Details
| Original language | English |
|---|---|
| Pages (from-to) | 49-70 |
| Number of pages | 22 |
| Journal | Journal of Mathematical Imaging and Vision |
| Volume | 22 |
| Issue number | 1 |
| Publication status | Published - Jan 2005 |
| Externally published | Yes |
Abstract
Part II uses the foundations of Part I [35] to define constraint equations for 2D-3D pose estimation of different corresponding entities. Most articles on pose estimation concentrate on specific types of correspondences, mostly between points, and only rarely use line correspondences. The first aim of this part is to extend pose estimation scenarios to correspondences of an extended set of geometric entities. In this context we are interested to relate the following (2D) image and (3D) model types: 2D point/3D point, 2D line/3D point, 2D line/3D line, 2D conic/3D circle, 2D conic/3D sphere. Furthermore, to handle articulated objects, we describe kinematic chains in this context in a similar manner. We ensure that all constraint equations end up in a distance measure in the Euclidean space, which is well posed in the context of noisy data. We also discuss the numerical estimation of the pose. We propose to use linearized twist transformations which result in well conditioned and fast solvable systems of equations. The key idea is not to search for the representation of the Lie group, describing the rigid body motion, but for the representation of their generating Lie algebra. This leads to real-time capable algorithms.
Keywords
- 2D-3D pose estimation, Circles, Kinematic chains, Pose constraints, Spheres, Twists
ASJC Scopus subject areas
- Mathematics(all)
- Statistics and Probability
- Mathematics(all)
- Modelling and Simulation
- Physics and Astronomy(all)
- Condensed Matter Physics
- Computer Science(all)
- Computer Vision and Pattern Recognition
- Mathematics(all)
- Geometry and Topology
- Mathematics(all)
- Applied Mathematics
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In: Journal of Mathematical Imaging and Vision, Vol. 22, No. 1, 01.2005, p. 49-70.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Pose estimation in conformal geometric algebra part II
T2 - Real-time pose estimation using extended feature concepts
AU - Rosenhahn, Bodo
AU - Sommer, Gerald
N1 - Funding information: This work has been supported by DFG Graduiertenkolleg No. 357 and by EC Grant IST-2001-3422 (VISATEC).
PY - 2005/1
Y1 - 2005/1
N2 - Part II uses the foundations of Part I [35] to define constraint equations for 2D-3D pose estimation of different corresponding entities. Most articles on pose estimation concentrate on specific types of correspondences, mostly between points, and only rarely use line correspondences. The first aim of this part is to extend pose estimation scenarios to correspondences of an extended set of geometric entities. In this context we are interested to relate the following (2D) image and (3D) model types: 2D point/3D point, 2D line/3D point, 2D line/3D line, 2D conic/3D circle, 2D conic/3D sphere. Furthermore, to handle articulated objects, we describe kinematic chains in this context in a similar manner. We ensure that all constraint equations end up in a distance measure in the Euclidean space, which is well posed in the context of noisy data. We also discuss the numerical estimation of the pose. We propose to use linearized twist transformations which result in well conditioned and fast solvable systems of equations. The key idea is not to search for the representation of the Lie group, describing the rigid body motion, but for the representation of their generating Lie algebra. This leads to real-time capable algorithms.
AB - Part II uses the foundations of Part I [35] to define constraint equations for 2D-3D pose estimation of different corresponding entities. Most articles on pose estimation concentrate on specific types of correspondences, mostly between points, and only rarely use line correspondences. The first aim of this part is to extend pose estimation scenarios to correspondences of an extended set of geometric entities. In this context we are interested to relate the following (2D) image and (3D) model types: 2D point/3D point, 2D line/3D point, 2D line/3D line, 2D conic/3D circle, 2D conic/3D sphere. Furthermore, to handle articulated objects, we describe kinematic chains in this context in a similar manner. We ensure that all constraint equations end up in a distance measure in the Euclidean space, which is well posed in the context of noisy data. We also discuss the numerical estimation of the pose. We propose to use linearized twist transformations which result in well conditioned and fast solvable systems of equations. The key idea is not to search for the representation of the Lie group, describing the rigid body motion, but for the representation of their generating Lie algebra. This leads to real-time capable algorithms.
KW - 2D-3D pose estimation
KW - Circles
KW - Kinematic chains
KW - Pose constraints
KW - Spheres
KW - Twists
UR - http://www.scopus.com/inward/record.url?scp=17044402497&partnerID=8YFLogxK
U2 - 10.1007/s10851-005-4782-9
DO - 10.1007/s10851-005-4782-9
M3 - Article
AN - SCOPUS:17044402497
VL - 22
SP - 49
EP - 70
JO - Journal of Mathematical Imaging and Vision
JF - Journal of Mathematical Imaging and Vision
SN - 0924-9907
IS - 1
ER -