Title: Linear Multi View Reconstruction and Camera Recovery
1Linear Multi View Reconstruction and Camera
Recovery
Kungl Tekniska Högskolan Computational Vision and
Active Perception Laboratory (CVAP)
By Carsten Rother and Stefan Carlsson
2Motivation
3Result
4What is new?
- Results
- Simultaneous Structure and Camera recovery
- Direct and linear method
- Arbitrary missing data
- Condition
- Reference plane visible in all views
5Previous 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)
6Notation
Point
Camera center
Image point
7Theory Overview
Projection equation
A plane visible in all views
8General case Planar case
Q
Q
9 General case Planar case
bilinear
linear
in Points and Cameras
10Linear relation for non-homogeneous Points and
Cameras
Which is
11The System-matrix for n Points and m Cameras
12Seperate points on and off the plane
View 1
View 2
Parallax Vector
P
Reference plane
Homography
13Why the plane at Infinity ?
Projection equation
If
then
14Method
4 coplanar points other corresponding points
Separate points on/off the plane
SVD on
Metric rectification
3D Model (SurfaceTexture)
15Teapot
16Tapeholder
17Tapeholder
18Theory Special case
3 orthogonal vanishing points
constrained camera
vp (ideal)
vp
vp
19Method Special case
3 orthogonal vanishing points other
corresponding points
Calculate K, R
SVD on
3D Model (SurfaceTexture)
20KTH / Stockholm
Visibilitymatrix
21KTH
22KTH
23City Hall / Stockholm
Visibilitymatrix
24City Hall
25City Hall
26Summary
- 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