1. Field of the Invention
The present invention relates to a screening method of and a screening apparatus for expressing a halftone by use of a halftone screen, and further relates to a screening method of and a screening apparatus for constructing a hexagonal cell on a square grid and suppressing the occurrence of a noise pattern in the horizontal direction and in the vertical direction.
2. Discussion of the Background
Generally, in an output device such as a printer with medium/low resolution, a halftone is not realized by a collective (concentrated) type dither nor is a halftone realized by a dispersion type random dither (error diffusion). Instead, in such a printer a halftone is typically realized by a dispersion type regular dither. The reasons for that are that, when the collective type dither is used, oozing-out or rosette due to ink closing-up together becomes prominent, and that, when the dispersion type random dither is used, memory requirements and calculation costs increase. Therefore, in particular, the technology of the dispersion type regular dither may become important in a color ink jet printer.
Generally, in the dispersion type regular dither screening, a square halftone cell is used. However, due to the property of the dither pattern, noise patterns easily recognizable by human eyes occur at some density. As a method of preventing the noise patterns from occurring in the horizontal and vertical directions, the document “Robert Ulichney. Digital Halftoning. The MIT Press” describes a regularly-hexagonal dither pattern. It has been thought that, according to the aforementioned dither, the dispersion type regular dither screening in which the above-mentioned patterns could be made not prominent.
However, since the hexagonal dither described in the aforementioned document is a symmetrical or regularly-hexagonal halftone cell realized on a 60-degree (60°) grid, an outputting device capable of marking dots on the 60° grid has to be prepared. Consequently, the above hexagonal dither cannot be applied to an outputting device for marking dots on a square grid.
In such a situation, since it is difficult to form a screen having a regularly-hexagonal cell which is spread all over the square grid, the present inventor has already proposed a method of expressing a hexagonal cell (not a regularly-hexagonal cell) having two sides (slanted sides) formed by removing a couple of corners from a square cell at positions opposing each other, and thereby suppressing the occurrence of the noise pattern in the horizontal and vertical directions as seen by the screening by use of the square halftone cell.
In such a situation, according to such a method of screening, it is necessary to arrange the cells such that the distance between the respective centers of adjacent cells is made as equal as possible in order to prevent the displacement of the pattern. As a result, the portion of the corner to be removed cannot be excessively large.
FIGS. 8A through 8C illustrate the case of forming a hexagonal cell on a 5×5 square grid as an example. On this occasion, the corners of two pieces of pixels in the 5×5 pixel opposing each other are removed as shown in the progression from FIGS. 8A to 8B. Thereby, a hexagonal cell of 24 (=5×5−1×1) pixels which is not regularly-hexagonal is formed as shown in FIG. 8B, and then, plural hexagonal cells thus formed are arranged on the square grid without any gaps therebetween as shown in FIG. 8C.
Furthermore, FIGS. 9 through 11 illustrate a method of forming the hexagonal cells with the goal of expressing a halftone to the extent of a 256-step halftone. At first, since each cell requires pixels situated at the centers thereof, each fundamental hexagonal cell is firstly formed on a 3×3 square grid as shown in FIG. 9A. The above-mentioned hexagonal cell can express 8-step halftones (=3×3−1×1) as shown in FIG. 9A. Next, an enlargement is performed by forming a further large hexagonal cell on the condition that the center of the cells respectively adjacent to the sides of the fundamental hexagonal cell is an apex as shown in FIG. 9B.
On this occasion, it is preferable to cause the apex of the shape-angle portion to be included in the hexagonal cell and not to cause the apex of both ends of the slanted sides to be inclined therein. That is, the sharp-angle portion of the adjacent cell. By use of the hexagonal cell as shown in FIG. 9B, a 24-step halftone (=5×5−1×1) can be expressed. The same enlargement can be repeated for the cell thus enlarged, and thereby a hexagonal size cell capable of expressing a 72-step halftone (=9×9−3×3) can be formed. Furthermore, a hexagonal size cell capable of expressing a 216-step halftone (=15×15−3×3) can be formed as shown in FIG. 10. Next, threshold values are set for respective pixels as shown in FIG. 11.
Moreover, as an example of another background art, the published specification of Japanese Laid-open Patent Publication No. 8-265,568 describes a method of comparing one after another input image data with respective elements of a threshold value arrangement and converting the input image data to binarized or multiple-value data in a digital raster device. Then, in that method a smooth halftone equal to or greater than a 150-step halftone is realized by repeating a small pattern of 15-step halftones by use of a dither matrix composed of eight pieces of the raster capable of expressing a halftone equal to or greater than 15-step halftones. According to the method of the above-mentioned proposal of the background art, both of high resolution and low cost can be realized.
Moreover, as an example of still another background art, the published specification of Japanese Laid-open Patent Publication No. 7-264,403 describes a method of dividing a threshold value matrix into plural sub-matrices of sizes equal to each other, and randomly arranging the plural threshold values in the respective sub-matrices. According to the method of the above-mentioned proposal of the other background art, it is possible to make a threshold value matrix of high spatial frequency capable of expressing a smooth halftone.
The present inventor has also already proposed a screening method including the steps of cutting off a couple of corners facing each other of a square cell on a square grid and thereby forming hexagonal cells excluding a regularly-hexagonal cell, and combining plural of the hexagonal cells into one and thereby forming a halftone cell, in order to increase the number of expressive halftones without decreasing the number of lines.
In FIG. 12, as an example, for a square matrix of the 6×6 pixels, both of a left-upper half of the 2×2 pixels on the left-upper side of the square matrix of the 6×6 pixels and a right-lower half of the 2×2 pixels on the right-lower side thereof are cut down, and thereby one hexagonal cell of 32 (=6×6−2×2) pixels not being of a regular hexagon shape are formed, and four of the above-mentioned hexagonal cells are combined into one.
Concerning another background art of expressing halftones, for example as proposed in the published specification of Japanese Laid-open Patent Publication No. 8-265,568, a digital raster device compares, one after another, input image data with respective elements of a threshold values arrangement, and converts the respective input image data to data of binarized values or data of multiple values. In such a digital raster device, the dither matrix constructed with 8 pieces of raster capable of expressing a halftone property equal to or greater than 15 halftones is employed, and thereby a smooth halftone property equal to or greater than 150 halftones can be realized by repeating the small pattern of an extent of 15 halftones. According to the above proposed method, a high resolution of image forming and a low-cost image forming can be realized at the same time.
Furthermore, concerning still another background art of expressing halftones, for example as proposed in the published specification of Japanese Laid-open Patent Publication No. 7-264,403, a threshold values matrix is divided into plural sub-matrices of an equal size. In the respective sub-matrices, plural threshold values are randomly arranged, and thereby the spatial frequency can be made high. In addition, the threshold value matrix capable of smoothly expressing halftones can be formed.
Furthermore, concerning still another background art of expressing halftones, for example, the published specifications of Japanese Laid-open Patent Publication Nos. 7-38,755 and 7-290,737 propose similar technology.