1. 1 Dr. Scott Schaefer Diffusion Curves

2. 2/38 Diffusion Curves Vector graphics-based representation for 2D images Images are piecewise smooth with discontinuities represented as curves Image taken from “Diffusion Curves: A Vector Representation for Smooth-Shaded Images”

3. Representation Bezier curves represent discontinuities Give each curve a color function on left/right side of curve  Original paper uses linear color change  Modification: Control points can have any color 3/49 Image taken from “Diffusion Curves: A Vector Representation for Smooth-Shaded Images”

4. Image Construction Use curves as boundary constraints Find a harmonic function that interpolates those boundary constraints 4/49 Image taken from “Diffusion Curves: A Vector Representation for Smooth-Shaded Images”

5. Implementation (Simplified) Define a left/right color for points Use a background color to represent no data (black) Draw curve as a polygon made of quads (thick) with smooth shading 5/49

6. Implementation (Simplified) Colored pixels are constraints Find a harmonic function satisfying constraints  Harmonic function has Laplacian zero everywhere 6/49

7. Implementation (Simplified) Colored pixels are constraints Find a harmonic function satisfying constraints  Harmonic function has Laplacian zero everywhere 7/49 -4 1 1 1 1 00 0 0

8. Implementation (Simplified) Colored pixels are constraints Find a harmonic function satisfying constraints  Harmonic function has Laplacian zero everywhere  Each value is average of its neighbors 8/49 -4 1 1 1 1 00 0 0

9. Implementation (Simplified) Draw curves as quads Read pixel buffer back from OpenGL Repeat a lot  For all pixels whose initial value was black, replace with average color of its neighbors from previous iteration 9/49

10. Problem 10/49

11. Problem 11/49 Final Result

12. Problem 12/49 100 Iterations

13. Problem 13/49 200 Iterations

14. Problem 14/49 400 Iterations

15. Problem 15/49 800 Iterations

16. Problem 16/49 1600 Iterations

17. Problem 17/49 6400 Iterations

18. Problem 18/49 Infinity Iterations

19. Problem 19/49 256

20. Simple Multi-Grid Create power of 2 down-sampled images  Average value of all non-black pixels For each level, starting at second to last  Up-sample previous level  Copy pixel value to black high-res pixels (non-black pixels are constraints)  For some number of iterations  For each non-constrained pixel, replace with average of its neighbors from last iteration 20/49

21. Example 21/49 Original 512x512

22. Example 22/49 Down-sampled 256x256

23. Example 23/49 Down-sampled 128x128

24. Example 24/49 Down-sampled 64x64

25. Example 25/49 Down-sampled 32x32

26. Example 26/49 Down-sampled 16x16

27. Example 27/49 Down-sampled 8x8

28. Example 28/49 Down-sampled 4x4

29. Example 29/49 Down-sampled 2x2

30. Example 30/49 Down-sampled 1x1

31. Example 31/49 Up-sampled

32. Example 32/49 Smoothed

33. Example 33/49 Up-sampled

34. Example 34/49 Smoothed

35. Example 35/49 Up-sampled

36. Example 36/49 Smoothed

37. Example 37/49 Up-sampled

38. Example 38/49 Smoothed

39. Example 39/49 Up-sampled

40. Example 40/49 Smoothed

41. Example 41/49 Up-sampled

42. Example 42/49 Smoothed

43. Example 43/49 Up-sampled

44. Example 44/49 Smoothed

45. Example 45/49 Up-sampled

46. Example 46/49 Smoothed

47. Example 47/49 Up-sampled

48. Example 48/49 Smoothed

49. Example 49/49