CS448f: Image Processing For Photography and Vision

1. CS448f: Image Processing For Photography and Vision Denoising

2. How goes the assignment?

3. The course so far… • We have a fair idea what image processing code looks like • We know how to treat an image as a continuous function • We know how to warp images • What should we do next?

4. What are the big problems in Photography and Computer Vision, and how can Image Processing help?

5. Today: Denoising

6. How do we know a pixel is bad? • It’s not like its neighbours • Solution: Replace each pixel with the average of its neighbors • I.e. Convolve by

7. 3x3 Rect Filter

8. 5x5 Rect Filter

9. Linear Filters • Why should a far-away pixel contribute the same amount as a nearby pixel • Gaussian blur:

10. Gaussian Blur

11. beta = 2

12. beta = 5

13. Some neat properties: • It’s radially symettric and separable at the same time: • Its Fourier transform is also a Gaussian • It’s not very useful for denoising

14. Linear Filters • Convolve by some kernel • Equivalent to multiplication in Fourier domain • Reduces high frequencies • But we wanted those - that’s what made the image sharp! • You don’t always need the high frequencies. The first step in many computer vision algorithms is a hefty blur.

15. Probabilistically... • What is the most probable value of a pixel, given its neighbors?

16. Probabilistically... • This is supposed to be dark grey:

17. Let’s ignore color for now

18. And inspect the distribution

19. And inspect the distribution Most probable pixel value

20. And inspect the distribution mean = mode = median

21. Denoising

22. Denoising

23. The distribution

24. The distribution The text The background

25. The distribution The mean

26. The distribution The mode

27. The distribution The median

28. Median Filters • Replace each pixel with the median of its neighbours • Great for getting rid of salt-and-pepper noise • Removes small details

29. Before:

30. Gaussian Blur:

31. After Median Filter:

32. The distribution • What is the most probable pixel value?

33. It depends on your current value • The answer should vary for each pixel

34. An extra prior • Method 1) Convolution • The pixel is probably looking at the same material as all of its neighbors, so we’ll set it to the average of its neighbors. • Method 2) Bilateral • The pixel is probably looking at the same material as SOME of its neighbors, so we’ll set it to the average of those neighbors only.

35. The Bilateral Filter • How do we select good neighbours? • The ones with roughly similar brightnesses are probably looking at the same material.

36. Before:

37. Gaussian Blur:

38. After Median Filter:

39. After Bilateral:

40. Dealing with Color • It turns out humans are only sensitive to high frequencies in brightness • not in hue or saturation • So we can blur in chrominance much more than luminance

41. Chroma Blurring • 1) Convert RGB to LAB • L is luminance, AB are chrominance (hue and saturation) • 2) Perform a small bilateral in L • 3) Perform a large bilateral in AB • 4) Convert back to RGB

42. Before:

43. After Regular Bilateral:

44. After Modified Bilateral:

45. Method Noise (Gaussian)

46. Method Noise (Bilateral)

47. Leveraging Similarity:Non-Local Means

48. What color should this pixel be?

49. What color should this pixel be?

50. Gaussian Blur: A weighted average of these: (all nearby pixels)