Recall: Gaussian smoothing/sampling

1. Recall: Gaussian smoothing/sampling G 1/8 G 1/4 Gaussian 1/2 • Solution: filter the image, then subsample • Filter size should double for each ½ size reduction.

2. Subsampling with Gaussian smoothing Gaussian 1/2 G 1/4 G 1/8

3. Image Pyramids • Known as a Gaussian Pyramid [Burt and Adelson, 1983] • In computer graphics, a mip map [Williams, 1983] • A precursor to wavelet transform

4. Motivations

5. Boundaries occur at different scales

6. Texture: consists of multiple size scales Original • Learn the statistics of texture to recognize it • Synthesize texture based on learned model Synthesis

8. Example: Image Blending

9. A bar in the big images is a hair on the zebra’s nose; in smaller images, a stripe; in the smallest, the animal’s nose Figure from David Forsyth

10. Gaussian pyramid construction filter mask • Repeat • Filter • Subsample • Until minimum resolution reached • can specify desired number of levels (e.g., 3-level pyramid) • The whole pyramid is only 4/3 the size of the original image!

11. What does blurring take away? (recall) original

12. What does blurring take away? (recall) smoothed (5x5 Gaussian)

13. Boundaries! smoothed – original

14. Band-pass filtering • Laplacian Pyramid (subband images) • Created from Gaussian pyramid by subtraction Gaussian Pyramid

15. Gaussian Pyramid Computer Vision - A Modern Approach Set: Pyramids and Texture Slides by D.A. Forsyth

16. Laplacian Pyramid Computer Vision - A Modern Approach Set: Pyramids and Texture Slides by D.A. Forsyth

17. Gaussian Pyramid Laplacian Pyramid

19. Applications • Compression • Set “most” coefficients in Laplacian pyramid to zero • Hide secret messages in images (eg, to check youtube plagiarism) • Image Restoration • Image Blending

20. 0 1 0 1 0 1 Application: Pyramid Blending Left pyramid blend Right pyramid

21. Image Blending Juxtaposition: too abrupt

22. + = 1 0 1 0 Feathering Ileft Iright right left Encoding transparency I(x,y) = (aR, aG, aB, a) Iblend = left Ileft + right Iright

23. 0 1 0 1 Affect of Window Size left right Blending window too big (compared to typical detail size)  transparency, “ghosts”

24. 0 1 0 1 Affect of Window Size Blending window too small (compared to typical detail size)  transition too abrupt

25. Problem and solution • Problem: Usually details of many different sizes! No single size of blending window works. • Solution Laplacian Pyramid separate images into levels. Each level has details of single size range. Blend corresponding levels for the two images using windows sized to match level

26. 0 1 Good Window Size “Optimal” Window: smooth but not ghosted Burt and Adelson (83): Choose by pyramids…

27. Pyramid Blending

28. Pyramid Blending (Color)

29. Laplacian Pyramid: Blending • General Approach: • Build Laplacian pyramids LA and LB from images A and B • Build a Gaussian pyramid GR from selected region R (black white corresponding images) • Form a combined pyramid LS from LA and LB using nodes of GR as weights: • LS(i,j) = GR(I,j,)*LA(I,j) + (1-GR(I,j))*LB(I,j) • Collapse the LS pyramid to get the final blended image

30. laplacian level 4 laplacian level 2 laplacian level 0 left pyramid right pyramid blended pyramid

31. Blending Regions

32. Constructing the Laplacian Pyramid • Worked out in class. To be posted later.