions in Low Dimensional Domainscited by 2,200
  5. 2018On the Spectral Bias of Neural Networkscited by 1,341
  6. 2017Mixed Precision Trainingcited by 1,156
  7. 2020Implicit Geometric Regularization for Learning Shapescited by 710
  8. 2021COIN: COmpression with Implicit Neural representationscited by 233
  9. 2017Sobolev Training for Neural Networkscited by 143
  10. 2021BACON: Band-limited Coordinate Networks for Multiscale Scene Representationcited by 143
  11. 2020Frequency Bias in Neural Networks for Input of Non-Uniform Densitycited by 140
  12. 2021SAPE: Spatially-Adaptive Progressive Encoding for Neural Optimizationcited by 59
12 more
  1. 2022COOL-CHIC: Coordinate-based Low Complexity Hierarchical Image Codeccited by 51
  2. 2024Where Do We Stand with Implicit Neural Representations? A Technical and Performance Surveycited by 42
  3. 2024Improved Implicit Neural Representation with Fourier Reparameterized Trainingcited by 36
  4. 2023INCODE: Implicit Neural Conditioning with Prior Knowledge Embeddingscited by 31
  5. 2022Exploring Differential Geometry in Neural Implicitscited by 26
  6. 2024Tuning the Frequencies: Robust Training for Sinusoidal Neural Networkscited by 19
  7. 2023High-performance Effective Scientific Error-bounded Lossy Compression with Auto-tuned Multi-component Interpolationcited by 9
  8. 2022Sobolev Training for Implicit Neural Representations with Approximated Image Derivativescited by 6
  9. 2024Critical Features Tracking on Triangulated Irregular Networks by a Scale-Space Methodcited by 4
  10. 2025A Unified Theory of Sinusoidal Activation Families for Implicit Neural Representationscited by 4
  11. 2024ImplicitTerrain: a Continuous Surface Model for Terrain Data Analysiscited by 3
  12. 2024Spatially-Adaptive Hash Encodings For Neural Surface Reconstructioncited by 3

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  3. 2026Beyond Edge Maps: Wavelet-Domain Conditioning for Multi-Adapter Map-to-Satellite Diffusion
  4. 2026SparseGF: A Height-Aware Sparse Segmentation Framework with Context Compression for Robust Ground Filtering Across Urban to Natural Scenes
  5. 2025A Diffusion-Based Framework for Terrain-Aware Remote Sensing Image Reconstruction
  6. 2026DELTA: Deformable Elevation-Based Local Terrain Attention Encoder for Sparse-Terrain Quadrupedal Locomotion
  7. 2024SatSynth: Augmenting Image-Mask Pairs through Diffusion Models for Aerial Semantic Segmentation
  8. 2025MESA: Text-Driven Terrain Generation Using Latent Diffusion and Global Copernicus Data