1 / 32

Multiscale Analysis of Images: Filtering, Subsampling, and Pyramid Blending Techniques

This resource covers multiscale image analysis, focusing on Gaussian pre-filtering, subsampling techniques, and the construction of image pyramids. It discusses Gaussian and Laplacian pyramids, offering methods for band-pass filtering and image reconstruction. The document highlights the significance of image resampling and interpolation, comparing various filtering techniques such as bilinear and bicubic interpolation. It also explores practical applications, including image denoising, restoration, and blending using Laplacian pyramids, maximizing image quality through optimal window sizes.

heba
Download Presentation

Multiscale Analysis of Images: Filtering, Subsampling, and Pyramid Blending Techniques

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Multiscale Analysis of Images Gilad Lerman Math 5467 (stealing slides from Gonzalez & Woods, and Efros)

  2. The Multiscale Nature of Images

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

  4. Subsampling with Gaussian pre-filtering Gaussian 1/2 G 1/4 G 1/8 • Solution: filter the image, then subsample • Filter size should double for each ½ size reduction.

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

  6. 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

  7. 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!

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

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

  10. High-Pass filter smoothed – original

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

  12. Laplacian Pyramid • How can we reconstruct (collapse) this pyramid into the original image? Need this! Original image

  13. Image resampling (interpolation) • So far, we considered only power-of-two subsampling • What about arbitrary scale reduction? • How can we increase the size of the image? d = 1 in this example 1 2 3 4 5 • Recall how a digital image is formed • It is a discrete point-sampling of a continuous function • If we could somehow reconstruct the original function, any new image could be generated, at any resolution and scale

  14. Image resampling • So far, we considered only power-of-two subsampling • What about arbitrary scale reduction? • How can we increase the size of the image? d = 1 in this example 1 2 3 4 5 • Recall how a digital image is formed • It is a discrete point-sampling of a continuous function • If we could somehow reconstruct the original function, any new image could be generated, at any resolution and scale

  15. Answer: guess an approximation • Can be done in a principled way: filtering 1 d = 1 in this example 1 2 2.5 3 4 5 • Image reconstruction • Convert to a continuous function • Reconstruct by cross-correlation: Image resampling • So what to do if we don’t know

  16. Resampling filters • What does the 2D version of this hat function look like? performs linear interpolation (tent function) performs bilinear interpolation • Better filters give better resampled images • Bicubic is common choice • Why not use a Gaussian? • What if we don’t want whole f, but just one sample?

  17. Bilinear interpolation • Smapling at f(x,y):

  18. Applications (more efficient with wavelets) • Coding • High frequency coefficients need fewer bits, so one can • collapse a compressed Laplacian pyramid • Denoising/Restoration • Setting “most” coefficients in Laplacian pyramid to zero • Image Blending

  19. 0 1 0 1 0 1 Application: Pyramid Blending Left pyramid blend Right pyramid

  20. Image Blending

  21. + = 1 0 1 0 Feathering Ileft Iright right left Encoding transparency I(x,y) = (aR, aG, aB, a) Iblend = left Ileft + right Iright

  22. 0 1 0 1 Affect of Window Size left right

  23. 0 1 0 1 Affect of Window Size

  24. 0 1 Good Window Size “Optimal” Window: smooth but not ghosted Burt and Adelson (83): Choose by pyramids…

  25. Pyramid Blending

  26. Pyramid Blending (Color)

  27. 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

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

  29. Blending Regions

  30. Simplification: Two-band Blending • Brown & Lowe, 2003 • Only use two bands: high freq. and low freq. • Blends low freq. smoothly • Blend high freq. with no smoothing: use binary mask Can be explored in a project…

More Related