Method for four-color zero-moire halftoning using non-orthogonal halftone cells
View Patent ↗The invention provides methods for using single-cell non-orthogonal cluster screens to satisfy the moiré-free conditions for four-color halftoning. The selection of these single-cell halftone screens is determined by identifying combinations of four of the halftone cells which satisfy moiré-free conditions provided in the respective frequency equations. Constraints may be applied and the combinations not meeting such constraints can be removed.
1. A method of generating a plurality of non-orthogonal halftone screens for substantially moiré-free four-color halftoning, comprising:
locating non-orthogonal halftone cells suitable for tiling an image plane that are substantially specified by two frequency vectors F n 1 =(fx n 1 , fy n 1 ) and F n 2 =(fx n 2 , fy n 2 ), where n=color indices a, b, c, d of four different colors;
identifying combinations of four of the non-orthogonal halftone cells which simultaneously satisfy:
F a 1 +F b 1 +F c 1 =0, and
F a 2 +F b 2 +F c 2 =0
and
F a 1 +F b 2 +F d 1 =0, and
F a 2 +F b 1 +F d 2 =0
where,
F d 1 ≠F c 1 , F d 1 ≠F c 2 , F d 2 ≠F c 1 , and F d 2 ≠F c 2 , and
| F n x ±F m y |>M
where,
M=minimum acceptable two-color moiré frequency
n=a, b, c, d
m=a, b, c, d
n≠m
x=1, 2,
y=1, 2;
selecting one of the identified combinations of four non-orthogonal halftone cells; and
associating each non-orthogonal halftone cell of the selected identified combination with one or more color separations of a color halftone printer.
2. The method defined in claim 1 further comprising:
identifying combinations of any three of the located non-orthogonal halftone cells prior to the step of identifying combinations of four of the non-orthogonal halftone cells, where the frequency vectors of the identified combinations satisfy:
F n 1 +F m 1 +F P 2 =0, and
F n 2 +F m 2 +F P 2 =0
where,
n=a, b, c, d
m=a, b, c, d
p=a, b, c, d
a, b, c, d are color indices of four different colors
n≠m≠p, and
| F n x ±F m y |>M
where,
M=minimum acceptable two-color moiré frequency
x=1, 2
y=1, 2.
3. The method defined in claim 1 wherein the two frequency vectors specifying each non-orthogonal halftone cell satisfy:
| F n 1 ±F n 2 |>|F n 1 | and
| F n 2 ±F n 2 |>|F n 2 |.
4. The method defined in claim 1 , wherein non-orthogonal halftone cells include cell shapes containing right angles.
5. The method defined in claim 1 , further comprising:
applying constraints to the located non-orthogonal halftone cells; and
removing non-orthogonal halftone cells that do not satisfy the constraints from the located non-orthogonal halftone cells.
6. The method defined in claim 5 , further comprising:
applying constraints to the identified combinations of non-orthogonal halftone cells; and
removing combinations of non-orthogonal halftone cells that do not satisfy the constraints from the identified combinations of non-orthogonal halftone cells.
7. The method defined in claim 1 , further comprising:
applying constraints to the identified combinations of non-orthogonal halftone cells; and
removing combinations of non-orthogonal halftone cells that do not satisfy the constraints from the identified combinations of non-orthogonal halftone cells.
8. An apparatus for generating non-orthogonal halftone screens for substantially moiré-free four-color halftoning, comprising:
a non-orthogonal halftone cell locating circuit, routine or agent that locates substantially non-orthogonal halftone cells suitable for tiling an image plane that are substantially specified by two frequency vectors F n 1 =(fx n 1 , fy n 1 ) and F n 2 =(fx n 2 , fy n 2 ) where n=color indices a, b, c, d of four different colors;
a first non-orthogonal halftone cell combination identifying circuit, routine or agent that identifies combinations of four of the located non-orthogonal halftone cells which simultaneously satisfy:
F a 1 +F b 1 +F c 1 =0, and
F a 2 +F b 2 +F c 2 =0
and
F n 1 +F b 2 +F d 1 =0, and
F a 2 +F b 1 +F d 2 =0
where,
F d 1 ≠F c 1 , F d 1 ≠F c 2 , F d 2 ≠F c 1 , and F d 2 ≠F c 2 , and
| F n x ±F m y |>M
where,
M=minimum acceptable two-color moiré frequency
n=a, b, c, d
m=a, b, c, d
n≠m
x=1, 2
y=1, 2; and
a non-orthogonal halftone cell selector circuit, routine or agent that selects one of the identified combinations of four halftone cells and associates each of the selected cells with a color separation of a color halftone printer.
9. The apparatus defined in claim 8 further comprising:
a second non-orthogonal halftone cell combination identifying circuit, routine or agent that identifies combinations of three of the located non-orthogonal halftone cells and provides them to said first non-orthogonal halftone cell combination identifying circuit, routine or agent, wherein the frequency vectors of the identified combinations of three non-orthogonal halftone cells satisfy:
F n 1 +F m 1 +F p 1 =0, and
F n 2 +F m 2 +F p 2 =0
where,
n=a, b, c, d
m=a, b, c, d
p=a, b, c, d
a, b, c, d are color indices of four different colors
n≠m≠p, and
| F n x ±F m y |>M
where,
M=minimum acceptable two-color moiré frequency
x=1, 2
y=1, 2.
10. The apparatus defined in claim 8 wherein the two frequency vectors specifying each non-orthogonal halftone cell satisfy:
| F n 1 ±F n 2 |>|F n 1 | and
| F n 1 ±F n 1 |>|F n 2 |.
11. The apparatus defined in claim 8 , wherein non-orthogonal halftone cells include cell shapes containing right angles.
12. The apparatus defined in claim 8 , further comprising:
a located non-orthogonal halftone cell removing circuit, routing or agent that removes located non-orthogonal cells according to a set of locating constraints.
13. The apparatus defined in claim 12 , further comprising:
a non-orthogonal halftone cell combination removing circuit, routine or agent that removes non-orthogonal halftone cell combinations according to a set of combination removing constraints.
14. The apparatus defined in claim 8 , further comprising:
a non-orthogonal halftone cell combination removing circuit, routine or agent that removes non-orthogonal halftone cell combinations according to a set of combination removing constraints.
15. A method for using a plurality of non-orthogonal halftone screens for substantially moiré-free color halftoning, comprising:
inputting an image data;
converting the image data to a halftone image data;
locating a plurality of tileable halftone screens that contain combinations of non-orthogonal halftone cells where each non-orthogonal halftone cell is substantially specified by two frequency vectors F n 1 =(fx n 1 , fy n 1 ,) and F n 2 =(fx n 2 , fy n 2 ), where n=color indices a, b, c, d of four different colors;
identifying combinations of four of the non-orthogonal halftone cells which simultaneously satisfy:
F a 1 +F b 1 +F c 1 =0, and
F a 2 +F b 2 +F c 2 =0
and
F a 1 +F b 2 +F d 1 =0, and
F a 2 +F b 1 +F d 2 =0
where,
F d 1 ≠F c 1 , F d 1 ≠F c 2 , F d 2 ≠F c 1 , and F d 2 ≠F c 2 , and
| F n x ±F m y |>M
where,
M=minimum acceptable two-color moiré frequency
n=a, b, c, d
m=a, b, c, d
n≠m
x=1, 2
y=1, 2; and
forming an image on an image recording medium using the halftone image data.
16. The method defined in claim 15 , wherein non-orthogonal halftone cells include cell shapes containing right angles.
17. The method defined in claim 15 , further comprising:
applying constraints to the located non-orthogonal halftone cells; and
removing non-orthogonal halftone cells that do not satisfy the constraints from the located non-orthogonal halftone cells.
18. The method defined in claim 17 further comprising:
applying constraints to the identified combinations of non-orthogonal halftone cells; and
removing combinations of non-orthogonal halftone cells that do not satisfy the constraints from the identified combinations of non-orthogonal halftone cells.