Diffusion Curves

1. Diffusion Curves Dr. Scott Schaefer

2. 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 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 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

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

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

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

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

10. Problem

11. Problem Final Result

12. Problem 100 Iterations

13. Problem 200 Iterations

14. Problem 400 Iterations

15. Problem 800 Iterations

16. Problem 1600 Iterations

17. Problem 6400 Iterations

18. Problem Infinity Iterations

19. Problem 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 color of its neighbors from previous iteration

21. Example Original 512x512

22. Example Down-sampled 256x256

23. Example Down-sampled 128x128

24. Example Down-sampled 64x64

25. Example Down-sampled 32x32

26. Example Down-sampled 16x16

27. Example Down-sampled 8x8

28. Example Down-sampled 4x4

29. Example Down-sampled 2x2

30. Example Down-sampled 1x1

31. Example Up-sampled

32. Example Smoothed

33. Example Up-sampled

34. Example Smoothed

35. Example Up-sampled

36. Example Smoothed

37. Example Up-sampled

38. Example Smoothed

39. Example Up-sampled

40. Example Smoothed

41. Example Up-sampled

42. Example Smoothed

43. Example Up-sampled

44. Example Smoothed

45. Example Up-sampled

46. Example Smoothed

47. Example Up-sampled

48. Example Smoothed

49. Example