Density-dependent sharpening
View Patent ↗A sharpening filter is disclosed for performing density-dependent sharpening on digital images. In one embodiment, a digital image to be sharpened is decomposed into a plurality of high-pass versions of the image at different resolutions. These high-pass images are gained at each resolution and recombined with the original image to produce a sharpened version of the image. The gains that are applied at each resolution are density-dependent. As a result, the effects of density-dependent blurring are counteracted, such that the sharpness of the final printed image is independent of the print density. Techniques are disclosed for performing such density-dependent sharpening with a high degree of computational efficiency.
1. A method for processing a source image, the method comprising steps of:
(A) identifying a first portion of the source image having a first density d 0 ;
(B) identifying a first gain g 0 based on the first density d 0 ;
(C) applying a sharpening filter with the first gain g 0 to produce a first portion of a sharpened image;
(D) identifying a second portion of the source image having a second density d 1 that differs from the first density d 0 ;
(E) identifying a second gain g 1 based on the second density d 1 , wherein the second gain g 1 differs from the first gain g 0 ; and
(F) applying the sharpening filter with the second gain g 1 to produce a second portion of the sharpened image.
2. The method of claim 1 , further comprising steps of:
(G) prior to step (C), identifying a first support so based on the first density d 0 ; and
(H) prior to step (F), identifying a second support s 1 based on the second density d 1 ;
wherein step (C) comprises a step of applying the sharpening filter with the first gain g 0 and the first support s 0 to produce the first portion of the sharpened image; and
wherein step (F) comprises a step of applying the sharpening filter with the second gain g 1 and the second support s 1 to produce the second portion of the sharpened image.
3. The method of claim 1 , wherein the step (B) comprises a step of:
(B)(1) identifying gains of a plurality of basis functions for the first density d 0 ; and
wherein the step (C) comprises steps of:
(C)(1) computing projections of the source image onto the plurality of basis functions; and
(C)(2) producing the first portion of the sharpened image by combining the projections using the gains.
4. A device for processing a source image, the device comprising:
first identification means for identifying a first portion of the source image having a first density d 0 ;
second identification means for identifying a first gain g 0 based on the first density d 0 ;
first application means for applying a sharpening filter with the first gain g 0 to produce a first portion of a sharpened image;
third identification means for identifying a second portion of the source image having a second density d 1 that differs from the first density d 0 ;
fourth identification means for identifying a second gain g 1 based on the second density d 1 , wherein the second gain g 1 differs from the first gain g 0 ; and
second application means for applying the sharpening filter with the second gain g 1 to produce a second portion of the sharpened image.
5. The device of claim 4 , further comprising:
means for identifying a first support s 0 based on the first density d 0 ; and
means for identifying a second support s 1 based on the second density d 1 ;
wherein the first application means comprises means for applying the sharpening filter with the first gain g 0 and the first support s 0 to produce the first portion of the sharpened image; and
wherein the second application means comprises means for applying the sharpening filter with the second gain g 1 and the second support s 1 to produce the second portion of the sharpened image.
6. The device of claim 4 , wherein the second identification means comprises:
means for identifying gains of a plurality of basis functions for the first density d 0 ; and
wherein the first application means comprises:
means for computing projections of the source image onto the plurality of basis functions; and
means for producing the first portion of the sharpened image by combining the projections using the gains.
7. A method for processing a source image, the method comprising steps of:
(A) initializing a sharpened version of the source image;
(B) for each of a plurality of resolutions l, performing steps of:
(1) identifying a gain G associated with resolution l;
(2) identifying a projection P of the source image onto a basis function B associated with resolution l;
(3) updating the sharpened version of the source image at resolution l based on the gain G and the projection P; and
(C) providing the updated sharpened version of the source image as a final sharpened version of the source image.
8. The method of claim 7 , wherein the step (B)(2) comprises steps of:
(B)(2)(a) obtaining a representation of the source image at resolution l;
(B)(2)(b) obtaining a low-pass band of the source image at resolution l; and
(B)(2)(c) obtaining a high-pass band of the source image at resolution l based on the representation of the source image at resolution l and the low-pass band of the source image at resolution l.
9. The method of claim 8 , wherein the step (B)(2)(a) comprises steps of:
(B)(2)(a)(i) low-pass filtering the source image to produce a low-pass image; and
(B)(2)(a)(ii) down-sampling the low-pass image to produce the representation of the source image at resolution l.
10. The method of claim 9 , wherein the step (B)(2)(b) comprises steps of:
(B)(2)(b)(i) up-sampling the representation of the source image at resolution l to produce up-sampled image; and
(B)(2)(b)(ii) low-pass filtering the up-sampled image to produce the low-pass band of the source image at resolution l.
11. The method of claim 10 , wherein the step (B)(2)(c) comprises a step of subtracting the low-pass band from the source image to produce the high-pass band.
12. The method of claim 7 , wherein step (B)(3) comprises steps of:
(B)(3)(a) multiplying the projection P by the gain G to produce a product; and
(B)(3)(b) adding the product to the sharpened version of the source image at resolution l to produce an updated sharpened version of the source image at resolution l.
13. The method of claim 7 , further comprising a step of:
(D) prior to the step (B), identifying average basis functions for each of the plurality of resolutions l; and
(E) prior to the step (B), for each of a plurality of densities d:
(1) identifying a desired frequency response for density d; and
(2) identifying gains for density d based on the average basis functions and the desired frequency response for density d;
wherein the step (B)(1) comprises a step of identifying as the gain G one of the gains identified in step (E)(2).
14. The method of claim 13 , wherein the step (E)(2) comprises steps of:
(E)(2)(a) identifying a weighting function; and
(E) (2) (b) identifying gains for density d based on the average basis functions, the desired frequency response for density d, and the weighting function.
15. A device for processing a source image, the device comprising:
means for initializing a sharpened version of the source image;
iteration means comprising, for each of a plurality of resolutions l:
first identification means for identifying a gain G associated with resolution l;
second identification means for identifying a projection P of the source image onto a basis function B associated with resolution l;
third identification means updating the sharpened version of the source image at resolution l based on the gain G and the projection P; and
provision means for providing the updated sharpened version of the source image as a final sharpened version of the source image.
16. The device of claim 15 , wherein the second identification means comprises:
first means for obtaining a representation of the source image at resolution l;
second means for obtaining a low-pass band of the source image at resolution l; and
third means for obtaining a high-pass band of the source image at resolution l based on the representation of the source image at resolution l and the low-pass band of the source image at resolution l.
17. The device of claim 16 , wherein the first means for obtaining comprises:
means for low-pass filtering the source image to produce a low-pass image; and
means for down-sampling the low-pass image to produce the representation of the source image at resolution l.
18. The device of claim 17 , wherein the second means for obtaining comprises:
means for up-sampling the representation of the source image at resolution l to produce up-sampled image; and
means for low-pass filtering the up-sampled image to produce the low-pass band of the source image at resolution l.
19. The device of claim 18 , wherein the third means for obtaining comprises means for subtracting the low-pass band from the source image to produce the high-pass band.
20. The device of claim 15 , wherein provision means comprises:
means for multiplying the projection P by the gain G to produce a product; and
means for adding the product to the sharpened version of the source image at resolution l to produce an updated sharpened version of the source image at resolution l.
21. The device of claim 15 , further comprising:
fourth identification means for identifying average basis functions for each of the plurality of resolutions l; and
iteration means comprising, for each of a plurality of densities d:
fifth identification means for identifying a desired frequency response for density d; and
sixth identification means for identifying gains for density d based on the average basis functions and the desired frequency response for density d;
wherein the first identification means comprises means for identifying as the gain G one of the gains identified by the sixth identification means.
22. The device of claim 21 , wherein the sixth identification means comprises:
means for identifying a weighting function; and
means for identifying gains for density d based on the average basis functions, the desired frequency response for density d, and the weighting function.