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The art of image restoration and completion has entered a new phase thanks to digital technology. Indeed, virtual restoration is sometimes the only feasible option available to us, and it has, under the name 'inpainting', grown, from methods developed in the mathematics and computer vision communities, to the creation of tools used routinely by conservators and historians working in the worlds of fine art and cinema. The aim of this book is to provide, for a broad audience, a thorough description of imaging inpainting techniques. The book has a two-layer structure. In one layer, there is a general and more conceptual description of inpainting; in the other, there are boxed descriptions of the essentials of the mathematical and computational details. The idea is that readers can easily skip those boxes without disrupting the narrative. Examples of how the tools can be used are drawn from the Fitzwilliam Museum, Cambridge collections.
Chapter 2 overviews local methods for inpainting, also referred to as geometric methods, starting in 1993. These approaches are typically based on the solution of partial differential equations (PDEs) arising from the minimisation of certain mathematical energies. Geometrical methods have proven to be powerful for the removal of scratches, long tiny lines or small damages such as craquelures in art-related images.
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