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Oversampling Errors in Multimodal Medical Imaging Are Due to the Gibbs Effect

Author

Listed:
  • Davide Poggiali

    (Padova Neuroscience Center, University of Padova, 35100 Padua, Italy)

  • Diego Cecchin

    (Padova Neuroscience Center, University of Padova, 35100 Padua, Italy
    Nuclear Medicine Unit, Department of Medicine—DIMED, Padua University Hospital, 35100 Padua, Italy)

  • Cristina Campi

    (Department of Mathematics, University of Genova, 16100 Genoa, Italy)

  • Stefano De Marchi

    (Padova Neuroscience Center, University of Padova, 35100 Padua, Italy
    Department of Mathematics “Tullio Levi-Civita”, University of Padova, 35100 Padova, Italy
    Current address: Department of Mathematics “Tullio Levi-Civita”, Via Trieste, 63, 35131 Padua, Italy.)

Abstract

To analyze multimodal three-dimensional medical images, interpolation is required for resampling which—unavoidably—introduces an interpolation error. In this work we describe the interpolation method used for imaging and neuroimaging and we characterize the Gibbs effect occurring when using such methods. In the experimental section we consider three segmented three-dimensional images resampled with three different neuroimaging software tools for comparing undersampling and oversampling strategies and to identify where the oversampling error lies. The experimental results indicate that undersampling to the lowest image size is advantageous in terms of mean value per segment errors and that the oversampling error is larger where the gradient is steeper, showing a Gibbs effect.

Suggested Citation

  • Davide Poggiali & Diego Cecchin & Cristina Campi & Stefano De Marchi, 2021. "Oversampling Errors in Multimodal Medical Imaging Are Due to the Gibbs Effect," Mathematics, MDPI, vol. 9(12), pages 1-20, June.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:12:p:1348-:d:573040
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    References listed on IDEAS

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    1. De Marchi, S. & Marchetti, F. & Perracchione, E. & Poggiali, D., 2021. "Multivariate approximation at fake nodes," Applied Mathematics and Computation, Elsevier, vol. 391(C).
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