ImplicitTerrain: a Continuous Surface Model for Terrain Data Analysis

Haoan Feng, Xin Xu, Leila De Floriani
University of Maryland, College Park
CVPR 2024 Workshop, Implicit Neural Representation for Vision
Paper Supplementary arXiv

Abstract

Fig 1.

Digital terrain models (DTMs) are pivotal in remote sensing, cartography, and landscape management, requiring accurate surface representation and topological information restoration. While topology analysis traditionally relies on smooth manifolds, the absence of an easy-to-use continuous surface model for a large terrain results in a preference for discrete meshes. Structural representation based on topology provides a succinct surface description, laying the foundation for many terrain analysis applications. However, on discrete meshes, numerical issues emerge, and complex algorithms are designed to handle them. This paper brings the context of terrain data analysis back to the continuous world and introduces ImplicitTerrain, an implicit neural representation (INR) approach for modeling high-resolution terrain continuously and differentiably. Our comprehensive experiments demonstrate superior surface fitting accuracy, effective topological feature retrieval, and various topographical feature extraction that are implemented over this compact representation in parallel. To our knowledge, ImplicitTerrain pioneers a feasible continuous terrain surface modeling pipeline that provides a new research avenue for our community.

Pipeline Overview
Pipeline

Surface-Plus-Geometry Model Accuracy

For input 1000x1000 raster Digital Elevation Model (DEM) data, our surface model and geometry model are configured as the same MLP network with 3 hidden layers, 256 hidden units, and sinusoidal activation function. The accurate reconstruction of both smoothed surface enables the following topological and topographical analyses, while the geometry model restores the missing details from the smoothed surface to achieve a high-fidelity reconstruction of the input data.

Topological Analysis Results

Topologically critical feature points and their connectivity are extracted from the surface model. Compared to the discrete mesh-based method (Forman method), critical point matching and Morse Incidence Graph (MIG) Wassertain distance are calculated and summarized in the table below. It shows the well-alignment between our surface model and the Forman method.

Tab 1.

Results from synthetic and real-world terrain datasets

Synthetic terrain

Fig 4.

Real-world terrain

Fig 5.

Topographical Analysis Results

For four tiles of real-world terrain datasets, common topographical features are defined based on the surface gradient and high-order derivatives. Among them, we calculate and plot four different topographical features, i.e. Normal mapping, Slope, Aspect, and Mean Curvature (detailed definition and computation from our surface model in the paper).

Appendix Fig 10.

Ablation: SPG model vs. Single model

Compared to the Single model with 3 hidden layers, 512 hidden units, and sinusoidal activation function, our progressive fitting of SPG model greatly reduces the fitting time (x4 faster) and improves the final reconstruction accuracy (+9 dBs).

Fig 6.

Moreover, from the view of freqency domain, SPG model demonstrates better parameter efficiency than the Single model. White regions denote the good fitting freqencies while red regions denote the frequencies that are not well represented.

Fig 7.

BibTeX


        @inproceedings{feng2024implicitterrain,
          title={ImplicitTerrain: a Continuous Surface Model for Terrain Data Analysis},
          author={Feng, Haoan and Xu, Xin and De Floriani, Leila},
          booktitle={Proceedings of the IEEE/CVF conference on computer vision and pattern recognition workshop},
          year={2024}
        }

Acknowledgment

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