Image stitching
Digital Visual Effects Yung-Yu Chuang
with slides by Richard Szeliski, Steve Seitz, Matthew Brown and Vaclav Hlavac
Image stitching
• Stitching = alignment + blending geometrical
registration
photometric registration
Applications of image stitching
• Video stabilization
• Video summarization
• Video compression
• Video matting
• Panorama creation
Video summarization
Video compression
Object removal
input video
Object removal
remove foreground
Object removal
estimate background
Object removal
background estimation
Panorama creation
Why panorama?
• Are you getting the whole picture?
– Compact Camera FOV = 50 x 35°
Why panorama?
• Are you getting the whole picture?
– Compact Camera FOV = 50 x 35°
– Human FOV = 200 x 135°
Why panorama?
• Are you getting the whole picture?
– Compact Camera FOV = 50 x 35°
– Human FOV = 200 x 135°
– Panoramic Mosaic = 360 x 180°
Panorama examples
• Like HDR, it is a topic of computational
photography, seeking ways to build a better camera mostly in software.
• Most consumer cameras have a panorama mode
• Mars:
http://www.panoramas.dk/fullscreen3/f2_mars97.html
• Earth:
http://www.panoramas.dk/new-year-2006/taipei.html http://www.360cities.net/
What can be globally aligned?
• In image stitching, we seek for a matrix to
globally warp one image into another. Are any two images of the same scene can be aligned this way?
– Images captured with the same center of projection
– A planar scene or far-away scene
A pencil of rays contains all views
real
camera synthetic
camera
Can generate any synthetic camera view
as long as it has the same center of projection!
Mosaic as an image reprojection
mosaic projection plane
• The images are reprojected onto a common plane
• The mosaic is formed on this plane
• Mosaic is a synthetic wide-angle camera
Changing camera center
• Does it still work? synthetic PP PP1
PP2
Planar scene (or a faraway one)
• PP3 is a projection plane of both centers of projection, so we are OK!
• This is how big aerial photographs are made
PP1
PP3
PP2
Motion models
• Parametric models as the assumptions on the relation between two images.
2D Motion models
Motion models
Translation
2 unknowns
Affine
6 unknowns
Perspective
8 unknowns
3D rotation
3 unknowns
A case study: cylindrical panorama
• What if you want a 360 field of view?
mosaic projection cylinder
Cylindrical panoramas
• Steps
– Reproject each image onto a cylinder – Blend
– Output the resulting mosaic
Cylindrical panorama
1. Take pictures on a tripod (or handheld) 2. Warp to cylindrical coordinate
3. Compute pairwise alignments
4. Fix up the end-to-end alignment 5. Blending
6. Crop the result and import into a viewer
It is required to do radial distortion correction for better stitching results!
Taking pictures
Kaidan panoramic tripod head
Translation model
Try to align this in PaintShop Pro
Where should the synthetic camera be
• The projection plan of some camera
• Onto a cylinder
real
camera synthetic
camera
Cylindrical projection
Adopted from http://www.cambridgeincolour.com/tutorials/image-projections.htm
Cylindrical projection
Cylindrical projection
Adopted from http://www.cambridgeincolour.com/tutorials/image-projections.htm
Cylindrical projection
unwrapped cylinder
y x
f
θ
x
z Cylindrical projection
unwrapped cylinder
y x
θ
x y
f
Cylindrical projection
unwrapped cylinder
y x
z x y
f s=f
gives lessdistortion
f = 180 (pixels)
Cylindrical reprojection
f = 380 f = 280
Image 384x300
top-down view Focal length – the dirty secret…
A simple method for estimating f
Or, you can use other software, such as AutoStich, to help.
d f w
p
Input images
Cylindrical warping
Blending
• Why blending: parallax, lens distortion, scene motion, exposure difference
Blending
Blending
Blending
Assembling the panorama
• Stitch pairs together, blend, then crop
Problem: Drift
• Error accumulation
– small errors accumulate over time
Problem: Drift
• Solution
– add another copy of first image at the end
– there are a bunch of ways to solve this problem
• add displacement of (y1 – yn)/(n -1) to each image after the first
• compute a global warp: y’ = y + ax
• run a big optimization problem, incorporating this constraint
– best solution, but more complicated – known as “bundle adjustment”
(x1,y1)
• copy of first image
(xn,yn)
End-to-end alignment and crop
Viewer: panorama
++
++
++ ++
example: http://www.cs.washington.edu/education/courses/cse590ss/01wi/projects/project1/students/dougz/index.html
Viewer: texture mapped model
example: http://www.panoramas.dk/
Cylindrical panorama
1. Take pictures on a tripod (or handheld) 2. Warp to cylindrical coordinate
3. Compute pairwise alignments
4. Fix up the end-to-end alignment 5. Blending
6. Crop the result and import into a viewer
Determine pairwise alignment?
• Feature-based methods: only use feature points to estimate parameters
• We will study the “Recognising panorama”
paper published in ICCV 2003
• Run SIFT (or other feature algorithms) for each image, find feature matches.
Determine pairwise alignment
• p’=Mp, where M is a transformation matrix, p and p’ are feature matches
• It is possible to use more complicated models such as affine or perspective
• For example, assume M is a 2x2 matrix
• Find M with the least square error
n i
p Mp
1
' 2
y x m
m
m m
y x
22 21
12 11
' '
Determine pairwise alignment
• Overdetermined system
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Normal equation
Given an overdetermined system
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Why?
Normal equation
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Normal equation
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Determine pairwise alignment
• p’=Mp, where M is a transformation matrix, p and p’ are feature matches
• For translation model, it is easier.
• What if the match is false? Avoid impact of outliers.
n
i
i i
i
i x m y y
x m
E
1
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RANSAC
• RANSAC = Random Sample Consensus
• An algorithm for robust fitting of models in the presence of many data outliers
• Compare to robust statistics
• Given N data points xi, assume that mjority of t hem are generated from a model with paramet ers , try to recover .
RANSAC algorithm
Run k times:
(1) draw n samples randomly
(2) fit parameters with these n samples (3) for each of other N-n points, calculate
its distance to the fitted model, count the number of inlier points, c
Output with the largest c
How many times?
How big?
Smaller is better
How to define?
Depends on the problem.
How to determine k
p: probability of real inliers
P: probability of success after k trials
k
p
nP 1 ( 1 )
n samples are all inliers a failure
failure after k trials
) 1
log(
) 1
log(
p
nk P
n p k
3 0.5 35
6 0.6 97
6 0.5 293 for P=0.99
Example: line fitting
Example: line fitting
n=2
Model fitting
Measure distances
Count inliers
c=3
Another trial
c=3
The best model
c=15
RANSAC for Homography
RANSAC for Homography
RANSAC for Homography
Applications of panorama in VFX
• Background plates
• Image-based lighting
Troy (image-based lighting)
http://www.cgnetworks.com/story_custom.php?story_id=2195&page=4
