ImplicitTerrain: a Continuous Surface Model for Terrain Data Analysis

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

CVPR 2024 Workshop on Implicit Neural Representation for Vision (INRV) · Oral

Project page · Paper (arXiv) · CVF Open Access · Demo · Follow-up: ImplicitTerrainV2

News

Dec 2024 - The demo code with a compiled binary for discrete forman method (forman) is released in the folder implicitterrain_demo. An example terrain 2494_1141 with experiment results are also included in the subfolder 2494_1141.

Introduction

ImplicitTerrain leverages Implicit Neural Representations (INR) to model high-resolution terrain continuously and differentiably, enhancing the accuracy of surface representation and topological information restoration. This project offers a novel pipeline, making use of the Surface-plus-Geometry (SPG) cascaded INR model for terrain surface modeling, maintaining high reconstruction fidelity and enabling direct topological analysis on the continuous manifold.

Key Features

• High Fidelity Surface Modeling: Utilizes a novel SPG model for precise terrain representation.
• Progressive Training Strategy: Improves convergence speed and efficiency during model training from coarse to fine scales.
• Topological and Topographical Analysis: Integrates extracted topological features with discrete Morse theory and supports calculations of various topographical features directly from surface derivatives.

Implementation Details

For ImplicitTerrain, the neural network structure and fitting is straightforward:

• The implementation of ImplicitTerrain is based on the PyTorch implementation of the SIREN. Model configuration and training settings are detailed in the Experiment section of the paper.
• Surface model's gradient calculation is based on the PyTorch autograd mechanism.
• Image downsampling and smoothing are implementation by Skimage and image gradient calculation is implemented by Numpy.
• Forman method results are based on an open-source library FormanGradient2D.

Related projects

• ImplicitTerrainV2 (ACM SIGSPATIAL 2026) · code — the follow-up. It keeps the cascade of a smooth surface model and a residual geometry model, gates the residual model's high frequencies in space with a wavelet complexity field, and compresses the trained weights into a compact stored format.
• Rethinking Amortized Neural Representations for Terrain (ACM SIGSPATIAL 2026, poster) · code — the amortized counterpart: instead of fitting a network per tile, one shared model maps each terrain tile to a compact token.
• Critical Features Tracking on TINs by a Scale-Space Method (ACM SIGSPATIAL 2024) — tracks critical topographic features across scales on triangulated irregular networks.

Citation

@InProceedings{Feng_2024_CVPR,
  author    = {Feng, Haoan and Xu, Xin and De Floriani, Leila},
  title     = {ImplicitTerrain: a Continuous Surface Model for Terrain Data Analysis},
  booktitle = {Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR) Workshops},
  month     = {June},
  year      = {2024},
  pages     = {899-909}
}

Acknowledgments

This work was supported by the US National Science Foundation under grant number IIS-1910766.

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