Efficient Terrain Stochastic Differential Efficient Terrain Stochastic Differential Equations for Multipurpose Digital Elevation Model Restoration

TL;DR

The proposed Efficient Terrain Stochastic Differential Equation (ET-SDE) models DEM degradation through SDE progression and restores it via a simulated reversal process, and demonstrates faster inference speeds and the capacity to generalize across various tasks, particularly for larger patches of DEMs.

Abstract

Digital Elevation Models (DEMs) are indispensable in the fields of remote sensing and photogrammetry, with their refinement and enhancement being critical for a diverse array of applications. Numerous methods have been developed for enhancing DEMs, but most of them concentrate on tackling specific tasks individually. This paper presents a unified generative model for multipurpose DEM restoration, diverging from the conventional approach that typically targets isolated tasks. We modify the mean-reverting stochastic differential equation, to generally refine the DEMs by conditioning on the learned terrain priors. The proposed Efficient Terrain Stochastic Differential Equation (ET-SDE) models DEM degradation through SDE progression and restores it via a simulated reversal process. Leveraging efficient submodules with lightweight channel attention, this adapted SDE boosts DEM quality and streamlines the training process. The experiments show that ET-SDE achieves highly competitive restoration performance on super-resolution, void filling, denoising, and their combinations, compared to the state-of-the-art work. In addition to its restoration capabilities, ET-SDE also demonstrates faster inference speeds and the capacity to generalize across various tasks, particularly for larger patches of DEMs.

Figures (10)

• Figure 1: Overview of the ET-SDE to restore DEM from $D_{LQ}$ low resolution and irregular voids. The forward process of ET-SDE serves as a degradation from a high-quality DEM $x(0)=D_{HQ}$ to its low-quality counterpart $x(T) = D_{LQ}$ by progressively adding estimated noise. Inversely, recovering $D_{HQ}$ is obtained by simulating the reverse-time process.
• Figure 2: The Unet-shaped pipeline of ET-SDE is composed of a Terrain Prior Encoder (TPE), and several efficient submodules. The noise predictor $F_{\Phi_{NN}}$ with parameters $\Phi_{NN}$ is optimized in the forward process in Algorithm \ref{['alg:train']}.
• Figure 3: A TPE in (a) is composed of 3 TABs with details in (b). A deformable convolution in a TAB is illustrated in (c).
• Figure 4: The Efficient Attention Block (EAB) of $F_{\Phi_{NN}}$ in the pipeline.
• Figure 5: The elevation histograms of the Pyrenees area and the Tai area.