用小模型实现高精度地形重建，支持任意点查询和导数计算。
ImplicitTerrainV2: Wavelet-Guided Spatially Adaptive Neural Terrain Representation
- 通过小波分析动态分配高频能力，只在复杂区域保留细节。
- 训练速度提升至每块55秒，参数减少3.2倍，重建质量提高5.7分贝。
- 适合需要高精度地形数据的地理信息系统与科研应用。
数字高程模型（DEMs）是地理信息系统（GIS）中地形分析的基础，但传统栅格表示依赖插值进行非网格采样，且基于有限差分的导数分析存在局限。隐式神经表示（INRs）提供连续替代方案，但现有地形INRs缺乏显式频率控制，忽略地形梯度结构，且模型过大、训练成本高。本文提出ImplicitTerrainV2，通过谱控机制、小波引导的空间自适应性、导数感知监督及训练后压缩，实现紧凑高效的神经地形数据格式。核心为小波复杂度场（WCF），基于解析计算的小波系数生成空间自适应频率掩码，仅在复杂地形区域保留高频容量；该场还指导复杂度感知的自适应采样，集中训练于高复杂度区域；梯度匹配增强地形连续流形结构，提升导数保真度。训练后采用混合精度量化与熵编码，存储降至1.23 bpp，PSNR仅下降0.28 dB。在50个瑞士地形块上，端到端PSNR达66.25 dB，相比前作提升5.70 dB，参数量减少3.2倍，单块训练仅需55秒（单卡）。压缩后的神经格式在率失真性能上媲美多种主流DEM编码器，同时支持非网格点查询、闭式导数计算与分辨率无关重建，适用于多种下游GIS任务。
原文摘要 · Abstract (English)
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.
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