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Twists – An Operational Representation of Shape

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Computer Algebra and Geometric Algebra with Applications (IWMM 2004, GIAE 2004)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 3519))

Abstract

We give a contribution to the representation problem of free-form curves and surfaces. Our proposal is an operational or kinematic approach based on the Lie group SE(3). While in Euclidean space the modelling of shape as an orbit of a point under the action of SE(3) is limited, we are embedding our problem into the conformal geometric algebra ℝ4,1 of the Euclidean space ℝ3. This embedding results in a number of advantages which makes the proposed method a universal and flexible one with respect to applications. It makes possible the robust and fast estimation of the pose of 3D objects from incomplete and noisy image data. Especially advantagous is the equivalence of the proposed shape model to that of the Fourier representations.

This work has been partially supported (G.S. and C.P.) by EC Grant IST-2001-3422 (VISATEC), by DFG Grant RO 2497/1-1 (B.R.), and by DFG Graduiertenkolleg No. 357 (B.R. and C.P.).

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Author information

Authors and Affiliations

  1. Institut für Informatik und Praktische Mathematik, Christian-Albrechts-Universität zu Kiel, Christian-Albrechts-Platz 4, 24118, Kiel, Germany

    Gerald Sommer & Christian Perwass

  2. Centre for Image Technology and Robotics, University of Auckland, Tamaki Campus, Auckland, New Zealand

    Bodo Rosenhahn

Authors
  1. Gerald Sommer
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  2. Bodo Rosenhahn
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  3. Christian Perwass
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Editor information

Editors and Affiliations

  1. Key Laboratory of Mathematics Mechanization, Academy of Mathematics and Systems Science, CAS, P.O. Box, 100080, Beijing, P.R. China

    Hongbo Li

  2. School of Mathematics, University of Minnesota, 55455, Minneapolis, MN, U.S.A.

    Peter J. Olver

  3. Institute of Computer Science, Christian-Albrecht-University, 24098, Kiel, Germany

    Gerald Sommer

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© 2005 Springer-Verlag Berlin Heidelberg

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Sommer, G., Rosenhahn, B., Perwass, C. (2005). Twists – An Operational Representation of Shape. In: Li, H., Olver, P.J., Sommer, G. (eds) Computer Algebra and Geometric Algebra with Applications. IWMM GIAE 2004 2004. Lecture Notes in Computer Science, vol 3519. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11499251_22

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  • DOI: https://doi.org/10.1007/11499251_22

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-26296-1

  • Online ISBN: 978-3-540-32119-4

  • eBook Packages: Computer ScienceComputer Science (R0)

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