3D models are subject to a wide variety of processing operations such as compression, simplification or watermarking, which may introduce some geometric artifacts on the shape. The main issue is to maximize the compression/simplification ratio or the watermark strength while minimizing these visual degradations. However few algorithms exploit the human visual system to hide these degradations, while perceptual attributes could be quite relevant for this task. Particularly, the masking effect defines the fact that one visual pattern can hide the visibility of another. In this context we introduce an algorithm for estimating the roughness of a 3D mesh, as a local measure of geometric noise on the surface. Indeed, a textured (or rough) region is able to hide geometric distortions much better than a smooth one. Our measure is based on curvature analysis on local windows of the mesh and is independent of the resolution/connectivity of the object. The accuracy and the robustness of our measure, together with its relevance regarding visual masking have been demonstrated through extensive comparisons with state-of-the-art and subjective experiment. Two applications are also presented, in which the roughness is used to lead (and improve) respectively compression and watermarking algorithms.