Why is the task important?
- Only line correspondences without any point correspondence
- Perspective projection is
often present.
- Many images are often available -> a technique treating
all data uniformly is needed.
Our solution
- It can be used on both wide base-line stereo and sequences.
- It is based on a factorization method -> a linear solution is
computed quickly; subsequent non-linear bundle adjustment is optional.
Notation: ... scale factor,
where | , is the i-th
point camera projection matrix
|
| is a 6-vector
of Pluecker line coordinates lying on the Klein quadric
|
projection of space lines into image lines:
Our algorithm
- Estimate
from partial
reconstructions on triplets of views.
- Factorize
into
by the singular value decomposition.
- Find a transformation
bringing rows of
and columns of
close to
the Klein quadric,
- Project rows of
and columns of
onto the Klein quadric.
Results
| ![](Cubes.gif)
![](Cubes3.gif) | ![](HouseOxford.gif)
|
| Cubes | House (Oxford)
|
| 5 images of 14 lines | 6 images of 31 lines |
|
| [576x768] | [576x768]
|
| manual detection | automatic detection
|
Mean / maximal errors [pxl]
       linear method | 2.42 / 13.41 | 0.80 / 10.53
|        lin. method + bundle adj. | 0.47 / 2.12 | 0.16 / 0.71
| |
References
Line Reconstruction from Many Perspective Images by
Factorization. Daniel Martinec and Tomas Pajdla. Accepted at
the Computer Vision and Pattern Recognition conference (CVPR),
Madison, USA, 2003.
Structure from many perspective images with occlusions.
Daniel Martinec and Tomas Pajdla. In Proceedings of the European
Conference on Computer Vision (ECCV), pp. 355-369,
Springer-Verlag, May 2002. [pdf],
[poster]
Demo on reconstruction from points