Curvature is one of the most relevant notions that links the metric properties of a surface to its geometry and to its topology (Gauss-Bonnet theorem). In the literature, a variety of approaches exist to compute curvatures in the discrete case. Several techniques are computationally intensive or suffer from convergence problems. In this paper, we discuss the notion of concentrated curvature, introduced by Troyanov [24]. We discuss properties of this curvature and compare with a widely-used technique that estimates the Gaussian curvatures on a triangulated surface. We apply our STD method [13] for terrain segmentation to segment a surface by using different curvature approaches and we illustrate our comparisons through examples.