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