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

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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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Authors and Affiliations

  1. Cognitive Systems Group, Institute of Computer Science and Applied Mathematics, Christian-Albrechts-University of Kiel, D-24105, Kiel, Germany

    Bodo Rosenhahn & Gerald Sommer

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  1. Bodo Rosenhahn
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  2. Gerald Sommer
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Correspondence to Bodo Rosenhahn.

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Bodo Rosenhahn gained his diploma degree in Computer Science in 1999. Since then he has been pursuing his Ph.D. at the Cognitive Systems Group, Institute of Computer Science, Christian-Albrechts University Kiel, Germany. He is working on geometric applications of Clifford algebras in computer vision.

Prof. Dr. Gerald Sommer received a diploma degree in physics from the Friedrich-Schiller-Universität Jena, Germany, in 1969, a Ph.D. degree in physics from the same university in 1975, and a habilitation degree in engineering from the Technical University Ilmenau, Germany, in 1988. Since 1993 he is leading the research group Cognitive Systems at the Christian-Albrechts-Universität Kiel, Germany. Currently he is also the scientific coordinator of the VISATEC project.

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Rosenhahn, B., Sommer, G. Pose Estimation in Conformal Geometric Algebra Part II: Real-Time Pose Estimation Using Extended Feature Concepts. J Math Imaging Vis 22, 49–70 (2005). https://doi.org/10.1007/s10851-005-4782-9

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