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Partial Differential Equation Methods for Image Inpainting
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  • Cited by 12
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    This book has been cited by the following publications. This list is generated based on data provided by CrossRef.

    Barbu, Tudor 2019. Novel Diffusion-Based Models for Image Restoration and Interpolation. p. 83.

    Karos, Lena Bheed, Pinak Peter, Pascal and Weickert, Joachim 2018. Advanced Concepts for Intelligent Vision Systems. Vol. 11182, Issue. , p. 547.

    Calatroni, Luca d’Autume, Marie Hocking, Rob Panayotova, Stella Parisotto, Simone Ricciardi, Paola and Schönlieb, Carola-Bibiane 2018. Unveiling the invisible: mathematical methods for restoring and interpreting illuminated manuscripts. Heritage Science, Vol. 6, Issue. 1,

    Hoeltgen, Laurent Peter, Pascal and Breuß, Michael 2018. Clustering-based quantisation for PDE-based image compression. Signal, Image and Video Processing, Vol. 12, Issue. 3, p. 411.

    Idelson, Antonio Iaccarino and Severini, Leonardo 2018. The Encyclopedia of Archaeological Sciences. p. 1.

    Calatroni, L. Estatico, C. Garibaldi, N. and Parisotto, S. 2017. Alternating Direction Implicit (ADI) schemes for a PDE-based image osmosis model. Journal of Physics: Conference Series, Vol. 904, Issue. , p. 012014.

    Barbu, Tudor 2017. Hybrid image interpolation technique based on nonlinear second and fourth-order diffusions. p. 1.

    Adam, Robin Dirk Peter, Pascal and Weickert, Joachim 2017. Scale Space and Variational Methods in Computer Vision. Vol. 10302, Issue. , p. 121.

    Barbu, Tudor 2017. Structural image interpolation using a nonlinear second-order hyperbolic PDE-based model. p. 5.

    Gonzalez-Hidalgo, Manuel Massanet, Sebastia Mir, Arnau and Ruiz-Aguilera, Daniel 2017. An iterative algorithm for image inpainting using aggregation functions. p. 1.

    Barbu, Tudor 2017. Nonlinear anisotropic diffusion-based structural inpainting framework. p. 207.

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Book description

This book is concerned with digital image processing techniques that use partial differential equations (PDEs) for the task of image 'inpainting', an artistic term for virtual image restoration or interpolation, whereby missing or occluded parts in images are completed based on information provided by intact parts. Computer graphic designers, artists and photographers have long used manual inpainting to restore damaged paintings or manipulate photographs. Today, mathematicians apply powerful methods based on PDEs to automate this task. This book introduces the mathematical concept of PDEs for virtual image restoration. It gives the full picture, from the first modelling steps originating in Gestalt theory and arts restoration to the analysis of resulting PDE models, numerical realisation and real-world application. This broad approach also gives insight into functional analysis, variational calculus, optimisation and numerical analysis and will appeal to researchers and graduate students in mathematics with an interest in image processing and mathematical analysis.

Reviews

'Since the late 1990s, there has been a substantial amount of academic works on the application of partial differential equations (PDEs) to the restoration of missing parts in images, which is usually referred to as the 'inpainting problem'. This book provides a very comprehensive, clear, and well-written account of the use of PDEs for inpainting, and this is no minor feat, given the sizeable literature on the subject and the mathematical complexity of many of the techniques described.'

Marcelo Bertalmío - Universitat Pompeu Fabra

'Image inpainting is a new mathematical and technological problem with manifold applications in science and entertainment. In the past twenty years, it has challenged mathematicians and computer scientists alike. They have deployed a treasure of imagination and mathematical skills to solve it. Incorporating striking experiments, reproducible algorithms, and a simple and complete mathematical account, this book is a must-read on the subject.'

Jean-Michel Morel - CMLA, Ecole Normale Supérieure de Cachan

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