Carola-Bibiane Schönlieb - Böcker

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.

For researchers, exposure to the state of the art of research works leads to an overall view of the entire field so as to guide new research directions and avoid pitfalls in moving the field forward and looking into the next decades of imaging and information services.

This book constitutes the refereed proceedings of the 26th Conference on Medical Image Understanding and Analysis, MIUA 2022, held in Cambridge, UK, in July 2022.

The two-volume set LNCS 15667 and 15668 constitutes the proceedings of the 10th International Conference on Scale Space and Variational Methods in Computer Vision, SSVM 2025, which took place in Dartington, UK, in May 2025. The total of 63 full papers accepted in the proceedings were carefully reviewed and selected from 81 submissions.