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CSCE 643 Computer Vision:Template Matching, Image Pyramids and Denoising
Jinxiang Chai
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Today’s class
• Template matching
• Gaussian Pyramids
• Laplacian Pyramids
• Image denoising
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Template matching• Goal: find in image
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Template matching• Goal: find in image
• Main challenge: What is a good similarity or distance measure between two patches?
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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
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Matching with filters• Goal: find in image• Method 0: filter the image with eye patch
Input Filtered Image
],[],[],[,
lnkmflkgnmhlk
What went wrong?
f = imageg = filter
Slide: Hoiem
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Problem with Correlation
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Problem with Correlation
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Solution
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Slide: Hoiem
Matching with filters• Goal: find in image• Method 1: filter the image with zero-mean eye
Input Filtered Image (scaled) Thresholded Image
],[)],[(],[,
lkgflnkmfnmhlk
True detections
False detections
mean of f
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Slide: Hoiem
Matching with filters• Goal: find in image• Method 2: SSD
Input 1- sqrt(SSD) Thresholded Image
2
,
)],[],[(],[ lnkmflkgnmhlk
True detections
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Relationship SSD and Correlation
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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
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Matching with filters• Goal: find in image• Method 3: Normalized cross-correlation - subtracting the mean - dividing by the standard deviation
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Matching with filters• Goal: find in image• Method 3: Normalized cross-correlation
5.0
,
2,
,
2
,,
)],[()],[(
)],[)(],[(],[
lknm
lk
nmlk
flnkmfglkg
flnkmfglkgnmh
Matlab: normxcorr2(template, im)
mean image patchmean template
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Slide: Hoiem
Matching with filters• Goal: find in image• Method 3: Normalized cross-correlation
Input Normalized X-Correlation Thresholded Image
True detections
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Matching with filters• Goal: find in image• Method 3: Normalized cross-correlation
Input Normalized X-Correlation Thresholded Image
True detections
Slide: Hoiem
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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
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Q: What if we want to find larger or smaller eyes?
A: Image Pyramid
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Gaussian Pyramid
Low-Pass Filtered ImageImage
GaussianFilter Sample Low-Res
Image
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Gaussian Pyramid
filter mask
Repeat– Filter– Subsample
Until minimum resolution reached – can specify desired number of levels (e.g., 3-level pyramid)
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Gaussian pyramid
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Template Matching with Image Pyramids
Input: Image, Template1. 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
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Laplacian pyramid
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Laplacian FilterThe filtering kernel for Laplacian is
Finite difference allows us to approximate the Laplacian using the following filtering kernel.
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Laplacian Pyramid
Laplacian Pyramid (subband images)- Created from Gaussian pyramid by subtraction
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The Laplacian of Gaussian Kernel
),()()),(( 22 yxIGyxIG
2
22
24
222222 2
yx
eyxxG
xGG
is the Laplacian operator:
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The Laplacian of Gaussian Filter Kernel
0.1
4.1
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Laplacian Pyramid
What happens in frequency domain?
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Laplacian Pyramid
What happens in frequency domain? Bandpass filters
Can we reconstruct the original from the laplacian pyramid?
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Laplacian Pyramid
What happens in frequency domain? Bandpass filters
Can we reconstruct the original from the laplacian pyramid?- Yes, laplacian pyramid is a complete image representation which encodes fine to course structure in a different level
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Image representation
• Pixels: great for spatial resolution, poor access to frequency
• Fourier transform: great for frequency, not for spatial info such as locations.
• Pyramids/filter banks: balance between spatial and frequency information
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Major uses of image pyramids
• Compression
• Object detection– Scale search– Features
• Detecting stable interest points
• Image blending/mosaicing
• Registration– Course-to-fine
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Multi-resolution SIFT Feature Detection
- Object recognition from local scale-invariant features [pdf link], ICCV 09
- David G. Lowe, "Distinctive image features from scale-invariant keypoints," International Journal of Computer Vision, 60, 2 (2004), pp. 91-110
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Pyramid Blending
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laplacianlevel
4
laplacianlevel
2
laplacianlevel
0
left pyramid right pyramid blended pyramid
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Hierarchical Image Registration1. Compute Gaussian pyramid2. Align with coarse pyramid3. Successively align with finer
pyramids– Search smaller range
Why is this faster?
- Hierarchical Model-Based Motion Estimation, ECCV 92
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Denoising
Additive Gaussian Noise
Gaussian Filter
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Gaussian
input Gaussian filter
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Median Filter
• For each neighbor in image, sliding the window• Sort pixel values• Set the center pixel to the median
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Median Filter
input Gaussian filter Median filter
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Median Filter Examples
input Median 7X7
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Median Filter Examples
Median 11X11Median 3X3
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Median Filter Examples
Median 11X11Median 3X3
Straight edges kept
Sharp features lost
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Median Filter Properties
Can remove outliers (peppers and salts)
Window size controls size of structure
Preserve some details but sharp corners and edges might get lost
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Comparison of Mean, Gaussian, and Median
original Mean with 6 pixels
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Comparison of Mean, Gaussian, and Median
original Gaussian with 6 pixels
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Comparison of Mean, Gaussian, and Median
original Median with 6 pixels
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Common Problems
Mean: blurs image, removes simple noise, no details are preserved
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Common Problems
Mean: blurs image, removes simple noise, no details are preserved
Gaussian: blurs image, preserves details only for small σ.
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Common Problems
Mean: blurs image, removes simple noise, no details are preserved
Gaussian: blurs image, preserves details only for small σ.
Median: preserves some details, good at removing strong noise
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Common Problems
Mean: blurs image, removes simple noise, no details are preserved
Gaussian: blurs image, preserves details only for small σ.
Median: preserves some details, good at removing strong noise
Can we find a filter that not only smooths regions but preserves sharp features such as edges?
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Common ProblemsMean: blurs image, removes simple noise, no details
are preservedGaussian: blurs image, preserves details only for small
σ.Median: preserves some details, good at removing
strong noise
Can we find a filter that not only smooths regions but preserves sharp features such as edges?
- yes, Tomasi's Bilateral Filter!
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Bilateral Filter Example
Gaussian filter Bilateral filter
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Bilateral Filter Example
Gaussian filter Bilateral filter
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1D Graphical ExampleCenter Sample u
It is clear that in weighting this neighborhood, we would like to preserve the step
Neighborhood
I(p)
p
)(uneighborp
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The Weights
)2
)(exp()( 2
2
cc
pupW
p
I(p)
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Filtered Values
)2
)(exp()( 2
2
cc
pupW
p
I(p)
Filtered value
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Edges Are Smoothed
)2
)(exp()( 2
2
cc
pupW
p
I(p)
Filtered value
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What Causes the Problem?
)2
)(exp()( 2
2
cc
pupW
p
I(p)
Filtered value
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What Causes the Problem?
)2
)(exp()( 2
2
cc
pupW
p
I(p)
Filtered value
Same weights for these two pixels!!
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The Weights
)2
))()((exp()( 2
2
ss
pIuIpW
)2
)(exp()( 2
2
cc
pupW
p
I(p)
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Bilateral filter
2
2 2
2
2 2
2 2
2 2
( )'
c s
c s
I u I pu p
p N u
I u I pu p
p N u
e e I pI u
e e
Denoise Feature preserving
Normalization
Bilateral Filtering
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Filter Parameters
As proposed by Tomasi and Manduchi, the filter is controlled by 3 parameters:
The filter can be applied for several iterations in order to further strengthen its edge-preserving smoothing
N(u) – The neighbor size of the filter support,c – The variance of the spatial distances,s – The variance of the value distances,
)(
)(
)(*)(
)(*)(*)()(
uNp sc
uNp sc
pWpW
pIpWpWuI
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Bilateral Filter Results
Original
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Bilateral Filter Results
σc = 3, σs = 3
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Bilateral Filter Results
σc = 6, σs = 3
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Bilateral Filter Results
σc = 12, σs = 3
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Bilateral Filter Results
σc = 12, σs = 6
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Bilateral Filter Results
σc = 15, σs = 8
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Summary– 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
– Image denoising