Linear Multi View Reconstruction and Camera Recovery

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Linear Multi View Reconstruction and Camera
Recovery

Kungl Tekniska Högskolan Computational Vision and
Active Perception Laboratory (CVAP)
By Carsten Rother and Stefan Carlsson
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Motivation
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Result
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What is new?

• Results
• Simultaneous Structure and Camera recovery
• Direct and linear method
• Arbitrary missing data

• Condition
• Reference plane visible in all views

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Previous Work

• Multi View Geometry of Plane Parallax
• Heyden and Åström (1995)
• Irani and Anandan (1996)
• Criminisi, Reid and Zisserman (1998)
• Triggs (2000)
• Plane used for Camera Recovery
• Hartley and Zisserman (2000)

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Notation
Point
Camera center
Image point
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Theory Overview
Projection equation
A plane visible in all views
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General case Planar case
Q
Q
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General case Planar case
bilinear
linear
in Points and Cameras
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Linear relation for non-homogeneous Points and
Cameras
Which is
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The System-matrix for n Points and m Cameras
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Seperate points on and off the plane
View 1
View 2
Parallax Vector
P
Reference plane
Homography
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Why the plane at Infinity ?
Projection equation
If
then
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Method
4 coplanar points other corresponding points
Separate points on/off the plane
SVD on
Metric rectification
3D Model (SurfaceTexture)
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Teapot
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Tapeholder
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Tapeholder
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Theory Special case

3 orthogonal vanishing points
constrained camera
vp (ideal)
vp
vp
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Method Special case
3 orthogonal vanishing points other
corresponding points
Calculate K, R
SVD on
3D Model (SurfaceTexture)
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KTH / Stockholm
Visibilitymatrix
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KTH
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KTH
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City Hall / Stockholm
Visibilitymatrix
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City Hall
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City Hall
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Summary

• Reconstruction of large and small scaled scenes
  with use of a reference plane
• Simultaneous Points and Cameras
• Linear and direct with SVD
• Arbitrary missing data
• Wide baselines Numerical stability