Method and apparatus for characterizing printer streaking
View Patent ↗Methods and systems are presented for characterizing printer streaking using a basis selection algorithm to determine parameters set for a streak template that best approximate a density profile derived from a scanned printed test image, with wavelet decomposition used to expedite the searching for position and width parameters.
1. A method of characterizing printer streaks, the method comprising:
(a) printing a test image onto a printable media according to an input characterization data set using a printing system;
(b) measuring the test image to generate a characterization data set representing measurements of intensity or color values observed from the test image; and
(c) generating a density profile using the characterization data set, the density profile representing intensity or color value variation of the test image in a cross-process direction transverse to a process direction of the printing system;
(d) using a processor, determining a descriptor parameter set for a streak template that best approximates the density profile using a basis selection algorithm, the descriptor parameter set including:
a location parameter along the cross-process direction,
a width parameter along the cross-process direction, and
an intensity parameter at the location;
(e) updating the density profile according to the streak template and the descriptor parameter set;
where updating the density profile according to the streak template and the descriptor parameter set comprises subtracting the streak template described using the descriptor parameter set from the current density profile;
(f) repeating steps (d) and (e) to determine at least a further descriptor parameter set and to further update the density profile; and
(g) generating a printer streak characterization according to the streak template and the descriptor parameter sets.
2. The method of claim 1 , where the descriptor parameter set is determined using a matching pursuit basis selection algorithm.
3. The method of claim 2 , where determining the descriptor parameter set for a streak template comprises:
performing a discrete wavelet decomposition using the density profile and a wavelet function to generate:
a location search range for the location parameter along the cross-process direction, and
a width parameter search range for the width parameter along the cross-process direction; and
restricting the basis selection algorithm according to the location search range and the width parameter search range.
4. The method of claim 3 , where performing the discrete wavelet decomposition comprises computing a projection of the density profile onto the wavelet function.
5. The method of claim 4 , where the wavelet function has a shape that is similar to the streak template.
6. The method of claim 3 , where the wavelet function has a shape that is similar to the streak template.
7. The method of claim 2 , where the printer streak characterization comprises estimates of a plurality of printer streaks individually characterized by a corresponding one of the descriptor parameter sets.
8. The method of claim 7 , where the individual streak estimates are characterized according to the following equation:
h i x (α i t−τ i ),
where τ i is the location parameter along the cross-process direction, α i is the width parameter along the cross-process direction, h i is the intensity parameter at the location τ i , and x(t) is the streak template.
9. The method of claim 1 , where the test image is printed according to an input characterization data set representing a uniform selected color or gray scale shade.
10. A method of characterizing printer streaks, the method comprising:
(a) printing a test image onto a printable media according to an input characterization data set using a printing system;
(b) measuring the test image to generate a characterization data set representing measurements of intensity or color values observed from the test image; and
(c) generating a density profile using the characterization data set, the density profile representing intensity or color value variation of the test image in a cross-process direction transverse to a process direction of the printing system;
(d) using a processor, determining a descriptor parameter set for a streak template that best approximates the density profile using a basis selection algorithm, the descriptor parameter set including:
a location parameter along the cross-process direction,
a width parameter along the cross-process direction, and
an intensity parameter at the location;
(e) updating the density profile according to the streak template and the descriptor parameter set;
(f) repeating steps (d) and (e) to determine at least a further descriptor parameter set and to further update the density profile; and
(g) generating a printer streak characterization according to the streak template and the descriptor parameter sets;
where determining the descriptor parameter set for a streak template comprises:
performing a discrete wavelet decomposition using the density profile and a wavelet function to generate:
a location search range for the location parameter along the cross-process direction, and
a width parameter search range for the width parameter along the cross-process direction; and
restricting the basis selection algorithm according to the location search range and the width parameter search range.
11. The method of claim 10 , where the printer streak characterization comprises estimates of a plurality of printer streaks individually characterized by a corresponding one of the descriptor parameter sets.
12. The method of claim 11 , where the individual streak estimates are characterized according to the following equation:
h i x (α i t−τ i ),
where τ i is the location parameter along the cross-process direction, α i is the width parameter along the cross-process direction, h i is the intensity parameter at the location τ i , and x(t) is the streak template.
13. The method of claim 10 , where performing the discrete wavelet decomposition comprises computing a projection of the density profile onto the wavelet function.
14. The method of claim 13 , where the projection of the density profile onto the following wavelet function:
v (2 k ( t −τ)),
where ψ(t) is the wavelet function ( 124 d ), where t and τ are discrete, and k is a decomposition level corresponding to a scale or width of 2 k .
15. The method of claim 14 , where the wavelet function has a shape that is similar to the streak template.
16. The method of claim 15 , where the streak template is a raised cosine shape and where the wavelet function has a Mexican hat shape.
17. The method of claim 10 , where the wavelet function has a shape that is similar to the streak template.
18. The method of claim 10 , where the printer streak characterization comprises estimates of a plurality of printer streaks individually characterized by a corresponding one of the descriptor parameter sets.
19. The method of claim 18 , where the individual streak estimates are characterized according to the following equation:
h i x (α i t−τ i ),
where τ i is the location parameter along the cross-process direction, α i is the width parameter along the cross-process direction, h i is the intensity parameter at the location τ i , and x(t) is the streak template.
20. The method of claim 10 , where generating the density profile comprises averaging or integrating the characterization data set.
21. A printer streak characterization system for characterizing printer streaks, comprising:
a memory storing a characterization data set representing measurements of intensity or color values observed from a test image printed in a printable media; and
a processor operative to generate a density profile using the characterization data set, the density profile representing intensity or color value variation of the test image in a cross-process direction transverse to a process direction of the printing system;
the processor being operative to determine a descriptor parameter set for a streak template that best approximates the density profile using a basis selection algorithm, the descriptor parameter set including:
a location parameter along the cross-process direction,
a width parameter along the cross-process direction, and
an intensity parameter at the location;
the processor being operative to update the density profile according to the streak template and the descriptor parameter set;
the processor being operative to iteratively determine further descriptor parameter sets and to further update the density profile; and
the processor being operative to generate a printer streak characterization according to the streak template and the descriptor parameter set;
where the processor is operative to determine the descriptor parameter set for a streak template by performing a discrete wavelet decomposition using the density profile and a wavelet function to generate:
a location search range for the location parameter along the cross-process direction, and
a width parameter search range for the width parameter along the cross-process direction; and
where the processor is operative to restrict the basis selection algorithm according to the location search range and the width parameter search range.
22. The printer streak characterization system of claim 21 , where the memory and the processor are integrated into a printing system, the printing system comprising:
at least one print engine operative to print the test image onto the printable media according to an input characterization data set; and
means for measuring the test image to generate the characterization data set representing measurements of intensity or color values observed from the test image.
23. The printer streak characterization system of claim 21 , where the processor is operative to determine the descriptor parameter set using a matching pursuit basis selection algorithm.
24. The printer streak characterization system of claim 21 , where the test image is printed according to an input characterization data set representing a uniform selected color or gray scale shade.