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Learning Bezier-Durrmeyer Type Descriptors for Classifying Curves – Preliminary Studies

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Artificial Intelligence and Soft Computing (ICAISC 2023)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 14125))

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Abstract

We aim to propose a new approach for generating descriptors for functional data that are represented by curves that may not be functions but rather parametrically described curves in 2D, 3D, etc. The idea of generating these descriptors is based on the Bezier curves, but instead of using classical control points, we propose to generalize the Durrmeyer approach for parametrically defined vector curves. The Durrmeyer-type descriptors are then estimated from noisy samples of the underlying curve and serve as input vectors to a selected classifier that is learned to recognize from which class of curves noisy observations come.

The Bezier curves are not rapidly convergent. However, our aim is not to reconstruct functions but to recognize them, maintaining the shape-preserving and variation-diminishing properties of these curves that increase the classification accuracy in the presence of noise without invoking pre-filtering procedures. For more complicated curves, one can directly apply our approach to their parts in a similar way as polynomial splines are used.

The proposed algorithm for learning descriptors of the Bezier-Durrmeyer type and training classifiers on them was tested on synthetic, but interesting per se, data from two families of the Lissajous curves observed with high amplitude noise.

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Author information

Authors and Affiliations

  1. Department of Computer Science, Concordia University, 1455 De Maisonneuve West, Montreal, QC, H3G 1M8, Canada

    Adam Krzyżak

  2. Department of Electrical Engineering, Westpomeranian University of Technology (WUT), Szczecin, Poland

    Adam Krzyżak

  3. Faculty of Information and Comunication Technology, Wroclaw University of Science and Technology, Wrocław, Poland

    Wojciech Rafajłowicz & Ewaryst Rafajłowicz

Authors
  1. Adam Krzyżak
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  2. Wojciech Rafajłowicz
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  3. Ewaryst Rafajłowicz
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Corresponding author

Correspondence to Ewaryst Rafajłowicz .

Editor information

Editors and Affiliations

  1. Systems Research Institute of the Polish Academy of Sciences, Warsaw, Poland

    Leszek Rutkowski

  2. Częstochowa University of Technology, Częstochowa, Poland

    Rafał Scherer

  3. Częstochowa University of Technology, Częstochowa, Poland

    Marcin Korytkowski

  4. University of Alberta, Edmonton, AB, Canada

    Witold Pedrycz

  5. AGH University of Krakow, Kraków, Poland

    Ryszard Tadeusiewicz

  6. University of Louisville, Louisville, KY, USA

    Jacek M. Zurada

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Krzyżak, A., Rafajłowicz, W., Rafajłowicz, E. (2023). Learning Bezier-Durrmeyer Type Descriptors for Classifying Curves – Preliminary Studies. In: Rutkowski, L., Scherer, R., Korytkowski, M., Pedrycz, W., Tadeusiewicz, R., Zurada, J.M. (eds) Artificial Intelligence and Soft Computing. ICAISC 2023. Lecture Notes in Computer Science(), vol 14125. Springer, Cham. https://doi.org/10.1007/978-3-031-42505-9_45

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  • DOI: https://doi.org/10.1007/978-3-031-42505-9_45

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-42504-2

  • Online ISBN: 978-3-031-42505-9

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