HFSM: High-Fidelity Surface Modeling for Accurate DEMs With Terrain Discontinuity Preservation

High-accuracy digital elevation models (DEMs) serve as critical inputs for quantitative geomorphic analysis, yet precise surface reconstruction from irregularly distributed ground points continues to pose significant challenges. Conventional spatial interpolation methods with the surface-continuity assumption systematically distort abrupt terrain discontinuities, such as escarpments, fault scarps, and ridgelines. To address this limitation, we present a high-fidelity surface modeling (HFSM) method that explicitly incorporates 1-D Hausdorff measures of both elevation and normal discontinuities into a variational energy minimization formulation. By framing the reconstruction as a free-discontinuity problem, HFSM adaptively balances surface smoothness with discontinuity localization through parameter-controlled energy terms, enabling the preservation of critical terrain features. Extensive validation conducted across six distinct terrain types, each with different sampling densities ranging from 30% to 90%, showcases the outstanding performance of HFSM when compared to five benchmark approaches. On average, HFSM attains a reduction in DEM root mean squared error (RMSE) by 7.3%–43.1% and enhances the preservation of terrain feature lines by 2.7%–22.2%. These results position HFSM as an effective solution for high-quality DEM generation in morphologically complex terrains, particularly valuable for geomorphometric applications requiring precise representation of surface discontinuities.