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Topology analysis of global and local RBF transformations for image registration

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  • Cavoretto, Roberto
  • De Rossi, Alessandra
  • Qiao, Hanli

Abstract

For elastic registration, topology preservation is a necessary condition to be satisfied, especially for landmark-based image registration. In this paper, we focus on the topology preservation properties of two different families of radial basis functions (RBFs), known as Gneiting and Matérn functions. Firstly, we consider a small number of landmarks, dealing with the cases of one, two and four landmark matching; in all these situations we analyze topology preservation and compare numerical results with those obtained by Wendland functions. Secondly, we discuss the registration properties of these two families of functions, when we have a larger number of landmarks. Finally, we analyze the behavior of Gneiting and Matérn functions, considering some test examples known in the literature and a real application.

Suggested Citation

  • Cavoretto, Roberto & De Rossi, Alessandra & Qiao, Hanli, 2018. "Topology analysis of global and local RBF transformations for image registration," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 147(C), pages 52-72.
    • Handle: RePEc:eee:matcom:v:147:y:2018:i:c:p:52-72
    DOI: 10.1016/j.matcom.2017.10.010
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    References listed on IDEAS

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    1. Gneiting, Tilmann & Kleiber, William & Schlather, Martin, 2010. "Matérn Cross-Covariance Functions for Multivariate Random Fields," Journal of the American Statistical Association, American Statistical Association, vol. 105(491), pages 1167-1177.
    2. Allasia, Giampietro & Cavoretto, Roberto & De Rossi, Alessandra, 2014. "Local interpolation schemes for landmark-based image registration: A comparison," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 106(C), pages 1-25.
    3. Gneiting, Tilmann, 2002. "Compactly Supported Correlation Functions," Journal of Multivariate Analysis, Elsevier, vol. 83(2), pages 493-508, November.
    4. Quatember, Bernhard & Mayr, Martin & Recheis, Wolfgang & Demertzis, Stefanos & Allasia, Giampietro & De Rossi, Alessandra & Cavoretto, Roberto & Venturino, Ezio, 2010. "Geometric modeling and motion analysis of the epicardial surface of the heart," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 81(3), pages 608-622.
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