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Computing Topology Preservation of RBF Transformations for Landmark-Based Image Registration

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Curves and Surfaces (Curves and Surfaces 2014)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9213))

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Abstract

In image registration, a proper transformation should be topology preserving. Especially for landmark-based image registration, if the displacement of one landmark is larger enough than those of neighbourhood landmarks, topology violation will be occurred. This paper aims to analyse the topology preservation of some Radial Basis Functions (RBFs) which are used to model deformations in image registration. Matérn functions are quite common in the statistic literature (see, e.g. [9, 13]). In this paper, we use them to solve the landmark-based image registration problem. We present the topology preservation properties of RBFs in one landmark and four landmarks model respectively. Numerical results of three kinds of Matérn transformations are compared with results of Gaussian, Wendland’s, and Wu’s functions.

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Acknowledgments

The work of the first author is partially supported by the University of Torino via grant “Approssimazione di dati sparsi e sue applicazioni”. The second author acknowledges financial support from the GNCS–INdAM. The authors also sincerely thank the anonymous referee for helping to significantly improve this paper.

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Authors and Affiliations

  1. Department of Mathematics “G. Peano”, University of Torino, Via Carlo Alberto 10, 10123, Torino, Italy

    Roberto Cavoretto, Alessandra De Rossi & Hanli Qiao

  2. Innsbruck Medical University, Anichstrasse 35, 6020, Innsbruck, Austria

    Bernhard Quatember & Wolfgang Recheis

  3. University of Applied Science, J. Gutenberg Straße 3, 2700, Wiener Neustadt, Austria

    Martin Mayr

Authors
  1. Roberto Cavoretto
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  2. Alessandra De Rossi
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  3. Hanli Qiao
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  4. Bernhard Quatember
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  5. Wolfgang Recheis
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  6. Martin Mayr
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Corresponding author

Correspondence to Alessandra De Rossi .

Editor information

Editors and Affiliations

  1. INRIA, Sophia Antipolis, Sophia Antipolis, France

    Jean-Daniel Boissonnat

  2. École Normale Supérieure, Paris, France

    Albert Cohen

  3. Arts Et Metiers ParisTech Lab de Sciences de l'Information, Paris, France

    Olivier Gibaru

  4. INSA de Rouen, LMI, Saint-Étienne-du-Rouvray, France

    Christian Gout

  5. Department of Mathematics, University of Oslo, Oslo, Norway

    Tom Lyche

  6. Université Joseph Fourier, Grenoble, France

    Marie-Laurence Mazure

  7. Department of Mathematics, Vanderbilt University, Nashville, Tennessee, USA

    Larry L. Schumaker

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Cavoretto, R., De Rossi, A., Qiao, H., Quatember, B., Recheis, W., Mayr, M. (2015). Computing Topology Preservation of RBF Transformations for Landmark-Based Image Registration. In: Boissonnat, JD., et al. Curves and Surfaces. Curves and Surfaces 2014. Lecture Notes in Computer Science(), vol 9213. Springer, Cham. https://doi.org/10.1007/978-3-319-22804-4_8

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  • DOI: https://doi.org/10.1007/978-3-319-22804-4_8

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  • Publisher Name: Springer, Cham

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  • Online ISBN: 978-3-319-22804-4

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