the image of fig1 is to be converted , for example , to 10 × 10 picture elements , i . e . with a scale factor of s = 10 / 13 . whether the image is thereby reduced is dependent on the resolution with which it is reproduced . with an unmodified resolution , the reduced dimensions b2 = 10 / r mm and h2 = 10 / r mm would result . given reproduction with , for example , a coarser resolution , it can even become larger despite the lower number of picture elements . a scale conversion can therefore not always be equated with a modification of the dimensions . the crux of the scale conversion , however , is that a new image having a different number of image lines and picture elements per image line is generated in every instance . fig2 shows the re - calculated picture elements 4 in relationship to the original image . their positions are identified with a cross . the first picture element in the first line of the newly calculated image is likewise placed into the origin of the x , y - coordinate system . for determining the positions of the new picture elements , the new picture elements are uniformly distributed onto the image area . when the spacing of the original picture elements in x - direction and y - direction is respectively assumed to be one , the image has the area 13 × 13 in these units . in order to cover the same area with ten picture elements per image line and with ten image lines , the new picture elements must have greater spacings dx or , respectively , dy . the spacing dx of the new picture elements in line direction derives from the relationship of the old number of picture elements per image line to the new number of picture elements per image line , i . e . dx = 13 / 10 = 1 / s . in the example , the spacing of the new image lines likewise derives as dy = 13 / 10 = 1 / s . different scale factors sx or , respectively , sy can be selected for the x - direction and the y - direction . the spacings of the new picture elements then derive as the x - position x ( n ) of the n th , new picture element in a new image line and the y - position y ( m ) of the m th , new image line are then x ( n )= n × d ×= n × 1 / sx y ( m )= m × dy = m × 1 / sy ( 4 ) in a universal coordinate conversion , the positions u ( n ) and v ( m ) of the new picture elements in a new coordinate system ( u , v ) are calculated with coordinate transformation equations fu ( x , y ) and fv ( x , y ) as function of the coordinates of the original picture elements in an original coordinate system ( x , y ). for this example , fig3 shows the image after the scale conversion when it is reproduced with the same resolution r of picture elements / mm as the original image . a reduced image having the dimensions b2 = 10 / r mm and h2 = 10 / r mm is then obtained . in a second step of the scale conversion of the prior art , the color values of the new picture elements are then calculated according to various methods from the color values of the original picture elements that are adjacent to the positions of the new picture elements . in the simplest case , the color value of a new picture element is equated with the color value of the original picture element that lies closest to the new picture element . this method is known as the “ nearest neighbor ” method . specifically for large image data sets , it has the advantage that it can be implemented very fast , but has the disadvantage that structures of the original image are falsified and disturbing patterns can be produced . in the example of fig2 , the original image lines or , respectively , image columns 2 , 6 and 11 are not covered by the nearest neighbor method , i . e . fine image structures in these lines or , respectively , columns that are only one picture element wide are lost in the scale conversion . moreover , the image lines or , respectively , image columns that are not covered occur with regular spacings , as a result whereof a disturbing pattern ( moirè ) can be produced . given a scale conversion for enlarging the number of new picture elements and the number of new image lines , the new picture elements lie closer together than the original picture elements . in this case , some image lines or , respectively , image columns are doubly acquired by the nearest neighbor method . the original image structures are also falsified as a result thereof and disturbing patterns can be produced . these disturbing effects can be alleviated when the color values of the new picture elements are interpolated by weighted addition of the color values of a number of neighboring , original picture elements . this known method , however , is calculation - intensive and is therefore less suited for large image data sets . moreover , disturbing patterns can also not always be avoided therewith . united states letters patent u . s . pat . no . 5 , 657 , 047 discloses such a method for scale modification of the picture screen display of an image . the weighted addition of the color values of a number of neighboring , original picture elements is referred to therein as “ blending ”. the patent also discloses a circuit - oriented realization of the interpolation that manages with a slight memory expense . methods are also known specifically for binary images having only two brightness values ( bit map images ) wherein the original picture elements in the environment of a new picture element are analyzed with methods of pattern recognition . the color value of the new picture element is determined from the result of the analysis , whereby , for example , an attempt is made to preserve fine image structures that would be lost given a pure nearest neighbor method or would be highly falsified . these methods of pattern recognition also require a high calculating outlay per picture element and are therefore too time - consuming for large image data sets . the described disadvantages — falsification of image structure and formation of disturbing patterns — are avoided by the inventive method without having to greatly increase the calculating outlay per picture element . it is therefore also suitable for extremely large image data sets as occur in electronic reproduction technology . this is achieved by a new way of determining the positions for the new picture elements . this new way of determining the positions can be combined with all known methods of calculating the color values for the new picture elements ( nearest neighbor method , interpolation , pattern recognition ). fig4 shows an excerpt of 2 × 2 neighboring , original picture elements 2 and the position of a new picture element 4 as derives according to the above - explained method of position identification from the spacings dx and dy between the new picture elements . according to the invention , the position of the new picture element is randomly modified in a range 5 of variation around this position . for this purpose , a random value having a numerical range from − ax through + ax can be added to the x - coordinate of the position , and a random value having a numerical range from − ay through + ay can be added to the y - coordinate of the position . as a result of this technique , the position of the new picture element is shifted with a certain probability into the area of the one original picture element on the one hand or into the area of the other original picture element on the other hand . when the color value of the new picture element is subsequently calculated , for example according to the nearest neighbor method , individual image lines or , respectively , image columns of the original image cannot be entirely lost ( given reduction ) or , respectively , they are not doubled in terms of their entire length ( given enlargement ). further , picture elements are no longer omitted or , respectively , doubled at regular intervals , as a result whereof the formation of disturbing patterns is avoided . in conjunction with the calculation of the color values of the new picture elements with interpolation from the neighboring , original picture elements , disturbing residual patterns are avoided since it is not always the same neighboring points of the original image that are utilized for the interpolation in a line or , respectively , column . the range of variation 5 is expediently selected in such a size that it covers approximately one - half through one picture element spacing of the original image . it also need not be symmetrical around the position of the new picture elements . it can be selected arbitrarily asymmetrically or such that only positive or negative random values are added to the coordinates of the picture element position . fig5 shows a simplified embodiment of the inventive method wherein new random values need not be produced for each new picture element . in this embodiment , all new picture elements of a new image line are shifted in position by the same random value in the x - direction , whereby the picture elements retain their fixed spacing dx from one another . a new random value is produced for each new image line . likewise , all new picture elements of a new image column can be shifted in position by the same random value in the y - direction , whereby the picture elements retain their fixed spacing dy relative to one another . in this way , new random values need only be generated at the start of each image line or , respectively , image column , as a result whereof the processing time is substantially shortened . expediently , the shift of the image lines in the x - direction and of the image columns in the y - direction are combined with one another . the generation of the random values can occur with a known random value generator during the processing . in order to save processing time , a list of random values can also be produced in advance and can be stored in one or more tables , for example , one table for the x - direction and one table for the y - direction . during the scale conversion , the respectively required random value is continuously read from the corresponding table . the present invention was explained with reference to the example of scale conversion . however , the application thereof is not limited thereto . it can be applied in any type of coordinate conversion for image data such as , for example , rotation of an image by an arbitrary angle , perspective distortion of an image , imaging of an image onto a curved surface in space , etc . such complex coordinate conversions play a part in many areas of digital image processing , for example in the presentation of three - dimensional objects or in the distortion correction of aerial and satellite pictures . as in the simple scale conversion , there is also the problem given these complex coordinate conversions that original image structures are falsified in the new image and disturbing patterns can arise . as in the scale conversion , the positions of the new picture elements in a new coordinate system are determined with coordinate transformation equations in a first step in the complex coordinate conversions , whereby the new picture element positions lie between the original picture elements . in this first step , the present invention can be applied for avoiding disturbing effects . in a second step , the color values are then calculated from the original picture elements , that lie in the environment of a new picture element , as in the scale conversion . the effect of the invention is illustrated with reference to the example of a simple , binary image in fig6 through 8 . fig6 shows an enlarged portion from an original image having a diagonal stripe pattern . fig7 shows the image reduced to 97 % without application of the inventive method , whereby the brightness values of the new picture elements were determined according to the nearest neighbor method . one can clearly see the omitted image lines and image columns that generate a disturbing box pattern . fig8 shows the reduced image with application of the inventive method . the box pattern no longer occurs . due to the random shift of the new picture elements , the edges of the diagonal stripes have become somewhat rougher . given the high resolution of images , particularly in reproduction technology , this effect , however , is far less disturbing then the regular patterns that are generated without the application of the invention . although various minor changes and modifications might be proposed by those skilled in the art , it will be understood that my wish is to include within the claims of the patent warranted hereon all such changes and modifications as reasonably come within my contribution to the art .