Many magnification algorithms have been proposed in past decades, most of which concentrate on the smooth reconstruction of edge structures. Edge reconstruction, however, can destroy corners, thus producing perceptually unpleasant rounded corner structures. In this work, corner shock filtering is designated for enhancing corners relative to the known edge shock filtering, based on a new measure of corner strength and the theory of level-sets motion under curvature. By combining directional diffusion, edge shock filtering, and corner shock filtering, a regularized partial differential equation (PDE) approach for magnification is proposed to imultaneously reconstruct the edges and preserve the corners. Moreover, the proposed PDE approach is also robust to random noises. Experimental results in both cases of grayscale and color images confirm the effectiveness of our approach.