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Image Reconstruction by the Patch Based Inpainting

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Information Processing and Management of Uncertainty in Knowledge-Based Systems (IPMU 2016)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 610))

Abstract

The paper is focused on demonstration of image inpainting technique using the F-transform theory. Side by side with many algorithms for the image reconstruction we developed a new method of patch-based filling of an unknown (damaged) image area. The unknown area is proposed to be recursively filled by those known patches that have non-empty overlaps with the unknown area and are the closest ones among others from a database. We propose to use the closeness measure on the basis of the F\(^1\)-transform.

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Notes

  1. 1.

    For the sake of simplicity, we consider this notion for a one-dimensional universe.

  2. 2.

    \(L_2(A_k)\) is a Hilbert space of square-integrable functions \(f:[x_{k-1},x_{k+1}] \rightarrow \mathbb {R}\), whose weighted inner product \(\langle f,g\rangle _{k}\) is given by

    $$\begin{aligned} \langle f,g\rangle _{k} = \int ^{x_{k+1}}_{x_{k-1}}f(x)g(x) A_k(x)dx, \end{aligned}$$

    where the weight function is equal to \(A_k\).

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Acknowledgment

This work was supported by the project LQ1602 IT4Innovations excellence in science.

Author information

Authors and Affiliations

  1. Institute for Research and Applications of Fuzzy Modeling, University of Ostrava, Ostrava, Czech Republic

    Pavel Vlašánek & Irina Perfilieva

Authors
  1. Pavel Vlašánek
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  2. Irina Perfilieva
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Corresponding author

Correspondence to Pavel Vlašánek .

Editor information

Editors and Affiliations

  1. INESC-ID,Instituto Superior Técnico, Universidade de Lisboa, Lisboa, Portugal

    Joao Paulo Carvalho

  2. LIP 6, Université Pierre et Marie Curie, Paris, France

    Marie-Jeanne Lesot

  3. School of Industrial Engineering, Eindhoven University of Technology, Eindhoven, The Netherlands

    Uzay Kaymak

  4. IDMEC,Instituto Superior Técnico, Universidade de Lisboa, Lisboa, Portugal

    Susana Vieira

  5. LIP6, Université Pierre et Marie Curie, CNRS, Paris, France

    Bernadette Bouchon-Meunier

  6. Machine Intelligence Institute, Iona College, New Rochelle, New York, USA

    Ronald R. Yager

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© 2016 Springer International Publishing Switzerland

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Vlašánek, P., Perfilieva, I. (2016). Image Reconstruction by the Patch Based Inpainting. In: Carvalho, J., Lesot, MJ., Kaymak, U., Vieira, S., Bouchon-Meunier, B., Yager, R. (eds) Information Processing and Management of Uncertainty in Knowledge-Based Systems. IPMU 2016. Communications in Computer and Information Science, vol 610. Springer, Cham. https://doi.org/10.1007/978-3-319-40596-4_49

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  • DOI: https://doi.org/10.1007/978-3-319-40596-4_49

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-40595-7

  • Online ISBN: 978-3-319-40596-4

  • eBook Packages: Computer ScienceComputer Science (R0)

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