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Mathematical Methods in Image Processing and Computer Vision

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Numerical Simulation in Physics and Engineering

Part of the book series: SEMA SIMAI Springer Series ((SEMA SIMAI,volume 9))

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Abstract

Image processing and computer vision are growing research fields that take advantage of the increasing power or modern computers linked with sophisticated techniques coming from many fields of expertise and in particular from mathematics. We present an introduction to some problems in computer vision and image processing and to some mathematical techniques and concepts that are nowadays routinely used to approach them.

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Notes

  1. 1.

    All derivatives have to be understood in a weak sense throughout the text.

  2. 2.

    Note that the unknown is now named u and hence I might denote the input image from now on.

  3. 3.

    http://structuralsegm.sourceforge.net/

  4. 4.

    The determination of the true 3D motion of objects is known as scene flow and will not be analyzed in these notes. The interested reader can refer to [26] and references therein.

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Acknowledgements

The author is grateful to the organizers and scientific committee of the Jacques-Louis Lions Spanish-French school for the invitation. This research was Partially supported by Spanish MINECO grant MTM 2014-54388. This work is dedicated to the memory of Vicent Caselles.

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Authors and Affiliations

  1. Facultat de Matemàtiques, Departament de Matemàtica Aplicada, Universitat de València, València, Spain

    Antonio Baeza

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  1. Antonio Baeza
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Correspondence to Antonio Baeza .

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Editors and Affiliations

  1. Ingeniería Matemática e Informática, Universidad Pública de Navarra, Pamplona, Spain

    Inmaculada Higueras

  2. Ingeniería Matemática e Informática, Universidad Pública de Navarra, Pamplona, Spain

    Teo Roldán

  3. Ingeniería Matemática e Informática, Universidad Pública de Navarra, Pamplona, Spain

    Juan José Torrens

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Baeza, A. (2016). Mathematical Methods in Image Processing and Computer Vision. In: Higueras, I., Roldán, T., Torrens, J. (eds) Numerical Simulation in Physics and Engineering. SEMA SIMAI Springer Series, vol 9. Springer, Cham. https://doi.org/10.1007/978-3-319-32146-2_3

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