Method and apparatus for halftone rendering of a gray scale image using a blue noise mask

• US 5,477,305 A
• Filed: 11/22/1994
• Issued: 12/19/1995
• Est. Priority Date: 12/04/1990
• Status: Expired due to Term

• Current Assignee: Research Corporation Technologies
• Original Assignee: Research Corporation Technologies
• Inventors: Mitsa, Theophano, Parker, Kevin J.
• Primary Examiner(s): Coles, Sr., Edward L.
• Assistant Examiner(s): LEE, CHEUKFAN
• Application Number:
  US08/345,788
• Time in Patent Office: 392 Days
• Field of Search: 358/456, 358/534, 358/457, 358/455, 358/465, 358/523, 382/240
• US Class Current: 358/3.19
• CPC Class Codes: G06T 3/40 Scaling of whole images or parts thereof, e.g. expanding or contracting
• CPC Class Codes: G06T 3/4084 in the transform domain, e.g. fast Fourier transform [FFT] domain scaling
• CPC Class Codes: H04N 1/40075 Descreening, i.e. converting a halftone signal into a corresponding continuous-tone signal; Rescreening, i.e. combined descreening and halftoning
• CPC Class Codes: H04N 1/4051 producing a dispersed dots halftone pattern, the dots having substantially the same size different sizes H04N1/4057
• CPC Class Codes: H04N 1/4105 for halftone screened pictures

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.

Claims

1. Apparatus for performing the halftoning of a gray scale image by utilizing a pixel-by-pixel comparison of said image against a blue noise mask array, comprising:

a) a first memory for storing said blue noise mask array;

b) a scanner for scanning said gray scale image to be halftoned to create a gray scale image array on a pixel-by-pixel basis;

c) a second memory for storing said gray scale image array;

d) a comparator for comparing, on a pixel-by-pixel basis, the value of each corresponding pixel in said blue noise mask array and said gray scale image array to produce a binary image array; and

e) a converter for converting said binary image array to the desired halftoned image.

2. The apparatus of claim 1, wherein said blue noise mask is comprised of a continuous, single valued aperiodic blue noise function.

3. The apparatus of claim 2, wherein said blue noise function is a random function and in which, when said blue noise mask is thresholded at any level, a dot profile with desirable blue noise characteristics is produced.

4. The apparatus of claim 1, wherein said blue noise mask is formed by an at least one dimensional function having predetermined properties of a thresholded dot profile using transform domain filtering and error criteria.

5. The apparatus of claim 4, wherein said blue noise mask is formed by an at least one dimensional function using spatial domain filtering and error criteria equivalent to said transform domain filtering and error criteria.

6. The apparatus of claim 1, wherein said scanner is connected to said comparator such that said gray scale image created by said scanner is fed directly to said comparator for producing said binary image array.

7. The apparatus of claim 1, wherein said halftoned image of said gray scale image is a multitoned image having multiple gray scale levels.

8. Apparatus for utilizing a blue noise mask for halftoning a gray scale image, comprising:

a) a first memory for storing, on a pixel-by-pixel basis, a representation of said gray scale image;

b) a second memory for storing said blue noise mask, said blue noise mask being comprised of a random non-deterministic, non-white noise single valued function which is designed to produce visually pleasing dot profiles when thresholded at any level of said gray scale image; and

c) a comparator for comparing said stored representation of said gray scale image, on a pixel-by-pixel basis, with said stored blue noise mask in order to produce a halftoned image of said gray scale image.

9. The apparatus of claim 8, wherein said blue noise mask is comprised of a continuous, single valued aperiodic blue noise function.

10. The apparatus of claim 9, wherein said blue noise function is a random function and in which, when said blue noise mask is thresholded at any level, a dot profile with desirable blue noise characteristics is produced.

11. The apparatus of claim 8, wherein said blue noise mask is formed by an at least one dimensional function having predetermined properties of a thresholded dot profile using transform domain filtering and error criteria.

12. The apparatus of claim 11, wherein said blue noise mask is formed by an at least one dimensional function using spatial domain filtering and error criteria equivalent to said transform domain filtering and error criteria.

13. The apparatus of claim 8, wherein said halftoned image of said gray scale image is a multitoned image having multiple gray scale levels.

14. Apparatus for halftoning a gray scale image using a blue noise mask, comprising:

a) a memory for storing said blue noise mask, said blue noise mask being comprised of a random non-deterministic, non-white noise single valued function which is designed to produce visually pleasing dot profiles when thresholded at any level of said gray scale image;

b) a generator for generating a gray scale image; and

c) a comparator for comparing said gray scale image on a pixel-by-pixel basis with said stored blue noise mask, thereby generating a halftoned image of said gray scale image.

15. The apparatus of claim 14, wherein said blue noise mask is comprised of a continuous, single valued aperiodic blue noise function.

16. The apparatus of claim 15, wherein said blue noise function is a random function and in which, when said blue noise mask is thresholded at any level, a dot profile with desirable blue noise characteristics is produced.

17. The apparatus of claim 14, wherein said blue noise mask is formed by an at least one dimensional function having predetermined properties of a thresholded dot profile using transform domain filtering and error criteria.

18. The apparatus of claim 17, wherein said blue noise mask is formed by an at least one dimensional function using spatial domain filtering and error criteria equivalent to said transform domain filtering and error criteria.

19. The apparatus of claim 14, wherein said halftoned image of said gray scale image is a multitoned image having multiple gray scale levels.

20. Apparatus for halftoning a gray scale image comprising an optical blue noise mask and a camera, wherein said gray scale image is photographed through said blue noise mask using said camera and is then printed onto high contrast film whereby a halftone image is provided.

21. Apparatus for halftoning color images using a blue noise mask, comprising;

a plurality of memory storage devices for storing a plurality of blue noise masks, each blue noise mask corresponding to one of a plurality of color planes of said color image to be halftoned, each of said plurality of blue noise masks being comprised of a random non-deterministic, non-white noise single valued function which is designed to provide visually pleasing dot profiles when thresholded at any level of said color images;

a shifting device for shifting the pixels of at least one of said plurality of blue noise masks by at least one pixel prior to comparing said blue noise mask to one of said color planes of said color images; and

a comparing device for comparing, on a pixel-by-pixel basis, each of said plurality of color planes of said color image against a corresponding one of said plurality of blue noise masks to produce a halftoned image.

22. The apparatus of claim 21, further including a replacing device for replacing such that, for a maximum size value for said at least one of said plurality of blue noise masks, each of the values of each pixel of said at least one of said plurality of blue noise masks is modified prior to comparing said color image against said plurality of blue noise masks to contain a value corresponding to the difference between the maximum size value and the pixel value.

23. The apparatus of claim 22, wherein said at least one modified blue noise mask array is independent and uncorrelated with any other blue noise mask array.

24. The apparatus of claim 21, wherein said at least one modified blue noise mask array is independent and uncorrelated with any other blue noise mask array.

25. Apparatus for halftoning a color image by utilizing a pixel-by-pixel comparison of said color image against a blue noise mask array, comprising:

a) a first memory for storing said blue noise mask array;

b) a shifting device for producing at least one modified blue noise mask array utilizing said blue noise mask array stored in said first memory, said at least one modified blue noise mask array being produced by shifting the pixels of said stored blue noise mask array by at least one pixel position from their position in said stored noise mask array;

c) a scanning device for scanning said color image to be halftoned on a pixel-by-pixel basis to generate a plurality of color plane image arrays;

d) a second memory for storing each of said plurality of color plane image arrays;

e) a comparison device for comparing, on a pixel-by-pixel basis, the value of each corresponding pixel in said blue noise mask array and said modified blue noise mask array and each of said plurality of color plane image arrays to produce a plurality of binary color plane image arrays; and

f) a converting device for converting said plurality of binary color plane image arrays to the desired halftoned color image.

26. The apparatus of claim 25, wherein said shifting device produces said at least one modified blue noise mask array by subtracting the value of each pixel of said blue noise mask array from a predetermined maximum value of said blue noise mask array.

27. The apparatus of claim 26, wherein said at least one modified blue noise mask array is independent and uncorrelated with any other blue noise mask array.

28. Apparatus for the halftoning of a color image, comprising a comparator for comparing, on a pixel-by-pixel basis, each of a plurality of color planes of said color image against a blue noise mask in which the blue noise mask is comprised of a random non-deterministic, non-white noise single valued function which is designed to provide visually pleasing dot profiles when thresholded at any level of said color images, wherein a plurality of blue noise masks are separately utilized to perform said pixel-by-pixel comparison and in which at least one of said blue noise masks is independent and is uncorrelated with the other blue noise masks and wherein an output of said comparator is used to produce a halftoned image.

29. Apparatus for the halftoning of color images comprising a comparator for comparing, on a pixel-by-pixel basis, a plurality of color planes of said color image against a blue noise mask in which the blue noise mask is comprised of a random non-deterministic, non-white noise single valued function which is designed to provide visually pleasing dot profiles when thresholded at any level of said color images, wherein an output of said comparator is used to produce a halftoned image.

30. Apparatus for the halftoning of color images comprising a comparator for comparing, on a pixel-by-pixel basis, a plurality of color planes of said color image against a blue noise mask in which the blue noise mask is comprised of a random non-deterministic, non-white noise single valued function which is designed to provide visually pleasing dot profiles when thresholded at any level of said color images;

and a shifting device for generating a modified blue noise mask by shifting the pixels of said blue noise mask by at least one pixel such that both a modified and non-modified blue noise mask are used by said comparator for comparing said plurality of color planes of said color images to halftone said color images.

31. Apparatus for the halftoning of color images comprising a comparator for comparing, on a pixel-by-pixel basis, a plurality of color planes of said color image against a blue noise mask in which the blue noise mask is comprised of a random non-deterministic, non-white noise single valued function which is designed to provide visually pleasing dot profiles when thresholded at any level of said color images;

and a modifying device for modifying the value of the pixels of said blue noise mask by replacing the value of each pixel of said blue noise mask with a value corresponding to the difference between a maximum size value of said blue noise mask and the pixel value to generate a modified blue noise mask such that at least said modified and a non-modified blue noise mask are used by said comparator for comparing said plurality of color planes of said color images to halftone said color images.

32. Apparatus for halftoning a color image by utilizing a pixel-by-pixel comparison of said color image against a blue noise mask array, comprising:

a) a first memory for storing said blue noise mask array;

b) a scanning device for scanning said color image to be halftoned on a pixel-by-pixel basis to generate a plurality of color plane image arrays;

c) a second memory for storing each of said plurality of color plane image arrays;

d) a comparison device for comparing, on a pixel-by-pixel basis, the value of each corresponding pixel in said blue noise mask array and each of said plurality of color plane image arrays to produce a plurality of binary color plane image arrays; and

e) a converting device for convening said plurality of binary color plane image arrays to the desired halftoned color image.

33. The apparatus of claim 32, further including a shilling device for producing at least one modified blue noise mask array utilizing said blue noise mask array stored in said first memory, said at least one modified blue noise mask array being produced by shifting the pixels of said stored blue noise mask array by at least one pixel position from their position in said stored blue noise mask array, wherein said comparison device also compares the value of each pixel in said at least one modified blue noise mask array to at least one of said binary color plane image arrays.

34. The apparatus of claim 32, further including a modifying device for modifying the value of the pixels of said blue noise mask by replacing the value of each pixel of said blue noise mask with a value corresponding to the difference between a maximum size value of said blue noise mask and the pixel value to generate a modified blue noise mask such that at least said modified and a non-modified blue noise mask are used by said comparator for comparing said plurality of color planes of said color images to halftone said color images.

35. The apparatus of claim 34, wherein said shifting device produces said at least one modified blue noise mask array by subtracting the value of each pixel of said blue noise mask array from a predetermined maximum value of said blue noise mask array.

36. The apparatus of claim 34, wherein said at least one modified blue noise mask array is independent and uncorrelated with any other blue noise mask array.

37. Apparatus for halftoning a color image by utilizing a pixel-by-pixel comparison of said color image, comprising:

a) first memory for storing a blue noise mask array;

b) an acquiring device for acquiring, on a pixel-by-pixel basis, said color image to be halftoned to create a plurality of color plane image arrays;

c) a second memory for storing each of said plurality of color plane image arrays;

d) a comparator for comparing, on a pixel-by-pixel basis, the value of each corresponding pixel in said blue noise mask array and each of said plurality of color plane image arrays to produce a plurality of binary color plane image arrays; and

e) a converter for convening said plurality of binary color plane image arrays to the desired halftoned image.

38. The apparatus of claim 37, wherein said at least one modified blue noise mask array is independent and uncorrelated with any other blue noise mask array.

39. Apparatus for halftoning an RGB image by utilizing a pixel-by-pixel comparison of said RGB image against at least one blue noise mask array, comprising:

a) a first memory for storing a first blue noise mask array;

b) an acquiring device for acquiring, on a pixel-by-pixel basis, said RGB image to be halftoned to create red, green and blue plane arrays;

c) a first shifting device for producing a second blue noise mask array by shifting the pixels of said first blue noise mask array at least one pixel position away from their position in said first blue noise mask array;

d) a first comparing device for comparing, on a pixel-by-pixel basis, the value of each corresponding pixel in said second blue noise mask array and one of said red, green and blue plane arrays to produce a first binary RGB plane image array;

e) a second comparing device for comparing, on a pixel-by-pixel basis, the value of each corresponding pixel in said first blue noise mask array and any remaining ones of said red, green and blue plane arrays not already compared to a different blue noise mask array to produce at least one of a second and third binary RGB plane image arrays; and

f) a convening device for converting said first, second and third binary RGB plane image arrays to the desired halftoned RGB image.

40. The apparatus of claim 39, further including:

a) a second shifting device for producing a third blue noise mask array by shifting the pixels of said first blue noise mask array at least one pixel position away from their position in said first blue noise mask array in a direction different from that used by said first shifting device producing said second blue noise mask array; and

b) a third comparing device for comparing, on a pixel-by-pixel basis, the value of each corresponding pixel in said third blue noise mask array and a different one of said red, green and blue plane arrays to which said second blue noise mask array was compared.

41. The apparatus of claim 40, wherein the comparison of said third blue noise mask array and a different one of said red, green and blue plane arrays to which said second blue noise mask array was compared occurs before said the operation of said second comparing device to compare said first blue noise mask array to any remaining ones of said red, green and blue plane arrays not already compared to another blue noise mask.

42. An apparatus for halftoning image information, comprising a comparator for comparing such information against at least one array, wherein said at least one array is comprised of multibit threshold values, and said at least one array, when thresholded, produces a dot pattern according to a substantially blue noise power spectrum and wherein an output of said comparator is used to produce a halftoned image.

43. An apparatus for halftoning an image, comprising a comparator for comparing information derived from said image against at least one array, wherein said at least one array is constructed to produce a locally aperiodic dot profile with wraparound properties and wherein an output of said comparator is used to produce a halftoned image.

44. An apparatus for halftoning an image, comprising a comparator for comparing information derived from said image against at least one array, wherein said at least one array, when thresholded, exhibits a power spectrum substantially characteristic of a blue noise power spectrum and wherein an output of said comparator is used to produce a halftoned image.

45. An apparatus for halftoning an image, comprising a comparator for comparing information derived from said image against at least one array, wherein said at least one array comprises a plurality of values and said at least one array, when thresholded, exhibits a power spectrum substantially characteristic of a blue noise power spectrum and wherein an output of said comparator is used to produce a halftoned image.

46. An apparatus for halftoning an image, comprising a comparator for comparing information derived from said image against at least one array, wherein said at least one array, when thresholded, produces a locally a periodic dot pattern having a power spectrum with a principal frequency and the majority of the power spectrum energy is present at frequencies higher than said principal frequency and wherein an output of said comparator is used to produce a halftoned image.

47. An apparatus for halftoning an image, comprising a comparator for comparing information derived from said image against at least one array, wherein said at least one array comprises a plurality of values at various gray scale levels, and wherein said comparison produces a visually pleasing locally aperiodic dot profile when thresholded at any gray scale level and wherein an output of said comparator is used to produce a halftoned image.

48. An apparatus for halftoning an image utilizing at least one second array, comprising:

(a) a first memory for storing a first array generated from said image;

(b) a second memory for storing said at least one second array, wherein said at least one second array, when thresholded, exhibits a power spectrum substantially characteristic of a blue noise power spectrum; and

(c) a comparator for comparing said first array against said at least one second array to produce a halftoned image of said image.

49. The apparatus of claim 48, further including a third memory for storing said halftoned image.

50. The apparatus of claim 48, further including a printer for printing said halftoned image.

51. The apparatus of claim 48, further including a transmitter for transmitting said halftoned image.

52. The apparatus of claim 48, wherein said at least one second array, when thresholded, produces a pattern that exhibits a power spectrum substantially characteristic of a blue noise power spectrum.

53. The apparatus of claim 52, wherein said pattern is a binary pattern.

54. The apparatus of claim 48, wherein said at least one second array, when thresholded, produces a pattern with a power spectrum having a principal frequency and the majority of the power spectrum energy is present at frequencies higher than said principal frequency.

55. The apparatus of claim 54, wherein said pattern is a binary pattern.

56. The apparatus of claim 48, wherein said at least one second array, when thresholded, produces a locally aperiodic dot pattern having a power spectrum with a principal frequency and the majority of the power spectrum energy is present at frequencies higher than said principal frequency.

57. Apparatus for halftoning an image, comprising a comparator for comparing information derived from said image against at least one array, wherein said at least one array, when thresholded, produces a pattern that exhibits a power spectrum having a principal frequency and the majority of the power spectrum energy is present at frequencies higher than said principal frequency and wherein an output of said comparator is used to produce a halftoned image.

58. The apparatus of claim 57, wherein said pattern is a binary pattern.

59. Apparatus for halftoning an image, comprising a comparator for comparing information derived from said image against at least one array, in which said at least one array is comprised of multibit threshold values according to a substantially blue noise power spectrum, wherein an output of said comparator is used to produce a halftoned image.

60. Apparatus for halftoning an image comprising a comparator for comparing information derived from said image against at least one array, wherein said at least one array comprises a plurality of values and at least one array, when thresholded, exhibits a power spectrum having a principal frequency and the majority of the power spectrum energy is present at frequencies higher than said principal frequency and wherein an output of said comparator is used to produce a halftoned image.

61. Apparatus for halftoning an image, comprising a comparator information derived from said image against at least one array, wherein said at least one array comprises a plurality of values and said at least one array, when thresholded, produces a locally aperiodic dot pattern having a power spectrum with a principal frequency and the majority of the power spectrum energy is present at frequencies higher than said principal frequency and wherein an output of said comparator is used to produce a halftoned image.

62. An apparatus for halftoning an image using at least one second array, comprising:

(a) means for producing a first array from said image;

(b) a first memory for storing said first array produced from said image;

(c) a second memory for storing said at least one second array, which at least one second array, when thresholded, produces a binary pattern that exhibits a power spectrum substantially characteristic of a blue noise power spectrum;

(d) a comparator for comparing said produced first array against said at least one second array to generate a binary resultant array; and

(e) a generator for generating a halftoned image from said resultant array.

63. The apparatus of claim 62, further including a third memory for storing said resultant array.

64. The apparatus of claim 62, wherein said at least one second array is comprised of multibit values according to a substantially blue noise power spectrum.

65. The apparatus of claim 62, wherein said at least one second array, when thresholded, produces a pattern that exhibits a power spectrum having a principal frequency and the majority of the power spectrum energy is present at frequencies higher than said principal frequency.

66. The apparatus of claim 65, wherein said pattern is a binary pattern.

67. The apparatus of claim 62, wherein said at least one second array, when thresholded, produces a locally aperiodic dot pattern having a power spectrum with a principal frequency and the majority of the power spectrum energy is present at frequencies higher than said principal frequency.

68. The apparatus of claim 62, wherein said at least one second array, when thresholded, exhibits a power spectrum substantially characteristic of a blue noise power spectrum.

69. The apparatus of claim 62, further including a printer for printing said binary resultant array.

70. The apparatus of claim 62, further including a transmitter for transmitting said binary resultant array.

71. The apparatus of claim 62, wherein said pattern is a binary pattern.

72. An apparatus for halftoning a color image, comprising a comparator for comparing information derived from at least one component color of such image against at least one array, wherein said at least one array, when thresholded, exhibits a power spectrum substantially characteristic of a blue noise power spectrum and wherein an output of said comparator is used to produce a halftoned image.

73. An apparatus for halftoning a color image, comprising a comparator for comparing information derived from at least one component color of such image against at least one array, wherein said at least one array comprises a plurality of values and said at least one array, when thresholded, has a power spectrum substantially characteristic of a blue noise power spectrum and wherein an output of said comparator is used to produce a halftoned image.

74. An apparatus for halftoning a color image, comprising a comparator for comparing information derived from at least one component color of such image against at least one array, wherein said at least one array, when thresholded, produces a locally aperiodic dot pattern having a power spectrum with a principal frequency and the majority of the power spectrum energy is present at frequencies higher than said principal frequency and wherein an output of said comparator is used to produce a halftoned image.

75. An apparatus for halftoning a color image, comprising a comparator for comparing information derived from at least one component color of such image against at least one array, wherein said at least one array comprises a plurality of values when thresholded, said comparison produces a visually pleasing dot profile and wherein an output of said comparator is used to produce a halftoned image.

76. An apparatus for halftoning a color image utilizing at least one array, comprising:

(a) a first memory for storing at least one component color array generated from image information derived from at least one component color of said color image;

(b) a second memory for storing said at least one array, wherein said at least one array, when thresholded, exhibits a power spectrum substantially characteristic of a blue noise power spectrum; and

(c) a comparator for comparing said at least one component color array against said at least one array to produce a halftoned image of said color image.

77. The apparatus of claim 76, further including a transmitter for transmitting said image.

78. The apparatus of claim 76, further including a third memory for storing said halftoned color image.

79. The apparatus of claim 76, further including a printer for printing said halftoned color image.

80. The apparatus of claim 76, wherein said at least one array, when thresholded, produces a pattern that exhibits a power spectrum having a principal frequency and the majority of the power spectrum energy is present at frequencies higher than said principal frequency.

81. The apparatus of claim 80, wherein said pattern is a binary pattern.

82. The apparatus of claim 76, wherein said at least one array, when thresholded, produces a locally aperiodic dot pattern having a power spectrum with a principal frequency and the majority of the power spectrum energy is present at frequencies higher than said principal frequency.

83. An apparatus for halftoning a color image using at least one array, comprising:

(a) means for deriving a component color array for each desired component color of said color image;

(b) a first memory means for storing each of said component color arrays derived from said image;

(c) second memory for storing said at least one array, wherein said at least one array, when thresholded, produces a pattern that exhibits a power spectrum substantially characteristic of a blue noise power spectrum;

(d) a comparator for comparing each of said component color arrays derived from said color image against said at least one array to generate a resultant array for each of said component color arrays; and

(e) a combining device for combining each of said resultant arrays to produce a halftoned color image.

84. The apparatus of claim 83, further including a third memory for storing at least one resultant array.

85. The apparatus of claim 83, further including a printer for printing said resultant array.

86. The apparatus of claim 83, further including means for combining each of said resultant arrays in a color display.

87. The apparatus of claim 83, further including a generator for generating a halftoned color image from the combined resultant arrays.

88. The apparatus of claim 87, further including a transmitter for transmitting said halftoned color image.

89. The apparatus of claim 83, wherein said at least one array, when thresholded, produces a pattern that exhibits a power spectrum having a principal frequency and the majority of the power spectrum energy is present at frequencies higher than said principal frequency.

90. The apparatus of claim 89, wherein said pattern is a binary pattern.

91. The apparatus of claim 83, wherein said at least one array, when thresholded, produces a locally aperiodic dot pattern having a power spectrum with a principal frequency and the majority of the power spectrum energy is present at frequencies higher than said principal frequency.

92. The apparatus of claim 83, further including a transmitter for transmitting at least one resultant array.

93. The apparatus of claim 83, wherein said pattern is a binary pattern.

94. Apparatus for halftoning an image, comprising a comparator for comparing information derived from said image against at least one array, wherein said at least one array comprises a plurality of values and said at least one array, when thresholded, produces a locally aperiodic dot pattern having a power spectrum with a principal frequency and the majority of the power spectrum energy is present at frequencies higher than said principal frequency and wherein an output of said comparator is used to produce a halftoned image.

95. An apparatus for halftoning a color image, comprising a comparator for comparing information derived from at least one component color of said color image against at least one array wherein said at least one array is constructed to produce a locally aperiodic dot profile with wraparound properties and wherein an output of said comparator is used to produce a halftoned image.