Triangulation of Points, Lines and Conics
Author
Summary, in English
The problem of reconstructing 3D scene features from multiple views with known camera motion and given image correspondences is considered. This is a classical and one of the most basic geometric problems in computer vision and photogrammetry. Yet, previous methods fail to guarantee optimal reconstructions—they are either plagued by local minima or rely on a non-optimal cost-function. A common framework for the triangulation problem of points, lines and conics is presented. We define what is meant by an optimal triangulation based on statistical principles and then derive an algorithm for computing the globally optimal solution. The method for achieving the global minimum is based on convex and concave relaxations for both fractionals and monomials. The performance of the method is evaluated on real image data.
Department/s
- Mathematics (Faculty of Engineering)
- Mathematical Imaging Group
Publishing year
2008
Language
English
Pages
215-225
Publication/Series
Journal of Mathematical Imaging and Vision
Volume
32
Issue
2
Full text
Links
Document type
Journal article
Publisher
Springer
Topic
- Computer Vision and Robotics (Autonomous Systems)
- Mathematics
Keywords
- Triangulation
- Global optimization
- RATIOS PROBLEM
- SUM
Status
Published
Research group
- Mathematical Imaging Group
ISBN/ISSN/Other
- ISSN: 0924-9907