Carola-Bibiane Schönlieb – författare

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.

This handbook gathers together the state of the art on mathematical models and algorithms for imaging and vision. Its emphasis lies on rigorous mathematical methods, which represent the optimal solutions to a class of imaging and vision problems, and on effective algorithms, which are necessary for the methods to be translated to practical use in various applications. Viewing discrete images as data sampled from functional surfaces enables the use of advanced tools from calculus, functions and calculus of variations, and nonlinear optimization, and provides the basis of high-resolution imaging through geometry and variational models. Besides, optimization naturally connects traditional model-driven approaches to the emerging data-driven approaches of machine and deep learning.  No other framework can provide comparable accuracy and precision to imaging and vision.Written by leading researchers in imaging and vision, the chapters in this handbook all start with gentle introductions, which make this work accessible to graduate students. For newcomers to the field, the book provides a comprehensive and fast-track introduction to the content, to save time and get on with tackling new and emerging challenges. 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 work can greatly benefit graduate students, researchers, and practitioners in imaging and vision; applied mathematicians; medical imagers; engineers; and computer scientists.

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 65 full papers presented were carefully reviewed and selected from 95 submissions. They were organized according to following topical sections: biomarker detection; image registration, and reconstruction; image segmentation; generative models, biomedical simulation and modelling; classification; image enhancement, quality assessment, and data privacy; radiomics, predictive models, and quantitative imaging.Chapter “FCN-Transformer Feature Fusion for Polyp Segmentation” is available open access under a Creative Commons Attribution 4.0 International License via link.springer.com.

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. They were organized in topical sections as follows: Part I: Inverse Problems in Imaging; machine and deep learning in imaging; Part II: Optimization for imaging: theory and methods; scale space, PDES, flow, motion and registration.