Bundle Adjustment using Conjugate Gradients with Multiscale Preconditioning
Author
Summary, in English
Bundle adjustment is a key component of almost any feature based 3D reconstruction
system, used to compute accurate estimates of calibration parameters and structure and
motion configurations. These problems tend to be very large, often involving thousands
of variables. Thus, efficient optimization methods are crucial. The traditional Levenberg
Marquardt algorithm with a direct sparse solver can be efficiently adapted to the special
structure of the problem and works well for small to medium size setups. However, for
larger scale configurations the cubic computational complexity makes this approach pro-
hibitively expensive. The natural step here is to turn to iterative methods for solving the
normal equations such as conjugate gradients. So far, there has been little progress in this
direction. This is probably due to the lack of suitable pre-conditioners, which are con-
sidered essential for the success of any iterative linear solver. In this paper, we show how
multi scale representations, derived from the underlying geometric layout of the problem,
can be used to dramatically increase the power of straight forward preconditioners such
as Gauss-Seidel.
system, used to compute accurate estimates of calibration parameters and structure and
motion configurations. These problems tend to be very large, often involving thousands
of variables. Thus, efficient optimization methods are crucial. The traditional Levenberg
Marquardt algorithm with a direct sparse solver can be efficiently adapted to the special
structure of the problem and works well for small to medium size setups. However, for
larger scale configurations the cubic computational complexity makes this approach pro-
hibitively expensive. The natural step here is to turn to iterative methods for solving the
normal equations such as conjugate gradients. So far, there has been little progress in this
direction. This is probably due to the lack of suitable pre-conditioners, which are con-
sidered essential for the success of any iterative linear solver. In this paper, we show how
multi scale representations, derived from the underlying geometric layout of the problem,
can be used to dramatically increase the power of straight forward preconditioners such
as Gauss-Seidel.
Department/s
- Mathematics (Faculty of Engineering)
- Centre for Mathematical Sciences
- Mathematical Imaging Group
Publishing year
2009
Language
English
Publication/Series
British Machine Vision Conference
Full text
- Available as PDF - 242 kB
- Download statistics
Document type
Conference paper
Topic
- Mathematics
Keywords
- Computer vision
- non-linear least squares problems
- simultaneous localization and mapping
- bundle adjustment
Conference name
British Machine Vision Conference, 2009
Conference date
2009-09-07 - 2009-09-10
Conference place
London, United Kingdom
Status
Published
Research group
- Mathematical Imaging Group