Image stitching

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Image stitching

Digital Visual Effects Yung-Yu Chuang

with slides by Richard Szeliski, Steve Seitz, Matthew Brown and Vaclav Hlavac

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Image stitching

• Stitching = alignment + blending geometrical

registration

photometric registration

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Applications of image stitching

• Video stabilization

• Video summarization

• Video compression

• Video matting

• Panorama creation

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Video summarization

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Video compression

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Object removal

input video

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Object removal

background estimation

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Panorama creation

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Why panorama?

• Are you getting the whole picture?

– Compact Camera FOV = 50 x 35°

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Why panorama?

– Human FOV = 200 x 135°

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Why panorama?

– Human FOV = 200 x 135°

– Panoramic Mosaic = 360 x 180°

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Panorama examples

• Similar to HDR, it is a topic of computational pho tography, seeking ways to build a better camera using either hardware or 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/

http://maps.google.com.tw/

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What can be globally aligned?

• In image stitching, we seek for a matrix to glob ally warp one image into another. Are any two i mages of the same scene can be aligned this wa y?

– Images captured with the same center of pro jection

– A planar scene or far-away scene

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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!

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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

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Changing camera center

• Does it still work? synthetic PP PP1

PP2

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What cannot

• The scene with depth variations and the camera has movement

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Planar scene (or a faraway one)

• PP3 is a projection plane of both centers of p rojection, so we are OK!

• This is how big aerial photographs are made

PP1

PP3

PP2

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Motion models

• Parametric models as the assumptions on the re lation between two images.

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2D Motion models

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Motion models

Translation

2 unknowns

Affine

6 unknowns

Perspective

8 unknowns

3D rotation

3 unknowns

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A case study: cylindrical panorama

• What if you want a 360 field of view?

mosaic projection cylinder

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Cylindrical panoramas

• Steps

– Reproject each image onto a cylinder – Blend

– Output the resulting mosaic

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applet

• http://graphics.stanford.edu/courses/cs178/ap plets/projection.html

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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!

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Taking pictures

Kaidan panoramic tripod head

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Translation model

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Where should the synthetic camera be

• The projection plane of some camera

• Onto a cylinder

real

camera synthetic

camera

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Cylindrical projection

Adopted from http://www.cambridgeincolour.com/tutorials/image-projections.htm

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Cylindrical projection

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Cylindrical projection

Adopted from http://www.cambridgeincolour.com/tutorials/image-projections.htm

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Cylindrical projection

unwrapped cylinder

y x

f

θ

x

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z Cylindrical projection

unwrapped cylinder

y x

θ

x y

f

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Cylindrical projection

unwrapped cylinder

y x

z x y

f s=f

gives less

distortion

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f = 180 (pixels)

Cylindrical reprojection

f = 380 f = 280

Image 384x300

top-down view Focal length – the dirty secret…

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A simple method for estimating f

Or, you can use other software, such as AutoStich , to help.

d f w

p

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Input images

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Cylindrical warping

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Blending

• Why blending: parallax, lens distortion, scene motion, exposure difference

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Blending

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Blending

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Blending

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Gradient-domain stitching

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Gradient-domain stitching

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Assembling the panorama

• Stitch pairs together, blend, then crop

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Problem: Drift

• Error accumulation

– small errors accumulate over time

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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 – y_n)/(n -1) to each image after the first

• compute a global warp: y’ = y + ax

• run a big optimization problem, incorporating this const raint

– best solution, but more complicated – known as “bundle adjustment”

(x₁,y₁)

• copy of first image

(x_n,y_n)

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End-to-end alignment and crop

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Rectangling panoramas

video

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Rectangling panoramas

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Rectangling panoramas

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Viewer: panorama

+

+ +

example: http://www.cs.washington.edu/education/courses/cse590ss/01wi/projects/project1/students/dougz/index.html

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Viewer: texture mapped model

example: http://www.panoramas.dk/

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365-GB panorama (biggest on the earth)

Mont Blanc / Canon 70D / 70,000 images / 2-week shooting / 2-month processing

video web

London

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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

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Determine pairwise alignment?

• Feature-based methods: only use feature points to estimate parameters

• We will study the “Recognising panorama” pape r published in ICCV 2003

• Run SIFT (or other feature algorithms) for each image, find feature matches.

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Determine pairwise alignment

• p’=Mp, where M is a transformation matrix, p a nd p’ are feature matches

• It is possible to use more complicated models s uch as affine or perspective

• For example, assume M is a 2x2 matrix

• Find M with the least square error

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Determine pairwise alignment

• Overdetermined system

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Normal equation

Given an overdetermined system

the normal equation is that which minimizes the sum of the square differences between left and right sides

Why?

b Ax 

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A

^T

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Normal equation

nxm, n equations, m variables

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Normal equation

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Normal equation

→

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Normal equation

 ^Ax ^ ^b 

²

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Normal equation

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Determine pairwise alignment

• p’=Mp, where M is a transformation matrix, p a nd p’ are feature matches

• For translation model, it is easier.

• What if the match is false? Avoid impact of outli ers.

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i i

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

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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 x_i, assume that majority of them are generated from a model with paramet ers , try to recover .

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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.

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How to determine k

p: probability of real inliers

P: probability of success after k trials

n samples are all inliers a failure

failure after k trials

n p k

3 0.5 35

6 0.6 97

6 0.5 293 for P=0.99

k

p

n

P  1  ( 1  )

) 1

log(

) 1

log(

p

n

k P



 

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Example: line fitting

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Example: line fitting

n=2

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Model fitting

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Measure distances

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Count inliers

c=3

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Another trial

c=3

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The best model

c=15

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RANSAC for Homography

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RANSAC for Homography

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RANSAC for Homography

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Tools for image stitching

• Hugin

• Image Composite Editor

• AutoStitch

• Google photo

• …

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Applications of panorama in VFX

• Background plates

• Image-based lighting

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Troy (image-based lighting)

http://www.cgnetworks.com/story_custom.php?story_id=2195&page=4

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Spiderman 2 (background plate)

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Reference

• Richard Szeliski, Image Alignment and Stitching: A Tutorial, Found ations and Trends in Computer Graphics and Computer Vision, 2(1) :1-104, December 2006.

• R. Szeliski and H.-Y. Shum.

Creating full view panoramic image mosaics and texture-mapped models

, SIGGRAPH 1997, pp251-258.

• M. Brown, D. G. Lowe, Recognising Panoramas, ICCV 2003.