Partial Symmetry in Polynomial Systems and Its Application in Computer Vision
Author
Summary, in English
Algorithms for solving systems of polynomial equations
are key components for solving geometry problems in computer
vision. Fast and stable polynomial solvers are essential
for numerous applications e.g. minimal problems or
finding for all stationary points of certain algebraic errors.
Recently, full symmetry in the polynomial systems has been
utilized to simplify and speed up state-of-the-art polynomial
solvers based on Gr¨obner basis method. In this paper, we
further explore partial symmetry (i.e. where the symmetry
lies in a subset of the variables) in the polynomial systems.
We develop novel numerical schemes to utilize such partial
symmetry. We then demonstrate the advantage of our
schemes in several computer vision problems. In both synthetic
and real experiments, we show that utilizing partial
symmetry allow us to obtain faster and more accurate polynomial
solvers than the general solvers.
are key components for solving geometry problems in computer
vision. Fast and stable polynomial solvers are essential
for numerous applications e.g. minimal problems or
finding for all stationary points of certain algebraic errors.
Recently, full symmetry in the polynomial systems has been
utilized to simplify and speed up state-of-the-art polynomial
solvers based on Gr¨obner basis method. In this paper, we
further explore partial symmetry (i.e. where the symmetry
lies in a subset of the variables) in the polynomial systems.
We develop novel numerical schemes to utilize such partial
symmetry. We then demonstrate the advantage of our
schemes in several computer vision problems. In both synthetic
and real experiments, we show that utilizing partial
symmetry allow us to obtain faster and more accurate polynomial
solvers than the general solvers.
Department/s
Publishing year
2014
Language
English
Pages
438-445
Publication/Series
[Host publication title missing]
Full text
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Links
Document type
Conference paper
Publisher
Computer Vision Foundation
Topic
- Mathematics
Keywords
- Systems of polynomial equations
- computer vision
- algebraic geometry
- minimal solvers
Conference name
IEEE Conference on Computer Vision and Pattern Recognition (CVPR 2014), 2014
Conference date
2014-06-24 - 2014-06-27
Conference place
Columbus, Ohio, United States
Status
Published
Research group
- Mathematical Imaging Group
ISBN/ISSN/Other
- ISSN: 1063-6919