Image stitching

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Image stitching

Digital Visual Effects, Spring 2006 Yung-Yu Chuang

2005/3/22

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

remove foreground

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Object removal

estimate background

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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

• Like HDR, it is a topic of computational

photography, seeking ways to build a better camera mostly in software.

• Panorama mode in consumer cameras

• Mars:

http://www.panoramas.dk/fullscreen3/f2_mars97.html

• Earth:

http://earthobservatory.nasa.gov/Newsroom/BlueMarble/

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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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Planar scene (or far away)

• 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

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Motion models

• Parametric models as the assumptions on the relation 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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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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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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Taking pictures

Kaidan panoramic tripod head

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Translation model

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– Map 3D point (X,Y,Z) onto cylinder

Cylindrical projection

X Y

Z

unit cylinder

unwrapped cylinder

– Convert to cylindrical coordinates

cylindrical image

– Convert to cylindrical image coordinates

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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.

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Distortion

• Radial distortion of the image

– Caused by imperfect lenses

– Deviations are most noticeable for rays that pass through the edge of the lens

No distortion Pin cushion Barrel

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Radial correction

• Correct for “bending” in wide field of view lenses

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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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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 constraint

– 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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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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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 for each image, find feature matches.

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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

• Avoid impact of outliers

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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 mjority of them are generated from a model with

parameters Θ, try to recover Θ.

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RANSAC algorithm

Run k times:

(1) draw n samples randomly

(2) fit parameters Θ 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 Θ 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

k

p

n

P = 1 − ( 1 − )

n samples are all inliers a failure

failure after k trials

) 1

log(

) 1

log(

p

n

k P

−

= −

293 0.5

6

97 0.6

6

35 0.5

3

k p

n for P=0.99

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Example: line fitting

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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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Applications of panorama in VFX

• Background plates

• Image-based lighting

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Spiderman 2 (background plate)

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Troy (image-based lighting)

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

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Project #2 Image stitching

• Assigned: 3/26

• Due: 11:59pm 4/23

• Work in pairs

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Reference software

• Autostitch

http://www.cs.ubc.ca/~mbrown/autostitch/autostitch.html

• Many others are available online.

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Tips for taking pictures

• Common focal point

• Rotate your camera to increase vertical FOV

• Tripod

• Fixed exposure?

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Bells & whistles

• Recognizing panorama

• Bundle adjustment

• Handle dynamic objects

• Better blending techniques

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Artifacts

• Take your own pictures and generate a stitched image, be creative.

• http://www.cs.washington.edu/education/courses/cse590ss/01wi/projec ts/project1/students/allen/index.html

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Submission

• You have to turn in your complete source, the executable, a html report and an artifact.

• Report page contains:

description of the project, what do you learn, algorithm, implementation details, results, bells and whistles…

• Artifacts must be made using your own program.

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Reference

• Richard Szeliski, Image Alignment and Stitching, unpublished draft, 2005.

• 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.