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Comparison and Evaluation of First Derivatives Estimation

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Computer Vision and Graphics (ICCVG 2016)

Part of the book series: Lecture Notes in Computer Science ((LNIP,volume 9972))

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Abstract

Computing derivatives from observed integral data is known as an ill-posed inverse problem. The ill-posed qualifier refers to the noise amplification that can occur in the numerical solution if appropriate measures are not taken (small errors for measurement values on specified points may induce large errors in the derivatives). For example, the accurate computation of the derivatives is often hampered in medical images by the presence of noise and a limited resolution, affecting the accuracy of segmentation methods. In our case, we want to obtain an upper airways segmentation, so it is necessary to compute the first derivatives as accurately as possible, in order to use gradient-based segmentation techniques. For this reason, the aim of this paper is to present a comparative analysis of several methods (finite differences, interpolation, operators and regularization), that have been developed for numerical differentiation. Numerical results are presented for artificial and real data sets.

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Notes

  1. 1.

    Insight Segmentation and Registration Toolkit, http://www.itk.org/.

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Authors and Affiliations

  1. Pontificia Universidad Javeriana, Bogotá, DC, Colombia

    César Bustacara-Medina & Leonardo Flórez-Valencia

Authors
  1. César Bustacara-Medina
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  2. Leonardo Flórez-Valencia
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Correspondence to César Bustacara-Medina .

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Editors and Affiliations

  1. Faculty of Applied Informatics and Math, Warsaw University of Life Sciences , Warsaw, Poland

    Leszek J. Chmielewski

  2. Computer Sci and Software Engineering, University of Western Australia , Perth, Australia

    Amitava Datta

  3. Faculty of Applied Informatics and Math, Warsaw University of Life Sciences SGGW , Warsaw, Poland

    Ryszard Kozera

  4. Institute of Computer Science, Silesian University of Technology , Gliwice, Poland

    Konrad Wojciechowski

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Bustacara-Medina, C., Flórez-Valencia, L. (2016). Comparison and Evaluation of First Derivatives Estimation. In: Chmielewski, L., Datta, A., Kozera, R., Wojciechowski, K. (eds) Computer Vision and Graphics. ICCVG 2016. Lecture Notes in Computer Science(), vol 9972. Springer, Cham. https://doi.org/10.1007/978-3-319-46418-3_11

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  • DOI: https://doi.org/10.1007/978-3-319-46418-3_11

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-46417-6

  • Online ISBN: 978-3-319-46418-3

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