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Intrinsic Second-Order Geometric Optimization for Robust Point Set Registration without Correspondence

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Energy Minimization Methods in Computer Vision and Pattern Recognition (EMMCVPR 2009)

Part of the book series: Lecture Notes in Computer Science ((LNIP,volume 5681))

Abstract

Determining Euclidean transformations for the robust registration of noisy unstructured point sets is a key problem of model-based computer vision and numerous industrial applications. Key issues include accuracy of the registration, robustness with respect to outliers and initialization, and computational speed.

In this paper, we consider objective functions for robust point registration without correspondence. We devise a numerical algorithm that fully exploits the intrinsic manifold geometry of the underlying Special Euclidean Group SE(3) in order to efficiently determine a local optimum. This leads to a quadratic convergence rate that compensates the moderately increased computational costs per iteration. Exhaustive numerical experiments demonstrate that our approach exhibits significantly enlarged domains of attraction to the correct registration. Accordingly, our approach outperforms a range of state-of-the-art methods in terms of robustness against initialization while being comparable with respect to registration accuracy and speed.

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Author information

Authors and Affiliations

  1. Image & Pattern Analysis Group (IPA), Heidelberg Collaboratory for Image Processing (HCI), University of Heidelberg, Speyerer Strasse 6, 69115, Heidelberg, Germany

    Dirk Breitenreicher & Christoph Schnörr

Authors
  1. Dirk Breitenreicher
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  2. Christoph Schnörr
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Editor information

Editors and Affiliations

  1. Institut für Informatik III, Rö, Universität Bonn, merstraße 164, 53117, Bonn, Germany

    Daniel Cremers

  2. Computer Science Department, University of Western Ontario, N6A 5A5, London, ON, Canada

    Yuri Boykov

  3. Microsoft Research, J.J. Thomson Avenue, CB3 OFB, Cambridge, United Kingdom

    Andrew Blake

  4. Institut für Informatik III, Universität Bonn, Römerstraße 164, 53117, Bonn, Germany

    Frank R. Schmidt

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© 2009 Springer-Verlag Berlin Heidelberg

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Breitenreicher, D., Schnörr, C. (2009). Intrinsic Second-Order Geometric Optimization for Robust Point Set Registration without Correspondence. In: Cremers, D., Boykov, Y., Blake, A., Schmidt, F.R. (eds) Energy Minimization Methods in Computer Vision and Pattern Recognition. EMMCVPR 2009. Lecture Notes in Computer Science, vol 5681. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-03641-5_21

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  • DOI: https://doi.org/10.1007/978-3-642-03641-5_21

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-03640-8

  • Online ISBN: 978-3-642-03641-5

  • eBook Packages: Computer ScienceComputer Science (R0)

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