Templates, Image Pyramids, and Filter Banks - Brown...
Transcript of Templates, Image Pyramids, and Filter Banks - Brown...
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Templates, Image Pyramids, and Filter Banks
Computer Vision
James Hays, Brown
09/19/11
Slides: Hoiem and others
![Page 2: Templates, Image Pyramids, and Filter Banks - Brown Universitycs.brown.edu/courses/cs143/2011/lectures/06.pdfJames Hays, Brown 09/19/11 Slides: Hoiem and others . Review 1. Match the](https://reader033.fdocuments.in/reader033/viewer/2022060513/5f82097fdd549f04d112a95a/html5/thumbnails/2.jpg)
Review
1. Match the spatial domain image to the Fourier magnitude image
1 5 4
A
3 2
C
B
D
E
Slide: Hoiem
![Page 3: Templates, Image Pyramids, and Filter Banks - Brown Universitycs.brown.edu/courses/cs143/2011/lectures/06.pdfJames Hays, Brown 09/19/11 Slides: Hoiem and others . Review 1. Match the](https://reader033.fdocuments.in/reader033/viewer/2022060513/5f82097fdd549f04d112a95a/html5/thumbnails/3.jpg)
Reminder
• Project 1 due in one week
![Page 4: Templates, Image Pyramids, and Filter Banks - Brown Universitycs.brown.edu/courses/cs143/2011/lectures/06.pdfJames Hays, Brown 09/19/11 Slides: Hoiem and others . Review 1. Match the](https://reader033.fdocuments.in/reader033/viewer/2022060513/5f82097fdd549f04d112a95a/html5/thumbnails/4.jpg)
Today’s class
• Template matching
• Image Pyramids
• Filter banks and texture
• Denoising, Compression
![Page 5: Templates, Image Pyramids, and Filter Banks - Brown Universitycs.brown.edu/courses/cs143/2011/lectures/06.pdfJames Hays, Brown 09/19/11 Slides: Hoiem and others . Review 1. Match the](https://reader033.fdocuments.in/reader033/viewer/2022060513/5f82097fdd549f04d112a95a/html5/thumbnails/5.jpg)
Template matching
• Goal: find in image
• Main challenge: What is a good similarity or distance measure between two patches? – Correlation
– Zero-mean correlation
– Sum Square Difference
– Normalized Cross Correlation
Slide: Hoiem
![Page 6: Templates, Image Pyramids, and Filter Banks - Brown Universitycs.brown.edu/courses/cs143/2011/lectures/06.pdfJames Hays, Brown 09/19/11 Slides: Hoiem and others . Review 1. Match the](https://reader033.fdocuments.in/reader033/viewer/2022060513/5f82097fdd549f04d112a95a/html5/thumbnails/6.jpg)
Matching with filters
• Goal: find in image
• Method 0: filter the image with eye patch
Input Filtered Image
],[],[],[,
lnkmflkgnmhlk
What went wrong?
f = image
g = filter
Slide: Hoiem
![Page 7: Templates, Image Pyramids, and Filter Banks - Brown Universitycs.brown.edu/courses/cs143/2011/lectures/06.pdfJames Hays, Brown 09/19/11 Slides: Hoiem and others . Review 1. Match the](https://reader033.fdocuments.in/reader033/viewer/2022060513/5f82097fdd549f04d112a95a/html5/thumbnails/7.jpg)
Slide: Hoiem
Matching with filters
• Goal: find in image
• Method 1: filter the image with zero-mean eye
Input Filtered Image (scaled) Thresholded Image
)],[()],[(],[,
lnkmgflkfnmhlk
True detections
False
detections
mean of f
![Page 8: Templates, Image Pyramids, and Filter Banks - Brown Universitycs.brown.edu/courses/cs143/2011/lectures/06.pdfJames Hays, Brown 09/19/11 Slides: Hoiem and others . Review 1. Match the](https://reader033.fdocuments.in/reader033/viewer/2022060513/5f82097fdd549f04d112a95a/html5/thumbnails/8.jpg)
Slide: Hoiem
Matching with filters
• Goal: find in image
• Method 2: SSD
Input 1- sqrt(SSD) Thresholded Image
2
,
)],[],[(],[ lnkmflkgnmhlk
True detections
![Page 9: Templates, Image Pyramids, and Filter Banks - Brown Universitycs.brown.edu/courses/cs143/2011/lectures/06.pdfJames Hays, Brown 09/19/11 Slides: Hoiem and others . Review 1. Match the](https://reader033.fdocuments.in/reader033/viewer/2022060513/5f82097fdd549f04d112a95a/html5/thumbnails/9.jpg)
Matching with filters
• Goal: find in image
• Method 2: SSD
Input 1- sqrt(SSD)
2
,
)],[],[(],[ lnkmflkgnmhlk
What’s the potential
downside of SSD?
Slide: Hoiem
![Page 10: Templates, Image Pyramids, and Filter Banks - Brown Universitycs.brown.edu/courses/cs143/2011/lectures/06.pdfJames Hays, Brown 09/19/11 Slides: Hoiem and others . Review 1. Match the](https://reader033.fdocuments.in/reader033/viewer/2022060513/5f82097fdd549f04d112a95a/html5/thumbnails/10.jpg)
Matching with filters
• Goal: find in image
• Method 3: Normalized cross-correlation
5.0
,
2
,
,
2
,
,
)],[()],[(
)],[)(],[(
],[
lk
nm
lk
nm
lk
flnkmfglkg
flnkmfglkg
nmh
Matlab: normxcorr2(template, im)
mean image patch mean template
Slide: Hoiem
![Page 11: Templates, Image Pyramids, and Filter Banks - Brown Universitycs.brown.edu/courses/cs143/2011/lectures/06.pdfJames Hays, Brown 09/19/11 Slides: Hoiem and others . Review 1. Match the](https://reader033.fdocuments.in/reader033/viewer/2022060513/5f82097fdd549f04d112a95a/html5/thumbnails/11.jpg)
Slide: Hoiem
Matching with filters
• Goal: find in image
• Method 3: Normalized cross-correlation
Input Normalized X-Correlation Thresholded Image
True detections
![Page 12: Templates, Image Pyramids, and Filter Banks - Brown Universitycs.brown.edu/courses/cs143/2011/lectures/06.pdfJames Hays, Brown 09/19/11 Slides: Hoiem and others . Review 1. Match the](https://reader033.fdocuments.in/reader033/viewer/2022060513/5f82097fdd549f04d112a95a/html5/thumbnails/12.jpg)
Matching with filters
• Goal: find in image
• Method 3: Normalized cross-correlation
Input Normalized X-Correlation Thresholded Image
True detections
Slide: Hoiem
![Page 13: Templates, Image Pyramids, and Filter Banks - Brown Universitycs.brown.edu/courses/cs143/2011/lectures/06.pdfJames Hays, Brown 09/19/11 Slides: Hoiem and others . Review 1. Match the](https://reader033.fdocuments.in/reader033/viewer/2022060513/5f82097fdd549f04d112a95a/html5/thumbnails/13.jpg)
Q: What is the best method to use?
A: Depends
• SSD: faster, sensitive to overall intensity
• Normalized cross-correlation: slower, invariant to local average intensity and contrast
![Page 14: Templates, Image Pyramids, and Filter Banks - Brown Universitycs.brown.edu/courses/cs143/2011/lectures/06.pdfJames Hays, Brown 09/19/11 Slides: Hoiem and others . Review 1. Match the](https://reader033.fdocuments.in/reader033/viewer/2022060513/5f82097fdd549f04d112a95a/html5/thumbnails/14.jpg)
Q: What if we want to find larger or smaller eyes?
A: Image Pyramid
![Page 15: Templates, Image Pyramids, and Filter Banks - Brown Universitycs.brown.edu/courses/cs143/2011/lectures/06.pdfJames Hays, Brown 09/19/11 Slides: Hoiem and others . Review 1. Match the](https://reader033.fdocuments.in/reader033/viewer/2022060513/5f82097fdd549f04d112a95a/html5/thumbnails/15.jpg)
Review of Sampling
Low-Pass Filtered Image
Image
Gaussian
Filter Sample Low-Res Image
Slide: Hoiem
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Gaussian pyramid
Source: Forsyth
![Page 17: Templates, Image Pyramids, and Filter Banks - Brown Universitycs.brown.edu/courses/cs143/2011/lectures/06.pdfJames Hays, Brown 09/19/11 Slides: Hoiem and others . Review 1. Match the](https://reader033.fdocuments.in/reader033/viewer/2022060513/5f82097fdd549f04d112a95a/html5/thumbnails/17.jpg)
Template Matching with Image Pyramids
Input: Image, Template
1. Match template at current scale
2. Downsample image
3. Repeat 1-2 until image is very small
4. Take responses above some threshold, perhaps with non-maxima suppression
Slide: Hoiem
![Page 18: Templates, Image Pyramids, and Filter Banks - Brown Universitycs.brown.edu/courses/cs143/2011/lectures/06.pdfJames Hays, Brown 09/19/11 Slides: Hoiem and others . Review 1. Match the](https://reader033.fdocuments.in/reader033/viewer/2022060513/5f82097fdd549f04d112a95a/html5/thumbnails/18.jpg)
Coarse-to-fine Image Registration
1. Compute Gaussian pyramid
2. Align with coarse pyramid
3. Successively align with finer pyramids
– Search smaller range
Why is this faster?
Are we guaranteed to get the same result?
Slide: Hoiem
![Page 19: Templates, Image Pyramids, and Filter Banks - Brown Universitycs.brown.edu/courses/cs143/2011/lectures/06.pdfJames Hays, Brown 09/19/11 Slides: Hoiem and others . Review 1. Match the](https://reader033.fdocuments.in/reader033/viewer/2022060513/5f82097fdd549f04d112a95a/html5/thumbnails/19.jpg)
Laplacian filter
Gaussian unit impulse
Laplacian of Gaussian
Source: Lazebnik
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2D edge detection filters
is the Laplacian operator:
Laplacian of Gaussian
Gaussian derivative of Gaussian
![Page 21: Templates, Image Pyramids, and Filter Banks - Brown Universitycs.brown.edu/courses/cs143/2011/lectures/06.pdfJames Hays, Brown 09/19/11 Slides: Hoiem and others . Review 1. Match the](https://reader033.fdocuments.in/reader033/viewer/2022060513/5f82097fdd549f04d112a95a/html5/thumbnails/21.jpg)
Laplacian pyramid
Source: Forsyth
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Computing Gaussian/Laplacian Pyramid
http://sepwww.stanford.edu/~morgan/texturematch/paper_html/node3.html
Can we reconstruct the original
from the laplacian pyramid?
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Hybrid Image
Slide: Hoiem
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Hybrid Image in Laplacian Pyramid
High frequency Low frequency
Slide: Hoiem
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Image representation
• Pixels: great for spatial resolution, poor access to frequency
• Fourier transform: great for frequency, not for spatial info
• Pyramids/filter banks: balance between spatial and frequency information
Slide: Hoiem
![Page 26: Templates, Image Pyramids, and Filter Banks - Brown Universitycs.brown.edu/courses/cs143/2011/lectures/06.pdfJames Hays, Brown 09/19/11 Slides: Hoiem and others . Review 1. Match the](https://reader033.fdocuments.in/reader033/viewer/2022060513/5f82097fdd549f04d112a95a/html5/thumbnails/26.jpg)
Major uses of image pyramids
• Compression
• Object detection
– Scale search – Features
• Detecting stable interest points
• Registration – Course-to-fine
Slide: Hoiem
![Page 27: Templates, Image Pyramids, and Filter Banks - Brown Universitycs.brown.edu/courses/cs143/2011/lectures/06.pdfJames Hays, Brown 09/19/11 Slides: Hoiem and others . Review 1. Match the](https://reader033.fdocuments.in/reader033/viewer/2022060513/5f82097fdd549f04d112a95a/html5/thumbnails/27.jpg)
Denoising
Additive Gaussian Noise
Gaussian
Filter
Slide: Hoiem
![Page 28: Templates, Image Pyramids, and Filter Banks - Brown Universitycs.brown.edu/courses/cs143/2011/lectures/06.pdfJames Hays, Brown 09/19/11 Slides: Hoiem and others . Review 1. Match the](https://reader033.fdocuments.in/reader033/viewer/2022060513/5f82097fdd549f04d112a95a/html5/thumbnails/28.jpg)
Smoothing with larger standard deviations suppresses noise, but also blurs the
image
Reducing Gaussian noise
Source: S. Lazebnik
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Reducing salt-and-pepper noise by Gaussian smoothing
3x3 5x5 7x7
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Alternative idea: Median filtering
• A median filter operates over a window by selecting the median intensity in the window
• Is median filtering linear? Source: K. Grauman
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Median filter
• What advantage does median filtering have over Gaussian filtering? – Robustness to outliers
Source: K. Grauman
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Median filter Salt-and-pepper noise Median filtered
Source: M. Hebert
• MATLAB: medfilt2(image, [h w])
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Median vs. Gaussian filtering 3x3 5x5 7x7
Gaussian
Median
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Other non-linear filters
• Weighted median (pixels further from center count less)
• Clipped mean (average, ignoring few brightest and darkest pixels)
• Bilateral filtering (weight by spatial distance and intensity difference)
http://vision.ai.uiuc.edu/?p=1455 Image:
Bilateral filtering
![Page 35: Templates, Image Pyramids, and Filter Banks - Brown Universitycs.brown.edu/courses/cs143/2011/lectures/06.pdfJames Hays, Brown 09/19/11 Slides: Hoiem and others . Review 1. Match the](https://reader033.fdocuments.in/reader033/viewer/2022060513/5f82097fdd549f04d112a95a/html5/thumbnails/35.jpg)
Review of last three days
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0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0
0 0 0 90 90 90 90 90 0 0
0 0 0 90 90 90 90 90 0 0
0 0 0 90 90 90 90 90 0 0
0 0 0 90 0 90 90 90 0 0
0 0 0 90 90 90 90 90 0 0
0 0 0 0 0 0 0 0 0 0
0 0 90 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0
0
0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0
0 0 0 90 90 90 90 90 0 0
0 0 0 90 90 90 90 90 0 0
0 0 0 90 90 90 90 90 0 0
0 0 0 90 0 90 90 90 0 0
0 0 0 90 90 90 90 90 0 0
0 0 0 0 0 0 0 0 0 0
0 0 90 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0
Credit: S. Seitz
],[],[],[,
lnkmglkfnmhlk
[.,.]h[.,.]f
Review: Image filtering
1 1 1
1 1 1
1 1 1
],[g
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0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0
0 0 0 90 90 90 90 90 0 0
0 0 0 90 90 90 90 90 0 0
0 0 0 90 90 90 90 90 0 0
0 0 0 90 0 90 90 90 0 0
0 0 0 90 90 90 90 90 0 0
0 0 0 0 0 0 0 0 0 0
0 0 90 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0
0 10
0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0
0 0 0 90 90 90 90 90 0 0
0 0 0 90 90 90 90 90 0 0
0 0 0 90 90 90 90 90 0 0
0 0 0 90 0 90 90 90 0 0
0 0 0 90 90 90 90 90 0 0
0 0 0 0 0 0 0 0 0 0
0 0 90 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0
],[],[],[,
lnkmglkfnmhlk
[.,.]h[.,.]f
Image filtering
1 1 1
1 1 1
1 1 1
],[g
Credit: S. Seitz
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0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0
0 0 0 90 90 90 90 90 0 0
0 0 0 90 90 90 90 90 0 0
0 0 0 90 90 90 90 90 0 0
0 0 0 90 0 90 90 90 0 0
0 0 0 90 90 90 90 90 0 0
0 0 0 0 0 0 0 0 0 0
0 0 90 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0
0 10 20
0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0
0 0 0 90 90 90 90 90 0 0
0 0 0 90 90 90 90 90 0 0
0 0 0 90 90 90 90 90 0 0
0 0 0 90 0 90 90 90 0 0
0 0 0 90 90 90 90 90 0 0
0 0 0 0 0 0 0 0 0 0
0 0 90 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0
],[],[],[,
lnkmglkfnmhlk
[.,.]h[.,.]f
Image filtering
1 1 1
1 1 1
1 1 1
],[g
Credit: S. Seitz
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Filtering in spatial domain -1 0 1
-2 0 2
-1 0 1
* =
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Filtering in frequency domain
FFT
FFT
Inverse FFT
=
Slide: Hoiem
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Review of Last 3 Days
• Linear filters for basic processing
– Edge filter (high-pass)
–Gaussian filter (low-pass)
FFT of Gaussian
[-1 1]
FFT of Gradient Filter
Gaussian
Slide: Hoiem
![Page 42: Templates, Image Pyramids, and Filter Banks - Brown Universitycs.brown.edu/courses/cs143/2011/lectures/06.pdfJames Hays, Brown 09/19/11 Slides: Hoiem and others . Review 1. Match the](https://reader033.fdocuments.in/reader033/viewer/2022060513/5f82097fdd549f04d112a95a/html5/thumbnails/42.jpg)
Review of Last 3 Days
• Derivative of Gaussian
Slide: Hoiem
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Review of Last 3 Days
• Applications of filters – Template matching (SSD or Normxcorr2)
• SSD can be done with linear filters, is sensitive to overall intensity
– Gaussian pyramid • Coarse-to-fine search, multi-scale detection
– Laplacian pyramid • More compact image representation
• Can be used for compositing in graphics
– Downsampling • Need to sufficiently low-pass before downsampling
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Next Lectures
• Machine Learning Crash Course