Generation of an optimal triangulated irregular network for topographic surface via optimal transport theory - Feng Li; Haihong Zhu; Wei Li; Chengcheng Liu; Jianfang Ma; Lin Li (Geo-spatial Information Science)
A digital elevation model (DEM) is widely recognized as the most effective digital representation of the Earth’s surface and serves as the fundamental platform for simulating various Earth systems. Extensive efforts have been devoted to exploring methods for generating high-fidelity DEM datasets that are computationally efficient for diverse applications. However, the existing methods do not guarantee the optimal digital representation of the Earth’s surface. This study proposed a novel curvature-based geodesic centroidal Voronoi tessellation method for generating a topographic triangulated irregular network (TIN) DEM based on optimal transport theory. This study is the first to present a globally optimized digital representation of the Earth’s surface with a predetermined number of vertices, which is crucial for computational feasibility. This study achieves the optimal TIN by measuring mean curvature and introducing geodesic distances on the topographic surface. Representative vertices that best adapt to the topography are identified through an optimal surface approximation process. Experimental results confirm that the proposed method effectively generates the optimal digital representation of the topographic surface with the lowest elevation errors and minimal deviations from the original topographic features. By generating optimal TIN DEM with any desired number of vertices, the proposed method not only balances high-precision representation and computational efficiency but also offers a novel approach to deepening the understanding of topographic structures. Furthermore, it provides an effective solution for compressing extensive topographic data and facilitating multiscale representation of the Earth’s surface.