Interpolation of Digital Elevation Models using Generative Adversarial Networks

Abstract

A digital elevation model (DEM) is a three-dimensional representation of elevation data of a terrain such as a terrestrial terrain acquired by a reconnaissance aircraft or a lunar terrain acquired using a Chandrayaan rover. Terrestrial DEMs are used in hydrological modeling, geomorphology, and glaciology. Lunar DEMs can be used to locate natural resources and to identify prospective landing sites for exploratory missions. Hence, high quality, reliable DEMs are of great significance. DEMs are generally captured using LiDAR (Light Detection and Ranging), stereophotogrammetry, and time-of-flight cameras. However, a reliable DEM cannot be constructed if there are no adequate landmark points/features. This is the case with smooth terrains, occlusions, presence of multiple voids. The measurements are nonuniform in general. Hence, there is a need for interpolation and void-filling techniques that can estimate the elevation with a high accuracy.

Inverse distance weighting (IDW), De Launay triangulation, and Kriging are some of the popular benchmark algorithms for interpolating scattered and nonuniformly spaced data. Manual parameter tuning, inability to recover high-frequency information, and high computational complexity are some of the issues that these traditional interpolation techniques suffer from. Deep Learning (DL) has proven to be effective in providing excellent results in the field of image processing and computer vision, specifically in the tasks of super resolution, image in-painting, extrapolation, and segmentation. With the massive success of DL in several image processing and computer vision applications, its applicability has been explored for solving the DEM interpolation problem as well. However, convolutions are not readily defined if the measurements are nonuniform. Hence, the recent DL based research on DEM interpolation has only focused only on regularly spaced data.

We address the realistic problem of DEM interpolation from irregularly spaced measurements, with the density of measurements varying spatially. This is a new and unexplored direction in the deep learning setting. We propose a new and a robust DL architecture based on Generative Adversarial Networks (GANs) to perform interpolation and result in a uniform DEM with a user-specified resolution. The generator comprises three modules: Learnable Distance Weighting Module (LDW), DEM in-painting architecture, and Continuous Convolution (CC) modules. We design the novel LDW module as a learnable counterpart to the popular IDW algorithm that operates on the distances between the measurements and grid locations. This reduces the problem to that of inpainting post the LDW transformation. The proposed method is evaluated on synthetically generated data and on standard publicly available NASA (LOLA LRO) datasets using the mean relative error and PSNR as performance metrics. Extensive experiments justify the effectiveness and accuracy of the proposed approach in comparison with the benchmark techniques. We conclude the thesis by discussing possible future directions for DL based DEM interpolation.