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Advanced Image Denoising Techniques for Photography and Computer Vision

This course delves into essential image processing techniques focused on denoising, an important aspect of photography and computer vision. We explore the concepts behind pixel behavior, convolution with linear filters, and the applications of Gaussian and median filters. The curriculum investigates probabilistic approaches to determine pixel values based on neighboring pixels and employs advanced methods like bilateral filtering. Emphasis is placed on noise reduction while preserving image details, highlighting the balance between luminance and chrominance adjustments.

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Advanced Image Denoising Techniques for Photography and Computer Vision

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  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)

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