This paper addresses an old, yet challenging issue - curvature estimation from discrete sampling points over a curve. We introduce a novel algorithm based on performing line integrals. The proposed method is computationally more efficient than the previous integration-based methods because of the constant computation time. Qualitative tests on synthesized shapes in the presence of noise are performed, which show the robustness of our approach. Also, the discriminative capability of the estimated curvature is evaluated by conducting experiments on the FRGC (Face Recognition Grand Challenge) v2.0 dataset which contains 4007 3D facial images recorded from 466 subjects. The results show that recognition performance is significantly improved by using our curvature estimation method. This novel approach presents potential for a broad class of multimedia applications.