Pascal Monasse École Nationale des Ponts-et-Chaussées Level sets and level lines are useful features in image processing. The mean curvature map is also an important low level ingredient in classifying textures, detecting salient shapes, etc. While their computation seems easy, with closed-form formulas, we show that ignoring the discrete nature of a digital image leads to disastrous results. It is mandatory to smooth the image to erase the pixel effects, using the mean curvature motion or the affine curvature motion. Actually, any finite difference scheme will involve some diffusion, which is inconsistent with the theory. We show that a more involved process must be performed, based on decomposition of the image into its level lines, which can be achieved by an efficient algorithm, geometric evolution of the individual level lines, followed by a simple geometric curvature computation scheme. The method will be illustrated by experiments.