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Linear Multi View Reconstruction and Camera Recovery

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Plane used for Camera Recovery: Hartley and Zisserman (2000) Notation. Point: Camera center: ... for n Points and m Cameras: Seperate points on and off the ... – PowerPoint PPT presentation

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Title: Linear Multi View Reconstruction and Camera Recovery


1
Linear Multi View Reconstruction and Camera
Recovery

Kungl Tekniska Högskolan Computational Vision and
Active Perception Laboratory (CVAP)
By Carsten Rother and Stefan Carlsson
2
Motivation
3
Result
4
What is new?
  • Results
  • Simultaneous Structure and Camera recovery
  • Direct and linear method
  • Arbitrary missing data
  • Condition
  • Reference plane visible in all views

5
Previous Work
  • Multi View Geometry of Plane Parallax
  • Heyden and Ã…ström (1995)
  • Irani and Anandan (1996)
  • Criminisi, Reid and Zisserman (1998)
  • Triggs (2000)
  • Plane used for Camera Recovery
  • Hartley and Zisserman (2000)

6
Notation
Point
Camera center
Image point
7
Theory Overview
Projection equation
A plane visible in all views
8
General case Planar case
Q
Q
9
General case Planar case
bilinear
linear
in Points and Cameras
10
Linear relation for non-homogeneous Points and
Cameras
Which is
11
The System-matrix for n Points and m Cameras
12
Seperate points on and off the plane
View 1
View 2
Parallax Vector
P
Reference plane
Homography
13
Why the plane at Infinity ?
Projection equation
If
then
14
Method
4 coplanar points other corresponding points
Separate points on/off the plane
SVD on
Metric rectification
3D Model (SurfaceTexture)
15
Teapot
16
Tapeholder
17
Tapeholder
18
Theory Special case

3 orthogonal vanishing points
constrained camera
vp (ideal)
vp
vp
19
Method Special case
3 orthogonal vanishing points other
corresponding points
Calculate K, R
SVD on
3D Model (SurfaceTexture)
20
KTH / Stockholm
Visibilitymatrix
21
KTH
22
KTH
23
City Hall / Stockholm
Visibilitymatrix
24
City Hall
25
City Hall
26
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
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