Computing array of high-resolution halftone pixel values by addressing halftone dot function and averaging values to determine value at printer resolution

1. A computational halftoning process for determining a halftoned image for printing using a digital printing system, comprising:

defining a halftone dot function which computes a halftoned pixel value as a function of dot coordinates in a halftone dot coordinate system;

receiving input digital image data for an array of input pixels specifying a code value as a function of printer coordinates in a printer coordinate system having a printer resolution;

for each input pixel using a data processing system to perform the following operations:

defining an array of high-resolution printer coordinates at a higher spatial resolution than the printer resolution;

transforming the array of high-resolution printer coordinates into a corresponding array of high-resolution dot coordinates in the halftone dot coordinate system;

computing an array of high-resolution halftoned pixel values responsive to the code value of the input pixel by addressing the halftone dot function using the array of high-resolution dot coordinates; and

averaging the high-resolution halftoned pixel values in the array of high-resolution halftoned pixel values to determine a halftoned pixel value at the printer resolution; and

storing the halftoned pixel values in a processor accessible memory.

2. The computational halftoning process of claim 1 , wherein an N×N array of high-resolution printer coordinates are defined for each input pixel, N being an integer greater than one, so that the spatial resolution of the high-resolution printer coordinates is N× greater than the printer resolution.

3. The computational halftoning process of claim 1 , wherein the halftoned image has an associated halftone screen angle and an associated halftone screen frequency.

4. The computational halftoning process of claim 3 , wherein the high-resolution printer coordinates are transformed into the corresponding high-resolution dot coordinates by applying a coordinate transformation that rotates the coordinates in accordance with the halftone screen angle, and scales the coordinates in accordance with a ratio of the printer resolution to the halftone screen frequency.

5. The computational halftoning process of claim 1 , further including determining relative coordinates within a halftone cell responsive to the high-resolution dot coordinates, wherein the halftone dot function is addressed with the relative coordinates.

6. The computational halftoning process of claim 1 , wherein the halftone dot function has the form:

H ( u,v )= T E ( h ( u,v ))

where h(u,v) is a halftone shape function specifying a halftone dot shape as a function of dot coordinates (u,v), and T E (h) is an edge shape function.

7. The computational halftoning process of claim 6 , wherein the halftone shape function has the form:

h ( u,v )=( u′ p +v′ p ) 1/p

where p is a dot shape parameter, u′=|(u−Int(u))−0.5|, v′=|(v−Int(v))−0.5|, and Int(•) is a function that returns the integer portion of a number.

8. The computational halftoning process of claim 6 , where the edge shape function has the form:

T

E

⁡

(

h

)

=

{

1

;

h

<

T

L

1

-

h

-

T

L

T

H

-

T

L

T

L

≤

h

≤

T

H

0

;

h

>

T

H

where h is a halftone shape value, and T L and T H are low and high threshold values, respectfully.

9. The computational halftoning process of claim 8 , wherein T L =T(C)−ΔT(C), T H =T(C)+ΔT(C), T(C) is a threshold value function specifying a threshold value as a function of input code value C, and ΔT(C) is an edge softness function which controls a halftone dot edge softness as a function of the input code value.

10. The computational halftoning process of claim 1 , wherein the input pixels of the input digital image data have a bit-depth greater than the halftone pixel values.

11. The computational halftoning process of claim 1 , wherein a bit depth of the input pixels of the input digital image data is greater than or equal to 10 bits.

12. The computational halftoning process of claim 1 , further including using the digital printing system to print the stored halftoned pixel values.

13. The computational halftoning process of claim 1 , wherein the data processing system is a sub-system within the digital printing system.

14. The computational halftoning process of claim 13 , wherein the data processing system is a field-programmable gate array.

15. A print engine that performs a computational halftoning process, comprising:

a printer module for printing halftoned pixel values at a printer resolution;

a data processing system;

a memory system communicatively connected to the data processing system and storing instructions configured to cause the data processing system to implement a halftoning process that determines halftone pixel values, wherein the halftoning process includes:

receiving input digital image data for an array of inputs specifying a code value as a function of printer coordinates in a printer coordinate system at the printer resolution;

for each input pixel performing the following operations:

defining an array of high-resolution printer coordinates at a higher spatial resolution than the printer resolution;

transforming the array of high-resolution printer coordinates into a corresponding array of high-resolution dot coordinates in a halftone dot coordinate system;

computing an array of high-resolution halftoned pixel values responsive to the code value of the input pixel by addressing a halftone dot function using the array of high-resolution dot coordinates, wherein the halftone dot function computes a halftoned pixel value as a function of dot coordinates in the halftone dot coordinate system; and

averaging the high-resolution halftoned pixel values in the array of high-resolution halftoned pixel values to determine the halftoned pixel value at the printer resolution; and

printing the halftoned pixel values using the printer module.