In a method for converting the coordinates of image data, the positions of new picture elements in a new coordinate system are calculated by means of coordinate transformation equations from the positions of initial picture elements in an initial coordinate system. The positions of the new picture elements are randomly modified in a variation range around the positions calculated by way of the coordinate transformation. For this purpose, random values are added to the calculated coordinates of the new picture elements. The method can be used in case of scale conversions, image rotation, etc. to improve the quality of the converted image. The method avoids both the corruption of the image structures caused by coordinate conversion and the formation of disruptive moire patterns. The method can be combined with known methods for calculating the color values of the new picture elements, such as the nearest-neighbor method or the interpolation method.