1. Half Toning

2. Continuous Half Toning

3. Color Half Toning

4. Half toning and Colors

5. Digital Half Toning

7. Emulating 5 different levels Half Toning

8. 10 levels

9. Original

10. Half Toning

11. Original

12. Dithering

13. Dithering and Halftoning Trade spatial for intensity resolution (works well for printing where dot printing is very high) Thresholding. Random dither; Robert’s algorithm Ordered dither Error diffusion Your eye will average over an area - Spatial Integration

14. Thresholding Assume we want to quantize a gray-level image to a binary colormap. Map the upper half of the gray-level scale to white, and the lower half to black – a simple threshold operation, preformed independently at each pixel.

15. Thresholding Original image. Simple threshold. n = 0.5 Errors are low spatial frequencies.

16. Robert’s Algorithm First add noise Then quantize x i 0 1 r r + 1 Quantized to 1 Quantized to 0 Moves errors to higher spatial frequencies. -> eye averages over an area.

17. Threshold

18. Threshold + Noise

19. Robert’s Algorithm PinkBlue

20. Robert’s Algorithm Moves low frequency (average error) to high frequency Pink(low), Blue (high), White(all) frequency noise PinkBlue

21. The trouble with noise Difficult to compute quickly. Not reproducible. Pre-compute pseudo-random function and store in table. Small tiled patterns sufficient

22. Dithering It is possible to improve the quality of a quantized image by distributing the quantized error. Let’s have a closer look.

23. Dithering ThresholdingDithering

24. Each pixel produces a quatization error The quality of the result may be improved by adjusting the threshold locally, so that adjacent pixels in small areas are quantized with different thresholds. This reduces the average local quantization error. Matrices of these threshold are called dither matrices. Dithering

25. Threshold + Noise

26. Dithering

27. Ordered Dithering Trade off spatial resolution for intensity resolution. Use dither patterns. Can be represented as a matrix.

28. Bayer Ordered Dither Patterns

29. Other possibilities

30. 948 612 573 For all Xpixels For all Ypixels v = approximate(x,y) i = x mod 3 j = y mod 3 if v >= M[i,j] then Set_Pixel(x,y, BLACK) else Set_Pixel(x,y, WHITE) The dithering matrix (3x3)

31. Dithering 948 612 573 12 22 3 3 844 948 612 573 010 011 000 Dithering mask Image Binary image

32. Original

33. Dithering

35. Error Diffusion

36. Floyd-Steinberg Error Diffusion With this method, the average quatization error is reduced by propagating the error from each pixel to some of its neighbors in the scan order.

37. 1D Error Diffusion 0 1 1

38. 0 1

39. 0 1

40. 0 1

41. 0 1 01

42. 0 1 011

43. 0 1

44. 0 1

45. 0 1

46. Floyd-Steinberg Error Diffusion With this method, the average quatization error is reduced by propagating the error from each pixel to some of its neighbors in the scan order. Note that the error propagation weights must sum to one e -3e/8 -e/4 e -3e/8 -e/4

47. Dither vs. Floyd-Steinberg

49. Original Picture

50. Dithering resultError diffusion result

51. Examples – Continue

52. Dithering Dithering: Note that each square ring is of different brightness

53. Error Diffusion Error Diffusion: Note that the error is distributed across the layers

54. Examples – Continue Original:

55. Dithering

56. Error Diffusion

59. Set AccErr[] to zero; For each pixel in the image scanning from left to right: value= Pixel_value(x,y) + AccErr[x,y]; if (value > WHITE/2) { Set_pixel(x,y, WHITE); Error = value - WHITE; } else { Set_pixel(x,y, BLACK); Error = value - BLACK; } if scanning from left to right { AccErr[x+1, y] += 3/8 * Error; AccErr[x, y+1] += 3/8 * Error; AccErr[x+1,y+1] += 2/8 * Error; } Error Diffusion

60. Space Filling Curves order of scan

61. Space Filling Curves Hilbert curve (1-4)

62. Space Filling Curves Hilbert curve (1-4)

63. Space Filling Curves Hilbert curve (1-4)

64. Space Filling Curves Hilbert curve (1-4)

65. Space Filling Curves Peano curve

66. Context Based SFC

67. Original Image

68. Threshholding

69. Bayer’s Ordered Dithering

70. Error Diffusion

71. Median Cut (4 levels)

72. Median Cut (8 levels)