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United States Patent5726772
Parker , ; et al.March 10, 1998
Title
Method and apparatus for halftone rendering of a gray scale image using a blue noise mask
Abstract
A method of and system for rendering a halftone image of a gray scale image by utilizing a pixel-by-pixel comparison of the gray scale image against a blue noise mask is disclosed in which the gray scale image is scanned on a pixel-by-pixel basis and compared on a pixel-by-pixel basis to an array of corresponding data points contained in a blue noise mask stored in a PROM or computer memory in order to produce the desired halftoned image. Both digital and optically implemented halftone methods are disclosed. Application specific modifications of the blue noise mask as well as its use for producing halftoned color images are also disclosed.
Inventors:Parker; Kevin J. (Rochester, NY), Mitsa; Theophano  (Iowa City, IA)
Assignee:Research Corporation Technologies (Tucson, AZ)
Appl. No.:540038
Filed:October 6, 1995
Current U.S. Class:358/3.19 358/465 
Field of Search:358/456,465,466,455,457,460,444,534,535,523,524,533 395/112,117
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Primary Examiner: Coles, Sr.; Edward L.
Assistant Examiner: Lee; Fan
Attorney, Agent or Firm:Wigman, Cohen, Leitner & Myers, P.C.
Parent Case Text


This is a continuation of co-pending application Ser. No. 08/251,140 filed on May 31, 1994, which was a continuation application of U.S. Pat. No. 5,341,228 filed on Dec. 3, 1991, which was a C-I-P application of U.S. Pat. No. 5,111,310 filed Dec. 4, 1990.

This application is a continuation-in-part of U.S. patent application Ser. No. 07/622,056, filed Dec. 4, 1990 and entitled METHOD AND APPARATUS FOR HALFTONE RENDERING OF A GRAY SCALE IMAGE USING A BLUE NOISE MASK.
Claims

What is claimed is:
1. A machine comprising a computer readable storage device which stores a dither matrix for use in halftoning image information and a comparator responsive to said computer readable storage device, said dither matrix comprising at least one array, said at least one array, when thresholded at a number of levels produces a number of dot profiles, a plurality of said number of dot profiles each having a power spectrum substantially characteristic of a blue noise power spectrum for the level at which such dot profile is produced.

2. The machine of claim 1, wherein said computer readable storage device comprises a computer memory.

3. The machine of claim 1, wherein a majority of said number of dot profiles have a power spectrum substantially characteristic of a blue noise power spectrum for the level at which such dot profile is produced.

4. The machine of claim 1, wherein substantially all of said number of dot profiles have a power spectrum substantially characteristic of a blue noise power spectrum for the level at which such dot profile is produced.

5. The machine of claim 1, wherein the power spectra are modified by human visual response.

6. A machine comprising a computer readable storage device which stores a dither matrix for use in halftoning image information and comparator responsive to said dither matrix, said dither matrix comprising at least one thresholdable array designed to produce a plurality of locally aperiodic dot profiles with wraparound properties.

7. The machine of claim 6, wherein said array comprises a multibit array.

8. The machine of claim 6, wherein each of said dot profiles is associated with a respective threshold level.

9. The machine of claim 6, wherein said array comprises a cumulative array.

10. The machine of claim 6, wherein each of said dot profiles is visually pleasing.

11. The machine of claim 6, wherein said comparator is further responsive to information derived from said image information.

12. The machine of claim 6, wherein said image comprises a color image.

13. The machine of claim 6, wherein said computer readable storage device comprises a computer memory.

14. The machine of claim 6, wherein each dot profile is matched to a blue noise power spectrum modified by human visual response.

15. A machine comprising a computer readable storage device which stores a dither matrix for a halftoning process and a comparator responsive to said computer readable storage device, said dither matrix comprising a thresholdable multibit array, said multibit array, when thresholded at a number of levels, producing a plurality of substantially blue noise dot profiles, each dot profile appropriate for the respective level.

16. The machine of claim 15, wherein said multibit array comprises a two-dimensional array.

17. The machine of claim 15, wherein said computer readable storage device comprises a computer memory.

18. The machine of claim 17, wherein said computer memory comprises a read only memory.

19. The machine of claim 15, wherein said computer readable storage device is incorporated into a digital computer.

20. The machine of claim 15, wherein the dot profiles are matched to respective blue noise power spectra modified by human visual response.

21. The machine of claim 15, wherein said multibit array, when thresholded at a number of levels, produces a majority of substantially blue noise dot profiles.

22. The machine of claim 15, wherein said multibit array, when thresholded at a number of levels, produces substantially all substantially blue noise dot profiles.

23. A machine comprising a computer readable storage device which stores a dither matrix for a halftoning process and a comparator responsive to said computer readable storage device, said dither matrix comprising a thresholdable array that, when thresholded at a number of levels, produces a number of dot profiles, a plurality of said dot profiles being visually pleasing.

24. The machine of claim 23, wherein a plurality of said number of dot profiles are respectively locally aperiodic and substantially isotropic dot profiles having small low-frequency components.

25. The machine of claim 24, wherein said dot profiles each have a power spectrum characterized by a respective principal frequency, said small low-frequency components being below the principal frequency, and at least a plurality of said dot profiles each having high-frequency components above the respective principal frequency, at least some of said high-frequency components being larger than said low-frequency components.

26. The machine of claim 25, wherein each of said plurality of levels is associated with a respective level, and said principal frequency varies with said level.

27. The machine of claim 26, wherein said principal frequency varies with said level according to a nonlinear function.

28. The machine of claim 23, wherein said computer readable storage device comprises a computer memory.

29. The machine of claim 23, wherein the dot profiles are matched to respective power spectra modified by human visual response.

30. The machine of claim 23, wherein a plurality of said number of dot profiles are substantially isotropic.

31. The machine of claim 23, wherein a majority of said number of dot profiles are visually pleasing.

32. The machine of claim 31, wherein said majority of said number of said dot profiles are respectively locally aperiodic and substantially isotropic dot profiles having small low-frequency components.

33. The machine of claim 23, wherein substantially all of said number of dot profiles are visually pleasing.

34. The machine of claim 33, wherein substantially all of said number of said dot profiles are respectively locally aperiodic and substantially isotropic dot profiles having small low-frequency components.

35. An apparatus for use in halftoning an image, said apparatus comprising a dither matrix stored in a computer readable storage device and a comparator responsive to said computer readable storage device, said dither matrix comprising a multibit array that can be thresholded, said multibit array, when thresholded at a plurality of respective levels, producing a plurality of substantially blue noise dot profiles, each dot profile appropriate for the respective level.

36. The apparatus of claim 35, further comprising a display device responsive to said comparator, said display device receiving a halftoned array output from said comparator and producing a halftoned output image.

37. The apparatus of claim 35, wherein said computer readable storage device comprises a computer memory.

38. The apparatus of claim 35, wherein the dot profiles are matched to respective power spectra modified by human visual response.

39. A computer readable memory device comprising a thresholdable halftoning mask, said halftoning mask producing a plurality of dot profiles when thresholded at respective levels, and at least a plurality of said dot profiles having a substantially blue noise power spectrum appropriate for the respective level and a comparator responsive to said computer readable memory device.

40. The computer readable memory device of claim 39, wherein said mask is stored as an array.

41. The computer readable memory device of claim 40, wherein said array comprises a plurality of storage elements, each storage element containing a respective multibit data value.

42. A combination of a printing device and the computer readable memory device of claim 41.

43. The combination of claim 42, wherein said printing device comprises at least one of a laser printer, an ink jet printer, a thermal printer, a thermal wax printer, a dye-sublimation printer and a bubble jet printer.

44. A combination of a comparator and the computer readable memory device of claim 43, said comparator having a first input, a second input, and an output, said first input responsive to said memory device.

45. The combination of claim 44, further comprising a scanner for digitizing an input image and generating an image array, said image array comprising a plurality of values, and wherein said second input is responsive to said scanner.

46. The combination of claim 45, wherein said comparator performs a comparison between signals appearing on said first and second inputs.

47. The combination of claim 46, further comprising a display responsive to said comparator.

48. The combination of claim 47, wherein said display comprises a binary display.

49. A combination of a recording device and the computer readable memory device of claim 41.

50. In combination, a facsimile machine and the computer readable memory device of claim 39.

51. The memory device of claim 39, wherein the power spectra are modified by human visual response.

52. A machine comprising a computer readable storage device which stores a dither matrix for use in halftoning image information and a comparator responsive to said computer readable storage device, said dither matrix comprising at least one thresholdable array designed to produce a plurality of locally aperiodic, non-white noise dot profiles when thresholded at respective levels.

53. The machine of claim 52, wherein the dot profiles are substantially blue noise dot profiles.

54. The machine of 52, wherein each of the dot profiles has a respective power spectrum substantially characteristic of a blue noise power spectrum.

55. The machine of claim 52, wherein the dot profiles have small low-frequency components.

56. The machine of claim 52, wherein the dot profiles have smaller low-frequency components than mid-range or high-frequency components.

57. A computer readable memory device comprising a thresholdable halftoning mask, said halftoning mask designed to produce a plurality of visually pleasing dot profiles when thresholded at a number of levels and a comparator responsive to said computer readable memory device.

58. The memory device of claim 57, wherein the dot profiles are substantially blue noise dot profiles.

59. The memory device of claim 57, wherein each of the dot profiles has a respective power spectrum substantially characteristic of a blue noise power spectrum.

60. The memory device of claim 57, wherein the dot profiles have small low-frequency components.

61. The computer readable memory device of claim 57, wherein said visually pleasing dot profiles are locally aperiodic, non-white noise dot profiles.

62. The computer readable memory device of claim 57, wherein said halftoning mask is designed to produce a majority of visually pleasing dot profiles when thresholded at a number of levels.

63. The computer readable memory device of claim 57, wherein said halftoning mask is designed to produce substantially all visually pleasing dot profiles when thresholded at a number of levels.

64. The computer readable memory device of claim 63, wherein said visually pleasing dot profiles are locally aperiodic, non-white noise dot profiles.

65. The computer readable memory device of claim 64, wherein said visually pleasing dot profiles are locally aperiodic, non-white noise dot profiles.

66. A machine comprising a computer readable storage device which stores an array for use in halftoning image information, said array comprising a non-white noise, locally aperiodic, thresholdable dither matrix and a comparator responsive to said dither matrix.

67. The machine of claim 66, wherein said array comprises a blue-noise, locally aperiodic thresholdable matrix.

68. The machine of claim 66, wherein said array comprises a multibit array.

69. The machine of claim 66, wherein said array produces a plurality of locally aperiodic dot profiles with wraparound properties, each of said dot profiles being associated with a respective threshold level.

70. The machine of claim 66, wherein said array comprises a cumulative array.

71. The machine of claim 66, wherein said dither matrix is designed to produce a plurality of locally aperiodic dot profiles, and wherein each of said dot profiles is visually pleasing.

72. The machine of claim 66, wherein said comparator is further responsive to information derived from an image.

73. The machine of claim 72, wherein said image comprises a color image.

74. The machine of claim 66, wherein said computer readable storage device comprises a computer memory.

75. A machine comprising a computer readable storage device which stores an array for use in halftoning image information, said array comprising a non-white noise, non-ordered thresholdable dither matrix and a comparator responsive to said dither matrix.

76. The machine of claim 75, wherein said array comprises a blue noise, non-ordered thresholdable dither matrix.

77. Apparatus for generating a modified blue noise mask array in which said modified blue noise mask array may be used to generate a more pleasing halftoned image than a non-modified blue noise mask array, comprising:
a) a reading device for reading each of the values of the blue noise mask array to be modified:
b) a receiving device for receiving maximum and minimum predetermined values input by a user;
c) a modifying device for modifying each value of said blue noise mask array using at least one of said maximum and minimum predetermined values and a direct value mapping function;
d) a first comparing device for comparing each of said values of said modified blue noise mask array to said maximum predetermined value and replacing said value if it exceeds said maximum predetermined value; and
e) a second comparing device for comparing each of said values of said modified blue noise mask array to said minimum predetermined value and replacing said value if it is less than said minimum predetermined value;
wherein said maximum and minimum predetermined values input by said user and said direct value mapping function are selected to compensate for characteristics of at least one of printer and display devices used by said user so as to form a more pleasing halftoned image.

78. The apparatus of claim 77, further including a memory for storing said modified blue noise mask array.
Description
BACKGROUND OF THE INVENTION

The present invention relates generally to the halftoning of images. More particularly, the present invention relates to a method of and system for rendering a halftone by utilizing a pixel-by-pixel comparison of the gray scale image against a blue noise mask.

Many printing devices are not capable of reproducing gray scale images because they are hi-level. As a result, the binary representation of a gray scale image is a necessity in a wide range of applications such as laser printers, facsimile machines, lithography (newspaper printing), liquid crystal displays and plasma panels. Gray scale images are typically converted to binary images using halftone techniques. Halftoning renders the illusion of various shades of gray by using only two levels, black and white, and can be implemented either digitally (facsimile machines, laser printers) or optically (newspaper printing).

Halftoning algorithms are classified into point and neighborhood algorithms according to the number of points from the input gray scale image required to calculate one output point in the output binary image. In the case of digital halftoning, points correspond to pixels. In point algorithms, the halftoning is accomplished by a simple pointwise comparison of the gray scale image against a nonimage, usually aperiodic (but not always) array or mask. For every point in the input image, depending on which point value (the gray scale image or the mask) is larger, either a 1 or 0 is placed respectively at the corresponding location in the binary output image. Halftoning using neighborhood algorithms is not done by simple pointwise comparison, but usually requires filtering operations that involve a number of points from the input gray scale image in order to calculate one point in the output image.

At present, given the existing halftoning algorithms, the choice for a specific halftoning algorithm depends on the target device and always requires a trade-off between image quality and speed. Neighborhood halftoning algorithms result in a good image quality (although the image is not completely artifact free), but they are slow and cannot be optically implemented. That leaves point algorithms as the only choice for optical applications such as newspaper printing. Point algorithms are fast and are suitable for all target devices, but the output usually suffers from artifacts such as periodic artifacts and false contours.

The halftoning system disclosed herein utilizes a point algorithm, and combines the output image quality of neighborhood algorithms with the speed and wide application range of point algorithms. A point algorithm is utilized and the halftoning is achieved by a pixelwise comparison against a nonimage array, called the "blue noise" mask.

The digital halftoning of images with multiple levels, such as gray scale levels, is known in the art. Two major techniques are currently in use. They are the ordered dither and the error diffusion methods. See Digital Halftoning by R. Ulichney, MIT Press, Cambridge, Mass. (1987). See also R. W. Floyd and L. Steinberg, "Adaptive algorithm for spatial gray scale", SID International Symposium Digest of Technical Papers, pps. 36-37. The Floyd and Steinberg paper is directed to the digital halftoning of a gray scale.

The major ordered dither techniques are the clustered-dot dither and dispersed-dot dither techniques. A white noise random dither technique is seldom utilized because it produces the poorest quality image and, of the other two dither techniques, clustered-dot is by far the most used. Both of those techniques are based upon a threshold screen pattern that is of a fixed size. For example, 6.times.6 threshold screens may be compared with the digital input values. If the input digital value is greater than the screen pattern number, a 1 is produced and, if it is less, a 0 value is assigned. The number of levels that can be represented using either technique depends on the size of the screen. For example, a 6.times.6 screen can produce 36
unique levels.

More levels can be achieved with larger patterns, however, a reduction in the effective resolution occurs because the ability to transition among levels is at a coarser pitch. At the pixel rate of about 300 to 500 per inch, which is the average pixel rate of copiers and laser printers, the pattern artifacts are visible for screen patterns larger than 4.times.4, and, since 16 levels do not provide an adequate precision for typical continuous-tone imagery, a suboptimal resolution is usually obtained.

One solution to such a problem is disclosed by Ulichney in a paper "Dithering with Blue Noise" published in the Proceedings of the IEEE, Vol. 76, No. 1, January 1988. In that article, a method of spatial dithering is described which renders the illusion of continuous-tone pictures on displays that are capable of only producing binary picture elements. The method produces a blue noise pattern high frequency white noise from a filter to provide desirable properties for halftoning. More specifically, Ulichney uses perturbed-weight error diffusion methods which when digitally implemented run at a much slower speed (approximately 100 times slower) than is attainable with the present invention.

Error diffusion techniques, such as that disclosed in the Ulichney IEEE article, are fundamentally different from ordered dither techniques in that there is no fixed screen pattern. Rather, a recursive algorithm is used that attempts to correct errors made by representing the continuous signal by binary values.

The error diffusion method described by Ulichney, and others, such as Floyd and Steinberg, also has the disadvantage that it requires scanning, convolution-style calculations and, although it can be implemented for use with copiers, facsimile machines, etc., requires local calculations. It cannot, however, be optically implemented. In addition, all error diffusion techniques, including those described by Ulichney and Floyd and Steinberg, show scanning and start-up artifacts, which are not present in the instant invention. Also, while Ulichney describes a method that produces blue noise, the blue noise patterns produced by the present invention are more isotropic than those produced by Ulichney or other error diffusion methods. Utilizing ordered dither methods produces notably periodic patterns that are even much more obtrusive than those produced by error diffusion methods.

In some prior art systems, all dot profiles corresponding to different gray levels were derived independently, as if each grade level was its own special case. Thus, for example, in U.S. Pat. No. 4,920,501, to Sullivan et al., many individual dot profiles, corresponding to the desired number of gray levels, must be stored. In the present invention, on the other hand, dot profiles are built "on top of" the profiles from lower gray levels, such that a single valued 2-dimensional function, that is, the cumulative array or blue noise mask, can be constructed. When that single valued function is thresholded at any level, the resulting binary pattern is exactly the blue noise dot profile design for that particular gray level, p(i,j,g), where p can be one or zero corresponding to black or white, i and j are coordinates of pixels, and g represents a gray level 0<g<1.

Another drawback to prior art methods is that the dot profile for a given gray level was designed to have blue noise properties by indirect methods, such as using an error diffusion filter with perturbed weights (Ulichney) or by a "simulated annealing" algorithm, as in U.S. Pat. No. 4,920,501. The method disclosed herein is advantageous with respect to the prior art in that the desired blue noise power spectrum is produced through the use of a filter on the dot profile and is implemented directly in the transform domain. Such filtering results in a nearly ideal blue noise pattern with implicit long-scale periodicity because of the circular convolution implicit in the use of discrete Fourier transforms. However, the filtered pattern is no longer binary. Thus, a minimization of error approach is utilized in which the largest differences between the ideal, filtered, blue noise pattern and the unfiltered dot profile are identified. The magnitude and location of those differences indicate the pixels in which ones and zeros could be changed to produce a more ideal blue noise dot profile.

Display devices, including printing devices as well as media, have their own unique input-output characteristics. In some uses, such as medical ultrasound imaging, the user has traditionally been provided with some control as to the final gray scale mapping. For example, the user may be able to select between high and low contrast images. The display and film characteristics, however, must be accounted for in each rendition.

In the area of halftone rendering, traditional halftone screens using small (for example, 8.times.8 pixel) kernels provide only limited degrees of freedom to alter the input-output characteristics and usually a linear cumulative distribution function (CDF) has been reported. See Digital Halftoning by R. Ulichney, MIT Press, Cambridge, Mass. (1987). See also, R. Bayer, "An Optimum Method for 2 Level Rendition of Continuous Tone pictures", IEEE International Conf. Comm, 1973, and G. C. Reid, Postscript Language Program Design (green book), Addison-Wesley Publishing Co., New York, N.Y. (1988), page 137. By a linear CDF, it is meant that 10% of the halftone kernel pixel contents will be less than 10% of the maximum value and that 50% of the pixels will contain values less than 50% of the maximum values, and so forth.

In the case of the blue noise mask method disclosed herein, a large unstructured pattern of, for example, 256.times.256 pixel kernels, provides sufficient degrees of freedom to modify the cumulative distribution function so as to provide both linear and non-linear mappings of input and output characteristics. That makes it possible to construct specialized blue noise masks in which a particular printer output and media characteristics can be compensated for by a modified blue noise mask generated as disclosed in this application.

The present inventive method herein may also be applied to color halftoning, by independently thresholding each of the component colors against the disclosed blue noise mask and then overprinting. Such method produces a pleasing pattern without any blurring of the image. Such method is a great improvement over the known prior art, which is discussed below.

In U.S. Pat. No. 5,010,398, there is disclosed a method for color corrections by dry dye etching using a photographically produced mask which may be used in the production of printing plates for printing reproductions of colored originals and in which a contact print is overexposed to a photographic mask. The photographic mask is constituted so as to isolate a selected area in addition to being exposed normally for obtaining an exact copy of an original halftone separation. The mask is electronically generated by scanning each separation, digitizing each signal and then storing the digital values in a digital storage device.

U.S. Pat. No. 4,974,067 relates to a multi-step digital color image reproducing method and apparatus which separates an original image into a plurality of color components to produce image data associated with each respective one of the color components. The image data are individually processed to provide record color component density data which data are used to record a halftone representation pattern of that color component.

An apparatus and methods for digital halftoning is disclosed in U.S. Pat. No. 4,924,301 for producing halftone screens or color separations from continuous tone intensity signals that are supplied by an optical scanner. Using a digital signal processor, the continuous tone intensity values are processed to establish memory maps which, in conjunction with a digital data output device such as a laser printer, produces the desired halftone screen. The digital signal processor utilizes a dither matrix in order to produce halftone screens having a screen angle that does not substantially differ from the screen angles of the yellow, cyan and magenta color separations in conventional four color halftone printing. A dither array is also utilized to produce the halftone screens having a screen angle that substantially differs from the screen angle used in the black halftone color separation in conventional four color halftone printing.

U.S. Pat. No. 4,342,046 relates to a contact screen for making color separation halftone blocks for use in a picture reproducing machine in which a plurality of halftone screens having different screen angles are arranged on a base film in the corresponding positions of color separation reproduction pictures to be reproduced on the base film and transparent blank spaces are formed between two adjacent halftone screens.

A method and apparatus for making monochrome facsimiles of color images on color displays is disclosed in U.S. Pat. No. 4,308,533 for making 35 MM color slides from a color image created on a color cathode tube terminal. U.S. Pat. No.
3,085,878 relates to the preparation of traditional halftone screens for color separation.

U.S. Pat. No. 4,657,831 relates to the production of electrophotographic color proofs of halftone dot pattern images which closely simulate the dot gain of prints made with lithographic plates and liquid inks.

A process for the production of photographic masks is disclosed in U.S. Pat. No. 4,997,733 in which such masks are used for the tonal correction by dry dot etching in which the selection of a particular halftone color separation image or overlaying registering combination of halftone color separation images is determined on the basis of optical density differences in at least one such halftone color separation. Such differences include differences in contrast, between each area to be isolated as a substantially transparent area, and at least one particular background area surrounding each area to be isolated.

U.S. Pat. No. 4,477,833 is directed to a method of color conversion with improved interpolation in which an apparatus for converting a color image from one colored space to another colored space includes a memory which stores a finite number of output signals which represent colors in the output space and which is addressed by signals representing a color in the input space. The interpolation process is utilized in order to derive an output color value for an input color located between colors stored in the memory.

A method and apparatus for producing halftone printing forms with rotated screens based upon randomly selected screen threshold values is disclosed in U.S. Pat. No. 4,700,235. The screens have arbitrary screen angles and screen width. Screen dots are exposed on a recording media by means of a recording element whose exposure beam is switched on and off by a control signal.

None of the foregoing references have the advantages of the use of the blue noise mask method disclosed herein in producing pleasing, isotropic, non-clumpy, moire resistant patterns with only some spreading out of the color or ink but with no blurring of the image.

SUMMARY AND OBJECTS OF THE INVENTION

In view of the foregoing, it should be apparent that there still exists a need in the art for a method of and apparatus for the halftone rendering of gray scale images in which a digital data processor is utilized in a simple and precise manner to accomplish the halftone rendering to provide a binary scale image which is characterized by the pixelwise comparison of the image being analyzed against a blue noise mask. There also exists a need for the modification of such halftone rendering process in order to counter some undesirable printer and media dependent effects such that the halftone rendering of gray scales is modified to produce input and output characteristics unique to a particular type of device or media and in which the images produced are superior to those produced without such modification process.

It should likewise be apparent that there still exists a need in the art for a method for color halftoning by independently thresholding each of the component colors against a blue noise mask in order to produce a pleasing, isotropic, non-clumpy, moire resistant pattern with only some spreading out of the color or ink but with no blurring of the image.

More particularly, it is an object of this invention to provide a system for the halftone rendering of a gray scale image which has a simple and reliable mechanism for producing the desired image.

Still more particularly, it is an object of this invention to provide a system for the halftone rendering of a gray scale image which can be implemented either digitally or optically.

It is another object of this invention to provide a system for the halftone rendering of a gray scale image which tailors the image thus produced to compensate for particular output printer and media characteristics such that the undesired display of media characteristics can be substantially eliminated.

It is yet another object of this invention to provide a system for the halftone rendering of continuous tone color images such that pleasing images are produced with little spreading out of the color and with no blurring of the image.

Briefly described, these and other objects of the invention are accomplished by generating a blue noise mask which, when thresholded at any gray level g, produces a blue noise binary pattern appropriate for that gray level. After the blue noise mask has been generated, it is stored in a PROM. The image to be halftoned is then read by a scanner on a pixel-by-pixel basis and compared to the corresponding stored pixel in the blue noise mask to produce the resulting binary array. The binary image array is then converted to a binary display which is the resultant halftoned image.

After the blue noise mask has been generated and stored, it may be modified to tailor it for a particular output printer and media characteristics such that compensation is provided in a blue noise mask for undesired display and media characteristics. The blue noise mask is modified by altering the first order statistics or the cumulative distribution function (CDF) to counter such undesirable printer and media dependent effects. The blue noise mask may be modified in a variety of ways, all of which usually include punching the blue noise mask. Punching the blue noise mask involves setting the extreme low values to a certain minimum value, for example, 0 and setting the extreme high values to a certain maximum value, for example
255. The values between the maximum and the minimum are then re-linearized.

The method of generating and utilizing the blue noise mask discussed above can also be applied to color halftoning, by independently thresholding each one of the component colors against the blue noise mask and then overprinting the halftoned component color images. The blue noise mask can also be shifted by one pixel before it is used on each of the different color planes. In that manner, the color energy is spread out over a larger space. For example, the blue noise mask can be shifted one pixel up or to the side, when the red image and blue image are being halftoned, respectively. Other variations and modifications for using the blue noise mask for color halftoning are discussed in the specification. Such principles may be used for either RGB halftoning or CMYK color printing.

In an optical implementation, the gray scale image is photographed through the generated blue noise mask and the resultant superposition is printed onto a high contrast film. An additive photographic process may also be utilized in which the blue noise mask is added to the gray scale image at the film plane, for example, by a double exposure process. The photographic blue noise mask can be obtained from a calculated blue noise array using a film printer interfaced to the PROM or computer in which the blue noise mask array is stored.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a drawing showing the power spectrum of a blue noise pattern formed in accordance with the present invention;

FIG. 2 is a diagram of a flow chart for the design of the blue noise mask of the present invention;

FIG. 3 is a diagram of a flow chart for the digital implementation of halftoning using a blue noise mask in accordance with the present invention;

FIG. 4 is a schematic block diagram of a hardware system for digitally implementing halftoning using the blue noise mask in accordance with the present invention;

FIG. 5 is a drawing of a multiplicative photographic process utilized for optically implementing halftoning using a blue noise mask in accordance with the present invention;

FIG. 6 is a drawing of an additive photographic process which may be utilized in the optical implementation of halftoning using a blue noise mask in connection with the process shown in FIG. 5;

FIG. 7 is a diagram of a flow chart showing the modification of a blue noise mask to produce a punched, linearized version of that blue noise mask;

FIG. 8 is a diagram of a flow chart for the modification of a blue noise mask using the concave down sigma curve modification to produce a high resolution version of the blue noise mask;

FIG. 9 is a diagram of a flow chart for the modification of a blue noise mask using the concave up sigma curve modification to produce a low resolution version of the blue noise mask;

FIG. 10 is a drawing showing the relationship of the number of pixels to the value of pixels for a linear blue noise mask;

FIG. 11 is a drawing showing the relationship between the number of pixels and the value of pixels for a non-linear, high contrast blue noise mask produced after applying the CDSC direct mapping processing with punch; and

FIG. 12 is a diagram of a flow chart showing the application of a blue noise mask to color halftoning.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT

Prior to referring to the drawings, the following description of the theoretical underpinnings of the present invention is provided.

As described above, the present invention is a halftone rendering system which accomplishes its function by a pixel-by-pixel comparison of a gray scale image against a "blue noise" mask. As referred to herein, the term "blue noise" is a pattern with negligible low frequency components which possesses certain visually pleasing properties, as described by R. Ulichney in his book, Digital Halftoning.

In the present invention, depending upon which pixel is larger, either the gray scale image or the blue noise mask, a 1 or a 0 is placed in the binary (black or white) image file which is the halftone rendered version of the gray scale image. Using the notation that the gray scale image is M.times.N pixels in size and B-bits of gray per pixel, the blue noise mask can be a smaller array J.times.K in size where J is less than or equal to M and K is less than or equal to N with only B-1 bits per pixel.

The blue noise mask described herein is constructed to have unique first and second order properties. When thresholded at any level, for example at A% of the maximum level, exactly A out of every 100 pixels will be greater than the threshold value. In addition, the spatial distribution of the pixels above the threshold is arranged in such a manner as to form a blue noise pattern which has been shown to be visually pleasing.

The disclosed blue noise mask, therefore, has the characteristic that the first order statistics are uniformly distributed over gray levels. That is, when the blue noise mask is thresholded at a gray level g, exactly g.times.100% of all values are below the threshold. For g=0.5, exactly 50% of the blue noise mask pixels are above, and 50% below the threshold value. The blue noise mask disclosed herein also has the characteristic that when thresholded at any level g, the resulting bit pattern has a power spectrum consistent with and approximating the ideal blue noise pattern for that threshold. In addition, since the blue noise image is constructed with explicit "wraparound" properties, a small blue noise pattern of J.times.K pixels can be used to halftone render a larger M.times.N pixel's image, because the pixel-by-pixel comparison can proceed modulo J and modulo K in the respective directions, with no apparent discontinuities or obvious periodicities. However, the value of (J.times.K) should not be smaller than X/2, where X is the number of levels of the original gray scale image.

It is also desirable to describe the digital halftoning system of the present invention for the analog case in which discrete space is replaced by continuous space. Using such notation, x and y represent continuous space, while i and j represent discrete space. Thus, the gray scale image is denoted by f(x,y), the blue noise mask is denoted by m(x,y) and the output (halftoned) binary image is denoted by h(x,y).

Thus, for a B-bit image array f(i,j), the blue noise mask array m(i,j) is a B-bit array such that, when thresholded against f(i,j), up to 2.sup.B levels of varying distribution of black and white dots can be represented on a rectangular grid. Note that the dimensions of the blue noise mask can be smaller than those of the gray scale image and that the halftoning of the gray scale image is achieved by a periodic repetition of m(i,j) over the entire image plane. For example, for a
256.times.256 8-bit class of images, a 128.times.128 8-bit blue noise mask array can be used.

The binary pattern that results after thresholding the blue noise mask at a constant level g is called the dot profile for that level. The dot profiles are arrays that have the same dimensions as the mask array, and consist of ones and zeros. The ratio of ones to zeros is different for every dot profile and depends on the gray level that particular dot profile represents. In the notation used herein, the higher the gray level, the more ones and less zeros that will be contained in the dot profile. p(i,j,g) is used to denote the value of the dot profile at pixel location (i,j) and for the gray level g. g=0 is used to represent black and g=1 is used to represent white. Thus, 0.ltoreq.g.ltoreq.1. Also, by denoting as f.sub.i,j the value of the discrete space function f(i,j) at pixel location (i,j), a N.times.N binary image h(x,y) can be written as follows in terms of the dot profiles: ##EQU1## where R is the spacing between the addressable points on the display device, and rect(x)=1 if .vertline.x.vertline.<1/2 and rect(x)=0 otherwise. Therefore, for any gray scale image, the corresponding binary image h(x,y) can be constructed as follows in terms of the dot profiles: For every pixel in the gray scale image array f(i,j) that is at the (i,j) location and has a value f.sub.i,j =g, the corresponding pixel in the binary image array h(i,j) has a value that is given by the value of the g-level dot profile at the (i,j) location.

The dot profiles for every level are designed and combined in such a way as to build a single valued function, the blue noise mask. The blue noise mask is constructed such that when thresholded at any level, the resulting dot profile is a locally aperiodic and isotropic binary pattern with small low-frequency components, which in the halftoning literature, is known as a blue noise pattern. Those dot profiles are not independent of each other, but the dot profile for level g.sub.1
+.DELTA.g is constructed from the dot profile for level g.sub.1 by replacing some selected zeros with ones. For example, for a N.times.N B-bit mask array and maximum pixel value given by 2.sup.B, .DELTA.g is given by .DELTA.g=1/2.sup.B and the number of zeros that will change to ones, in order to go from level g.sub.1 to level g.sub.1 +.DELTA.g is N.sup.2 /2.sup.B.

As the dot profile is changed from its pattern at g.sub.1 to g.sub.1 +.DELTA.g, another array called the cumulative array is incremented in such a way as to keep track of the changes in dot profiles from gray level to gray level. That cumulative array (not a binary array but a B-bit array) becomes the blue noise mask because, when thresholded at any level g, the resulting binary pattern reproduces the dot profile for that level.

Referring now to the figures wherein like reference numerals are used throughout, there is shown in FIG. 1 a diagram of the power spectrum of a blue noise pattern which is free of a low frequency component and is radially symmetric. The absence of low frequency components in the frequency domain corresponds to the absence of disturbing artifacts in the spatial domain. Radial symmetry in the frequency domain corresponds to isotropy in the spatial domain. Isotropy, aperiodicity and the lack of low-frequency artifacts are all desirable properties in halftoning because they lead to visually pleasing patterns.

As shown in FIG. 1, the cutoff frequency f.sub.g, which is termed the Principal Frequency, depends as follows on the gray level g: ##EQU2## where R, as before, is the distance between addressable points on the display and the gray level g is normalized between 0 and 1. As can be seen from the above equation, f.sub.g achieves its maximum value where g=1/2, since at that level the populations of black and white dots are equal and thus very high frequency components appear in the binary image.

For a N.times.N B-bit image with 2.sup.B as the maximum pixel value, the blue noise mask is constructed as follows: First, the dot profile p[i,j,1/2] that corresponds to the 50% gray level is created. That dot profile is generated from a white noise pattern after filtering it with a highpassed circularly symmetric filter and results in a binary pattern having visually annoying low frequency components. In order to give blue noise properties to the p[i,j,1/2] dot profile, the following iteration procedure is utilized, similar to that shown in FIG. 2, which is a flow chart showing the steps for designing a blue noise mask for generating level g+.DELTA.g from level g.

Step 1. Take the 2-dimensional Fourier transform of the dot profile p[i,j,1/2] and obtain the dot profile P[u,v,1/2], where u and v are the transformed coordinates, and P represents the Fourier Transform.

Step 2. Apply a blue noise filter D(u,v,1/2) to the spectrum P[u,v,1/2] and in that way obtain the new spectrum P'[u,v,1/2]=P[u,v,1/2].times.D(u,v,1/2). The blue noise filter is designed to produce in the dot profile spectrum P'[u,v,1/2] an average cross section along a radially symmetric line shown in FIG. 1. The principal frequency is given by f.sub.g =1/.sqroot.2 R.

Step 3. Take the Inverse Fourier transform of P'[u,v,1/2] and obtain p'[i,j,1/2], which is no longer binary but has much better blue noise properties.

Step 4. Form the difference e[i,j,1/2]=p'[i,j,1/2]-p[i,j,1/2]. That difference is referred to as the error array.

Step 5. Classify all pixels into two classes according to the value of p[i,j,1/2] for each pixel; all the zeros belong in the first class and all the ones in the second. Then, rank order all the pixels in those two classes according to the value of e[i,j,1/2] for each pixel.

Step 6. Set a limit, l.sub.t =t, for the magnitude of the highest acceptable error. That limit is usually set equal to the average magnitude error. For the zeros, l.sub.t =t and for the ones, l.sub.t =-t. Change all the pixels that contain a zero and have an error higher than the defined limit to ones. Similarly, change all the pixels that contain a one and have an error smaller than the defined negative limit to zeros. The number of zeros that are changed to ones must be equal to the number of ones that are changed to zeros so that the total average is preserved. The initialization process is then complete.

The above procedure is then repeated until no pixels have an error higher than some predetermined error. Note that the magnitude of the average error becomes lower for both zeros and ones every time the procedure is repeated.

In order to finish the initialization procedure, refer to another N.times.N array, which is denoted as c[i,j,1/2] and referred to as the cumulative array, and give a value of 2.sup.B-1 to every pixel whose corresponding pixel in the dot profile has a value of zero, and give a value of 2.sup.B-1 -1 otherwise. In that way, when the cumulative array, which eventually will become the blue noise mask, is thresholded at a 50% gray leve