Method for four-color zero-moire halftoning using non-orthogonal halftone cells

• US 6,985,262 B2
• Filed: 07/13/2001
• Issued: 01/10/2006
• Est. Priority Date: 07/13/2001
• Status: Active Grant

• Current Assignee: Xerox Corporation (Xerox Holdings Corp.)
• Original Assignee: Xerox Corporation (Xerox Holdings Corp.)
• Inventors: Wang, Shen-Ge
• Primary Examiner(s): Lee, Thomas D.
• Assistant Examiner(s): Thompson, James A.
• Application Number:
  US09/905,556
• Publication Number:
  US 20030035145A1
• Time in Patent Office: 1,642 Days
• Field of Search: 358/1.9, 358/2.1, 358/3.06, 358/3.09, 358/3.11, 358/3.2, 358/3.26, 358/3.3, 358/536
• US Class Current: 358/3.26
• CPC Class Codes: H04N 1/52 Circuits or arrangements for halftone screening

Abstract

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.

Claims

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_n1=(fx_n1, fy_n1) and F_n2=(fx_n2, fy_n2), 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_a1+F_b1+F_c1=0, and

F_a2+F_b2+F_c2=0

and

F_a1+F_b2+F_d1=0, and

F_a2+F_b1+F_d2=0

where,

F_d1≠

F_c1, F_d1≠

F_c2, F_d2≠

F_c1, and F_d2≠

F_c2, and

|F_nx±

F_my|>

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_n1+F_m1+F_P2=0, and

F_n2+F_m2+F_P2=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_nx±

F_my|>

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_n1±

F_n2|>

|F_n1| and

|F_n2±

F_n2|>

|F_n2|.

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_n1=(fx_n1, fy_n1) and F_n2=(fx_n2, fy_n2) 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_a1+F_b1+F_c1=0, and

F_a2+F_b2+F_c2=0

and

F_n1+F_b2+F_d1=0, and

F_a2+F_b1+F_d2=0

where,

F_d1≠

F_c1, F_d1≠

F_c2, F_d2≠

F_c1, and F_d2≠

F_c2, and

|F_nx±

F_my|>

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_n1+F_m1+F_p1=0, and

F_n2+F_m2+F_p2=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_nx±

F_my|>

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_n1±

F_n2|>

|F_n1| and

|F_n1±

F_n1|>

|F_n2|.

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_n1=(fx_n1, fy_n1,) and F_n2=(fx_n2, fy_n2), 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_a1+F_b1+F_c1=0, and

F_a2+F_b2+F_c2=0

and

F_a1+F_b2+F_d1=0, and

F_a2+F_b1+F_d2=0

where,

F_d1≠

F_c1, F_d1≠

F_c2, F_d2≠

F_c1, and F_d2≠

F_c2, and

|F_nx±

F_my|>

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.