1. Field of the Invention
This invention relates to an image processing system which outputs output image data having an output gradient number of n lower than the input gradient number m by carrying out multi-valued processing using a dither matrix on input image data having an input gradient number of m.
2. Description of the Related Art
When image data representing information of an image created by a personal computer or image data obtained by reading an original with a scanner or the like is to be output to a printer to be printed thereby or to a display to be displayed thereby, processing to conform the image data to the lower number of gradation of the output side and to have the same gradation as the information of the image or the original in appearance is generally carried out on the image data since the number of gradation of the output side device, the printer or the display, is lower than that of the information of the image created by the personal computer or the image data read-out by the scanner.
For example, when the multi-valued image data created by the personal computer is to be printed by a two-valued printer, an organizational dither method is employed. The organizational dither method is a method in which n×n pixels are considered to be the smallest unit of expressing the gradation, and a n×n matrix of threshold values (will be referred to as “a dither matrix”, hereinbelow) corresponding thereto is prepared, and the dither matrix is superposed on the image data as a kind of mask, whereby the density of each pixel is compared with the corresponding threshold value and “1” is output when the former is larger than the latter while “0” is output when the former is smaller than the latter. Then after the same processing is finished on a group of n×n pixels, the dither matrix is moved to another group of n×n pixels and the same processing is repeated, whereby each components of the whole image data is turned to one of the two values, “1” or “0”.
Further, when each pixel is turned to one of the multi-values (multi-valued) in place of the two values, there is proposed, in U.S. Pat. No. 5,640,249 (will be referred to as “the first paper”, hereinbelow.), a method where the density of each pixel is compared with a plurality of threshold values. For example, a plurality of dither matrices each having a threshold value necessary to the multi-valued processing (turning the density of each pixel to the multi-values) are prepared from one basic dither matrix, and the density of each pixel is multi-valued by comparing the density of each pixel with a plurality of threshold values on the same coordinates in a plurality of dither matrices. That is, in accordance with the first paper, (x−1) comparisons are necessary when the number of gradations into which each pixel is to be multi-valued is x.
Whereas, in “Digital Color Halftoning” by Henry R. Kang., IEEE PRESS, SPIE ISBNO-8194-3318-7, pp. 445-449, 1999/11/1 (will be referred to as “the second paper”, hereinbelow.), there is disposed a method where multi-valued processing can be realized by one comparison. More particularly, the method disclosed in the second paper is a method of obtaining output image data O(x,y) by the use of the following formula (3). Since the multi-valued processing can be executed according to one formula without using comparison operation, the method of the second paper can be executed at a higher speed as compared with the method of the first paper. Further, the method of the second paper requires less memory capacity for storing the dither matrix as compared with the method of the first paper where a plurality of dither matrices are used.O(x,y)=int[α+d(xd,yd)/(gmax+1)]  (3)wherein α=(n−1)/(m−1)*I(x,y), n represents output gradient number, m represents input gradient number, O(x,y) represents output image data (0≦O(x,y)≦(n−1)), I(x,y) represents input image data (0≦I(x,y)≦(m−1)), gmax represents the maximum value of the dither matrix, d(xd,yd) represents the value of the dither matrix (0≦d(xd,yd)≦gmax), xd=x mod dsize_x,    yd=y mod dsize_y, dsize_x represents the size of the dither matrix in x direction, dsize_y represents the size of the dither matrix in y direction, and int[ ] is an integer-valued function.
However, if the method disclosed in the first paper is employed, there arises a problem that, for instance, when a gradation image is to be output, the image data components at a particular density can be processed to one gradation and output in the gradation though the image data components at almost all the densities can be processed to two gradations and output in the gradations. The result obtained by carrying out the multi-valued processing on a gradation image by the use of, for instance, the dot dispersion type dither matrix and the above formula is shown in FIG. 5. As shown in FIG. 5, though, in a lateral view, almost all the regions are expressed in two different gradations, a region which is expressed in a single gradation exists near the center. When such an image is output, e.g., printed, though almost all the regions have a feeling of granulated material, the region expressed in a single gradation has no feeling of granulated material, whereby people visually feel as if there is different material in the region, and will feel unnatural.