Abstract: In the paper, the curvature of the line of level crossings of a surface as a description to the surface is introduced. The relation between the level crossing curvature and the Laplacian is derived and, by the relation, we analyse the location errors of the Laplacian when detecting bending step edges. Our results show that the level crossing curvature can cause location error of the Laplacian, particularly when the edges with large curvatures and small gradients. Thus there are three reasons for the location errors of the Marr-Hildreth edge detector, that is, the level crossing curvature, Gaussian filtering, and noise.