abstract: We show how the theory of varifolds can be usedadapted in the context of discrete geometry for robust approximation of surface features (mean curvature, second fundamental form) also in presence of singularities. We also propose a suitable modification of Hutchinson's definition of generalized second fundamental form for integral varifolds, which can be naturally regularized and associated with any varifold. Finally, we show some tests on point clouds providing an experimental validation of the theory. This is a joint work with Blanche Buet and Simon Masnou.