The invention relates to a method of smoothing the staircasing
which results from discretisation in twodimensional images, or in
a series of twodimensional images forming a threedimensional
data set. To start with, a first two or threedimensional
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 twodimensional
triangulated surfaces of objects, in a given chromatic or
monochrome value range, from the threedimensional data set or to
generate slice images in any desired planes not located in an
imaging plane.
