feature-based alignment chapter 6 r. szelisky · feature-based alignment chapter 6 r. szelisky...
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Feature-based AlignmentChapter 6 R. Szelisky
Guido GerigCS 6320 Spring 2012
Slide Credits: Trevor Darrell, Berkeley (C280 CV Course), Steve Seitz, Kristen Grauman, Alyosha Efros, L. Lazebnik, Marc Pollefeys
Original Slides Prof. Trevor Darrel (08Alignment, 06LocalFeatures): please visit http://www.eecs.berkeley.edu/~trevor/CS280Notes/
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Today: Alignment
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Motivation: Mosaics
• Getting the whole picture– Consumer camera: 50˚ x 35˚
Slide from Brown & Lowe 2003
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Motivation: Mosaics
• Getting the whole picture– Consumer camera: 50˚ x 35˚
– Human Vision: 176˚ x 135˚
• Panoramic Mosaic = up to 360 x 180°
Slide from Brown & Lowe 2003
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Motion models
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Motion models
• What happens when we take two images with a camera and try to align them?
• translation?• rotation?• scale?• affine?• perspective?
Szelisk
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Panoramas: generating synthetic views
realcamera
syntheticcamera
Can generate any synthetic camera viewas long as it has the same center of projection!
Source: Alyosha Efros
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mosaic PP
Image reprojection
• The mosaic has a natural interpretation in 3D– The images are reprojected onto a common plane– The mosaic is formed on this plane– Mosaic is a synthetic wide-angle camera
Source: Steve Seitz
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Motion models
Translation
2 unknowns
Affine
6 unknowns
Perspective
8 unknowns
3D rotation
3 unknowns
Szeliski
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2D coordinate transformations
• translation: x’ = x + t x = (x,y)• rotation: x’ = R x + t• similarity: x’ = s R x + t• affine: x’ = A x + t• perspective: x’ H x x = (x,y,1)
(x is a homogeneous coordinate)• These all form a nested group (closed w/ inv.)
Szelisk
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Basic 2D Transformations
• Basic 2D transformations as 3x3 matrices
11000cossin0sincos
1''
yx
yx
11001001
1''
yx
tt
yx
y
x
11000101
1''
yx
shsh
yx
y
x
Translate
Rotate Shear
11000000
1''
yx
ss
yx
y
x
Scale
Source: Alyosha Efros
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2D Affine Transformations
• Affine transformations are combinations of …– Linear transformations, and– Translations
• Parallel lines remain parallel
wyx
fedcba
wyx
100''
Grauman
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Projective Transformations
• Projective transformations:– Affine transformations, and– Projective warps
• Parallel lines do not necessarily remain parallel
wyx
ihgfedcba
wyx
'''
Grauman
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Image alignment
• Two broad approaches:– Direct (pixel-based) alignment
• Search for alignment where most pixels agree– Feature-based alignment
• Search for alignment where extracted featuresagree
• Can be verified using pixel-based alignment
Source: L. Lazebnik
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Fitting an affine transformation
• Assuming we know the correspondences, how do we get the transformation?
),( ii yx ),( ii yx
2
1
43
21
tt
yx
mmmm
yx
i
i
i
i
Grauman
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Fitting an affine transformation
• Assuming we know the correspondences, how do we get the transformation?
),( ii yx ),( ii yx
2
1
43
21
tt
yx
mmmm
yx
i
i
i
i
i
i
ii
ii
yx
ttmmmm
yxyx
2
1
4
3
2
1
10000100
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Fitting an affine transformation
• How many matches (correspondence pairs) do we need to solve for the transformation parameters?
• Once we have solved for the parameters, how do we compute the coordinates of the corresponding point for ?
i
i
ii
ii
yx
ttmmmm
yxyx
2
1
4
3
2
1
10000100
),( newnew yx
Grauman
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Panoramas
Obtain a wider angle view by combining multiple images.
image from
S. Seitz
. . .
Grauman
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Outliers• Outliers can hurt the quality of our
parameter estimates, e.g., – an erroneous pair of matching points from two
images– an edge point that is noise, or doesn’t belong to
the line we are fitting.
Grauman
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Example: least squares line fitting
• Assuming all the points that belong to a particular line are known
Grauman
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Outliers affect least squares fit
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Outliers affect least squares fit
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RANSAC
• RANdom Sample Consensus
• Approach: we want to avoid the impact of outliers, so let’s look for “inliers”, and use those only.
• Intuition: if an outlier is chosen to compute the current fit, then the resulting line won’t have much support from rest of the points.
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RANSAC• RANSAC loop:
1. Randomly select a seed group of points on which to base transformation estimate (e.g., a group of matches)
2. Compute transformation from seed group
3. Find inliers to this transformation
4. If the number of inliers is sufficiently large, re-compute least-squares estimate of transformation on all of the inliers
• Keep the transformation with the largest number of inliers
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RANSAC Line Fitting Example
Task:Estimate best line
Slide credit: Jinxiang Chai, CMU
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RANSAC Line Fitting Example
Sample two points
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RANSAC Line Fitting Example
Fit Line
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RANSAC Line Fitting Example
Total number of points within a threshold of line.
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RANSAC Line Fitting Example
Repeat, until get a good result
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RANSAC Line Fitting Example
Repeat, until get a good result
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RANSAC Line Fitting Example
Repeat, until get a good result
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RANSAC example: Translation
Putative matches
Source: Rick Szeliski
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RANSAC example: Translation
Select one match, count inliers
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RANSAC example: Translation
Select one match, count inliers
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RANSAC example: Translation
Find “average” translation vector
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Towards large‐scale mosaics…
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Feature‐based alignment outline
Source: L. Lazebnik
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Feature‐based alignment outline
• Extract features
Source: L. Lazebnik
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Feature‐based alignment outline
• Extract features• Compute putative matches
Source: L. Lazebnik
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Feature‐based alignment outline
• Extract features• Compute putative matches• Loop:
– Hypothesize transformation T (small group of putative matches that are related by T)
Source: L. Lazebnik
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Feature‐based alignment outline
• Extract features• Compute putative matches• Loop:
– Hypothesize transformation T (small group of putative matches that are related by T)
– Verify transformation (search for other matches consistent with T)
Source: L. Lazebnik
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Feature‐based alignment outline
• Extract features• Compute putative matches• Loop:
– Hypothesize transformation T (small group of putative matches that are related by T)
– Verify transformation (search for other matches consistent with T)
Source: L. Lazebnik
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RANSAC motion model
Szeliski
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Towards large‐scale mosaics…
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Richard SzeliskiImage Stitching 45
Probabilistic Feature Matching
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Probabilistic model for verification
Szeliski
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Other types of mosaics
• Can mosaic onto any surface if you know the geometry– See NASA’s Visible Earth project for some stunning
earth mosaics• http://earthobservatory.nasa.gov/Newsroom/BlueMarble/
Szeliski
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Final thought:What is a “panorama”?
• Tracking a subject
• Repeated (best) shots
• Multiple exposures
• “Infer” what photographer wants?
Szeliski
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Next time: 6.2 Pose Estimation
• 6.2 Pose Estimation• Chapter 7: Structure from Motion