The invention relates to a method of smoothing the staircasing which results from discretisation in two-dimensional images, or in a series of two-dimensional images forming a three-dimensional data set. To start with, a first two- or three-dimensional continuum data model of the images is generated in which adjacent or juxtaposed pixels form squares or cubes respectively which are in turn further divided into triangles or tetrahedrons. The corner points are assigned the chromatic or monochrome values of the pixels in the image. Chromatic or monochrome values at any intermediate values in the interior of the triangles or tetrahedrons can then be obtained, e.g. by linear interpolation. Smoothing the edges of the image is done by shifting the supporting points, preferably by not more than half a pixel. A further component of the invention is operators specially developed for this purpose representing a generalised measure of the curvature of the continuum model and dictating how the supporting points are to be shifted. The supporting points are shifted such that the curvature as a whole is reduced or minimised, after which the resulting image no longer exhibits the staircase lines of the original image. By relatively simple means, the continuum model thus achieved by using a plurality of now irregular triangles and tetrahedrons permits conversion of the resulting data set back into a regular, for example orthogonal, pixel image. It is likewise possible to extract two-dimensional triangulated surfaces of objects, in a given chromatic or monochrome value range, from the three-dimensional data set or to generate slice images in any desired planes not located in an imaging plane.