CS 691B Computational Photography Instructor: Gianfranco Doretto Image Warping.
CS 691B Computational Photography Instructor: Gianfranco Doretto Image Pyramids.
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Transcript of CS 691B Computational Photography Instructor: Gianfranco Doretto Image Pyramids.
![Page 1: CS 691B Computational Photography Instructor: Gianfranco Doretto Image Pyramids.](https://reader036.fdocuments.in/reader036/viewer/2022081516/5697bfd31a28abf838cac579/html5/thumbnails/1.jpg)
CS 691B Computational Photography
Instructor: Gianfranco DorettoImage Pyramids
![Page 2: CS 691B Computational Photography Instructor: Gianfranco Doretto Image Pyramids.](https://reader036.fdocuments.in/reader036/viewer/2022081516/5697bfd31a28abf838cac579/html5/thumbnails/2.jpg)
Linear image transformations
• In analyzing images, it’s often useful to make a change of basis.
Basis
fUF
Vectorized image
transformed image
![Page 3: CS 691B Computational Photography Instructor: Gianfranco Doretto Image Pyramids.](https://reader036.fdocuments.in/reader036/viewer/2022081516/5697bfd31a28abf838cac579/html5/thumbnails/3.jpg)
Spatial Domain Basis
Basis functions:
……
……
..
Tells you where things are….
… but no concept of what it is
![Page 4: CS 691B Computational Photography Instructor: Gianfranco Doretto Image Pyramids.](https://reader036.fdocuments.in/reader036/viewer/2022081516/5697bfd31a28abf838cac579/html5/thumbnails/4.jpg)
Identity transform
= *
Pixel domain image
Spatial bases are local: each transform coefficient depends on one pixel location.
Pixel domain
image
1000…01000…00100…
…0001…00010
000100…
…0001000…
![Page 5: CS 691B Computational Photography Instructor: Gianfranco Doretto Image Pyramids.](https://reader036.fdocuments.in/reader036/viewer/2022081516/5697bfd31a28abf838cac579/html5/thumbnails/5.jpg)
Fourier Domain Basis
Basis functions:
Tells you what (frequency) is in the image….
… but not where it is
……
……
……
![Page 6: CS 691B Computational Photography Instructor: Gianfranco Doretto Image Pyramids.](https://reader036.fdocuments.in/reader036/viewer/2022081516/5697bfd31a28abf838cac579/html5/thumbnails/6.jpg)
Fourier transform
= *
Pixel domain image
Fourier bases are global: each transform coefficient depends on all pixel locations.
Fourier transform
![Page 7: CS 691B Computational Photography Instructor: Gianfranco Doretto Image Pyramids.](https://reader036.fdocuments.in/reader036/viewer/2022081516/5697bfd31a28abf838cac579/html5/thumbnails/7.jpg)
Image Analysis
• Want representation that combines what and where.
Image Pyramids
![Page 8: CS 691B Computational Photography Instructor: Gianfranco Doretto Image Pyramids.](https://reader036.fdocuments.in/reader036/viewer/2022081516/5697bfd31a28abf838cac579/html5/thumbnails/8.jpg)
Overview
• Gaussian Pyramid• Laplacian Pyramid
![Page 9: CS 691B Computational Photography Instructor: Gianfranco Doretto Image Pyramids.](https://reader036.fdocuments.in/reader036/viewer/2022081516/5697bfd31a28abf838cac579/html5/thumbnails/9.jpg)
Image Pyramids
Known as a Gaussian Pyramid [Burt and Adelson, 1983]• In computer graphics, a mip map [Williams, 1983]• A precursor to wavelet transform
![Page 10: CS 691B Computational Photography Instructor: Gianfranco Doretto Image Pyramids.](https://reader036.fdocuments.in/reader036/viewer/2022081516/5697bfd31a28abf838cac579/html5/thumbnails/10.jpg)
Gaussian pyramid construction
filter mask
Repeat• Filter (keep filter the same size)• Subsample (by a factor of two)
Until minimum resolution reached • can specify desired number of levels (e.g., 3-level pyramid)
Total number of pixels in pyramid?• 1 + ¼ + 1/16 + 1/32…….. = 4/3
Over-complete representation
![Page 11: CS 691B Computational Photography Instructor: Gianfranco Doretto Image Pyramids.](https://reader036.fdocuments.in/reader036/viewer/2022081516/5697bfd31a28abf838cac579/html5/thumbnails/11.jpg)
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
![Page 12: CS 691B Computational Photography Instructor: Gianfranco Doretto Image Pyramids.](https://reader036.fdocuments.in/reader036/viewer/2022081516/5697bfd31a28abf838cac579/html5/thumbnails/12.jpg)
What are they good for?
• Improve Search– Search over translations
• Classic coarse-to-fine strategy
– Search over scale• Template matching• E.g. find a face at different scales
• Pre-computation– Need to access image at different blur levels– Useful for texture mapping at different resolutions (called mip-
mapping)
• Compression– Capture important structures with fewer bytes
• Denoising– Model statistics of pyramid sub-bands– Image blending
![Page 13: CS 691B Computational Photography Instructor: Gianfranco Doretto Image Pyramids.](https://reader036.fdocuments.in/reader036/viewer/2022081516/5697bfd31a28abf838cac579/html5/thumbnails/13.jpg)
Gaussian pyramid
= *Pixel domainimage
Overcomplete representation. Low-pass filters, sampled appropriately for their blur.
Gaussian pyramid
![Page 14: CS 691B Computational Photography Instructor: Gianfranco Doretto Image Pyramids.](https://reader036.fdocuments.in/reader036/viewer/2022081516/5697bfd31a28abf838cac579/html5/thumbnails/14.jpg)
Overview
• Gaussian Pyramid• Laplacian Pyramid
![Page 15: CS 691B Computational Photography Instructor: Gianfranco Doretto Image Pyramids.](https://reader036.fdocuments.in/reader036/viewer/2022081516/5697bfd31a28abf838cac579/html5/thumbnails/15.jpg)
What does blurring take away?
original
![Page 16: CS 691B Computational Photography Instructor: Gianfranco Doretto Image Pyramids.](https://reader036.fdocuments.in/reader036/viewer/2022081516/5697bfd31a28abf838cac579/html5/thumbnails/16.jpg)
What does blurring take away?
smoothed (5x5 Gaussian)
![Page 17: CS 691B Computational Photography Instructor: Gianfranco Doretto Image Pyramids.](https://reader036.fdocuments.in/reader036/viewer/2022081516/5697bfd31a28abf838cac579/html5/thumbnails/17.jpg)
High-Pass filter
smoothed – original
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Band-pass filtering
• Laplacian Pyramid (subband images)
• Created from Gaussian pyramid by subtraction
Gaussian Pyramid (low-pass images)
![Page 19: CS 691B Computational Photography Instructor: Gianfranco Doretto Image Pyramids.](https://reader036.fdocuments.in/reader036/viewer/2022081516/5697bfd31a28abf838cac579/html5/thumbnails/19.jpg)
Laplacian filter
GaussianUnit impulse Laplacian of Gaussian
- ≅
![Page 20: CS 691B Computational Photography Instructor: Gianfranco Doretto Image Pyramids.](https://reader036.fdocuments.in/reader036/viewer/2022081516/5697bfd31a28abf838cac579/html5/thumbnails/20.jpg)
Laplacian pyramid algorithm
blur
_
subsample blur
_
subsampleblur
_
subsample
![Page 21: CS 691B Computational Photography Instructor: Gianfranco Doretto Image Pyramids.](https://reader036.fdocuments.in/reader036/viewer/2022081516/5697bfd31a28abf838cac579/html5/thumbnails/21.jpg)
Can we reconstruct the original?
interpolateinterpolateinterpolate
Need this!
![Page 22: CS 691B Computational Photography Instructor: Gianfranco Doretto Image Pyramids.](https://reader036.fdocuments.in/reader036/viewer/2022081516/5697bfd31a28abf838cac579/html5/thumbnails/22.jpg)
The Laplacian Pyramid
• Synthesis– preserve difference between upsampled
Gaussian pyramid level and Gaussian pyramid level
– band pass filter - each level represents spatial frequencies (largely) unrepresented at other levels
• Analysis– reconstruct Gaussian pyramid, take top
layer
![Page 23: CS 691B Computational Photography Instructor: Gianfranco Doretto Image Pyramids.](https://reader036.fdocuments.in/reader036/viewer/2022081516/5697bfd31a28abf838cac579/html5/thumbnails/23.jpg)
Laplacian pyramid
![Page 24: CS 691B Computational Photography Instructor: Gianfranco Doretto Image Pyramids.](https://reader036.fdocuments.in/reader036/viewer/2022081516/5697bfd31a28abf838cac579/html5/thumbnails/24.jpg)
Laplacian pyramid
= *Pixel domain image
Overcomplete representation. Transformed pixels represent bandpassed image information.
Laplacian pyramid
![Page 25: CS 691B Computational Photography Instructor: Gianfranco Doretto Image Pyramids.](https://reader036.fdocuments.in/reader036/viewer/2022081516/5697bfd31a28abf838cac579/html5/thumbnails/25.jpg)
Hybrid Image in Laplacian Pyramid
High frequency Low frequencyExtra points for project 1
![Page 26: CS 691B Computational Photography Instructor: Gianfranco Doretto Image Pyramids.](https://reader036.fdocuments.in/reader036/viewer/2022081516/5697bfd31a28abf838cac579/html5/thumbnails/26.jpg)
Slide Credits
• This set of sides also contains contributionskindly made available by the following authors– Alexei Efros– Svetlana Lazebnik– Frédo Durand– Bill Freeman– Steve Seitz– Derek Hoiem– David Forsyth