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International Conference on Artificial Intelligence and Soft Computing

ICAISC 2018: Artificial Intelligence and Soft Computing pp 62–72Cite as

Image Completion with Smooth Nonnegative Matrix Factorization

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Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 10842))

Abstract

Nonnegative matrix factorization is an unsupervised learning method for part-based feature extraction and dimensionality reduction of nonnegative data with a variety of models, algorithms, structures, and applications. Smooth nonnegative matrix factorization assumes the estimated latent factors are locally smooth, and the smoothness is enforced by the underlying model or the algorithm. In this study, we extended one of the algorithms for this kind of factorization to an image completion problem. It is the B-splines ADMM-NMF (Nonnegative Matrix Factorization with Alternating Direction Method of Multipliers) that enforces smooth feature vectors by assuming they are represented by a linear combination of smooth basis functions, i.e. B-splines. The numerical experiments performed on several incomplete images show that the proposed method outperforms the other algorithms in terms of the quality of recovered images.

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Notes

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    http://www.plgrid.pl/en.

  2. 2.

    https://www.wcss.pl/en/.

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Acknowledgment

This work was partially supported by the grant 2015/17/B/ST6/01865 funded by National Science Center (NCN) in Poland. Calculations were performed at the Wroclaw Center for Networking and Supercomputing under grant no. 127.

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Authors and Affiliations

  1. Faculty of Electronics, Wroclaw University of Science and Technology, Wybrzeze Wyspianskiego 27, 50-370, Wroclaw, Poland

    Tomasz Sadowski & Rafał Zdunek

Authors
  1. Tomasz Sadowski
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  2. Rafał Zdunek
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Corresponding author

Correspondence to Tomasz Sadowski .

Editor information

Editors and Affiliations

  1. Częstochowa University of Technology, Częstochowa, 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 Science and Technology, Kraków, Poland

    Ryszard Tadeusiewicz

  6. University of Louisville, Louisville, KY, USA

    Jacek M. Zurada

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Sadowski, T., Zdunek, R. (2018). Image Completion with Smooth Nonnegative Matrix Factorization. In: Rutkowski, L., Scherer, R., Korytkowski, M., Pedrycz, W., Tadeusiewicz, R., Zurada, J. (eds) Artificial Intelligence and Soft Computing. ICAISC 2018. Lecture Notes in Computer Science(), vol 10842. Springer, Cham. https://doi.org/10.1007/978-3-319-91262-2_6

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  • DOI: https://doi.org/10.1007/978-3-319-91262-2_6

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  • Online ISBN: 978-3-319-91262-2

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