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Last Lecture

Last Lecture. photomatix.com. HDR Video. Assorted pixel (Single Exposure HDR). Assorted pixel. Assorted pixel. Pixel with Adaptive Exposure Control. light. T. t+1. attenuator element. controller. detector element. I. t. controllable modulator. image detector. relay

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Last Lecture

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  1. Last Lecture photomatix.com

  2. HDR Video

  3. Assorted pixel (Single Exposure HDR)

  4. Assorted pixel

  5. Assorted pixel

  6. Pixel with Adaptive Exposure Control light T t+1 attenuator element controller detector element I t

  7. controllable modulator image detector relay lens object imaging lens field lens ADR Imaging with Spatial Light Modulator

  8. ADR Camera with LCD Attenuator LCD Electronics LCD Attenuator Video Camera Imaging Lens

  9. Today • Image Processing: from basic concepts to latest techniques • Filtering • Edge detection • Re-sampling and aliasing • Image Pyramids (Gaussian and Laplacian) • Removing handshake blur from a single image

  10. Represented by a matrix Image as a discreet function

  11. 10 5 3 4 5 7 1 1 1 7 Some function Local image data Modified image data What is image filtering? • Modify the pixels in an image based on some function of a local neighborhood of the pixels.

  12. 0 0 0 0 0.5 0 0 1 0.5 10 5 3 4 7 5 1 1 1 7 Local image data kernel Modified image data Linear functions • Simplest: linear filtering. • Replace each pixel by a linear combination of its neighbors. • The prescription for the linear combination is called the “convolution kernel”.

  13. I Convolution

  14. coefficient 0 Pixel offset Linear filtering (warm-up slide) ? 1.0 original

  15. coefficient 0 Pixel offset Linear filtering (warm-up slide) 1.0 original Filtered (no change)

  16. coefficient 0 Pixel offset Linear filtering 1.0 ? original

  17. coefficient 0 Pixel offset shift 1.0 original shifted

  18. coefficient 0 Pixel offset Linear filtering ? 0.3 original

  19. coefficient 0 Pixel offset Blurring 0.3 original Blurred (filter applied in both dimensions).

  20. 8 coefficient 0 original Pixel offset Blur Examples 2.4 impulse 0.3 filtered

  21. 8 coefficient coefficient 0 0 original Pixel offset Pixel offset Blur Examples 2.4 impulse 0.3 filtered 8 8 edge 4 4 0.3 filtered original

  22. Linear filtering (warm-up slide) 2.0 1.0 ? 0 0 original

  23. Linear Filtering (no change) 2.0 1.0 0 0 Filtered (no change) original

  24. 0.33 0 Linear Filtering 2.0 ? 0 original

  25. coefficient 0 Pixel offset (remember blurring) 0.3 original Blurred (filter applied in both dimensions).

  26. 0.33 0 Sharpening 2.0 0 Sharpened original original

  27. Sharpening example 1.7 11.2 8 8 coefficient -0.25 -0.3 original Sharpened (differences are accentuated; constant areas are left untouched).

  28. Sharpening before after

  29. Spatial resolution and color R G B original

  30. R G B Blurring the G component processed original

  31. R G B Blurring the R component processed original

  32. R G B processed Blurring the B component original

  33. Lab Color Component L A rotation of the color coordinates into directions that are more perceptually meaningful: L: luminance, a: red-green, b: blue-yellow a b

  34. L a b processed Bluring L original

  35. L a b processed Bluring a original

  36. L a b processed Bluring b original

  37. Application to image compression • (compression is about hiding differences from the true image where you can’t see them).

  38. Edge Detection • Convert a 2D image into a set of curves • Extracts salient features of the scene • More compact than pixels

  39. How can you tell that a pixel is on an edge?

  40. Image gradient • The gradient of an image: • The gradient points in the direction of most rapid change in intensity • The gradient direction is given by: • how does the gradient relate to the direction of the edge? • The edge strength is given by the gradient magnitude

  41. Effects of noise • Consider a single row or column of the image • Plotting intensity as a function of position gives a signal How to compute a derivative? • Where is the edge?

  42. Look for peaks in Solution: smooth first • Where is the edge?

  43. Derivative theorem of convolution • This saves us one operation:

  44. Laplacian of Gaussian • Consider Laplacian of Gaussian operator • Where is the edge? • Zero-crossings of bottom graph

  45. Canny Edge Detector • Smooth image I with 2D Gaussian: • Find local edge normal directions for each pixel • Along this direction, compute image gradient • Locate edges by finding max gradient magnitude (Non-maximum suppression)

  46. Non-maximum Suppression • Check if pixel is local maximum along gradient direction • requires checking interpolated pixels p and r

  47. The Canny Edge Detector original image (Lena)

  48. The Canny Edge Detector magnitude of the gradient

  49. The Canny Edge Detector After non-maximum suppression

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