This paper introduces a class of iterative morphological image operators with applications to sharpen digitized gray-scale images. It is proved that all image operators using a concave structuring function have sharpening properties. By using a Laplacian property, we introduce the underlying partial differential equation that governs this class of iterative image operators. The parameters of the operator can be determined on the basis of an estimation of the amount of blur present in the image. For discrete implementations of the operator class it is shown that operators using a parabolic structuring function have an efficient implementation and isotropic sharpening behavior. © 2000 Pattern Recognition Society.