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  Pose Estimation in Conformal Geometric Algebra : Part II, Real-time Pose Estimation Using Extended Feature Concepts

Rosenhahn, B., & Sommer, G. (2005). Pose Estimation in Conformal Geometric Algebra: Part II, Real-time Pose Estimation Using Extended Feature Concepts. Journal of Mathematical Imaging and Vision, 0924-990722, 49-70. doi:10.1007/s10851-005-4782-9.

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Rosenhahn, Bodo1, Author           
Sommer, Gerald1, Author
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1External Organizations, ou_persistent22              

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 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.

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Language(s): eng - English
 Dates: 2006-05-312005
 Publication Status: Issued
 Pages: -
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 Table of Contents: -
 Rev. Type: Peer
 Identifiers: eDoc: 278981
DOI: 10.1007/s10851-005-4782-9
BibTex Citekey: RosenhahnJMIV2005b
Other: Local-ID: C125675300671F7B-5331C8D62651D1B5C12570DF00306C1D-RosenhahnJMIV2005b
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Title: Journal of Mathematical Imaging and Vision
Source Genre: Journal
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Publ. Info: Dordrecht : Kluwer
Pages: - Volume / Issue: 0924-990722 Sequence Number: - Start / End Page: 49 - 70 Identifier: ISBN: 0924-9907