Partial Differential Equation Methods for Image Inpainting
Partial Differential Equation Methods for Image Inpainting focuses on 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 modeling steps originating in Gestalt theory and arts restoration, to the analysis of resulting PDE models, numerical realization, and real-world application. This broad approach also provides insight into functional analysis, variational calculus, optimization, and numerical analysis. The content of this book will appeal to researchers and graduate students in mathematics with an interest in image processing and mathematical analysis.
A MATLAB implementation is included in the appendix. In addition, a supplemental set of MATLAB code files are available for download.
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