We here introduce an automatic Digital Terrain Model (DTM) extraction method. The proposed sparsitydriven DTM extractor (SD-DTM) takes a high-resolution Digital Surface Model (DSM) as an input and constructs a high-resolution DTM using the variational framework. To obtain an accurate DTM, an iterative approach is proposed for the minimization of the target variational cost function. Accuracy of the SD-DTM is shown in a real-world DSM data set. We show the efficiency and effectiveness of the approach both visually and quantitatively via residual plots in illustrative terrain types. Index Termsdigital surface model, digital terrain model, sparsity, variational inference 1. INTRODUCTION A Digital Terrain Model (DTM) is an elevation map of bare ground where man-made objects (buildings, vehicles, etc.) as well as vegetation (trees, bushes, etc.) are removed from the Digital Surface Model (DSM) [1]. In