1. Half Toning

2. Continuous Half Toning

3. Color Half Toning

4. Half toning and Colors

5. Digital Half Toning

6. Half Toning Emulating 5 different levels

7. Half Toning 10 levels

8. Original

9. Half Toning

10. Original

11. Dithering

12. 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

13. 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.

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

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

16. Threshold

17. Threshold + Noise

18. Robert’s Algorithm Pink Blue

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

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

21. Dithering Thresholding Dithering

22. Dithering 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.

23. Threshold + Noise

24. Dithering

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

26. Other possibilities

27. 3 7 5 6 1 2 9 4 8 The dithering matrix (3x3) 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)

28. 0 3 0 7 0 5 3 7 7 5 5 8 1 6 2 4 5 3 2 6 0 1 1 2 1 6 6 1 2 8 7 2 2 5 4 3 2 3 9 0 1 4 8 0 4 9 9 4 4 8 8 3 7 5 2 6 4 3 3 7 5 8 9 7 7 2 2 1 3 2 6 6 1 2 2 9 9 7 4 3 2 2 4 8 9 9 4 4 8 8 8 4 4 8 4 4 Dithering 3 7 5 6 1 2 Dithering mask 9 4 8 2 1 3 Image 3 2 2 4 8 4 Binary image

29. Original

30. Dithering

31. Dithering

32. Error Diffusion

33. 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.

34. 1D Error Diffusion 1 0 1

35. 1D Error Diffusion 1 0

36. 1D Error Diffusion 1 0

37. 1D Error Diffusion 1 0

38. 1D Error Diffusion 1 0 1 0

39. 1D Error Diffusion 1 0 1 0 1

40. 1D Error Diffusion 1 0

41. 1D Error Diffusion 1 0

42. 1D Error Diffusion 1 0

43. e e -3e/8 -3e/8 -e/4 -3e/8 -e/4 -3e/8 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

44. Dither vs. Floyd-Steinberg

46. Original Picture

47. Error diffusion result Dithering result

48. Examples – Continue

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

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