Handbook of Mathematical Models and Algorithms in Computer Vision and Imaging: Mathematical Imaging and Vision

ISBN-13: 9783030986605 / Angielski / Twarda / 2023 / 1900 str.

Ke Chen; Carola-Bibiane Schönlieb; Xue-Cheng Tai

Opis

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.

Spis treści

Part 1 --- Convex and non-convex large-scale optimisation in imaging 

Editors: X C Tai / C-B Schonlieb / K Chen 

Total Generalized Variation; Optimal Transport-Based Total Variation; Adaptive graph cuts; nonconvex regularised formulation; non-convex optimization; convex regulariazation; Relaxation of Nonconvex Energies; Directional Regularization; End-to-end learning of CNN; Fast Algorithms for Euler´s Elastica energy minimization; fractional derivatives regularization; Inpainting; Automating stochastic gradient methods; Geodesic models; Nonlinear spectral analysis; Stable schemes

Part 2 --- Model- and data-driven imaging including current mathematical approaches for machine learning in imaging 

Editors: C-B Schonlieb / L Younces / K Chen 

Spectral CT; Spectral Segmentation and Deep Learning; Geometry and Topology of Neural Network Optimization; Sparsely Connected Deep Neural Networks; PDE-based Algorithms for Convolution Neural Network; Denoising Geometric Image Features; Breaking the Curse of Dimensionality by CNN; Variational regularization for black-box models by learning; CNN on graphs; Sampling for MRI; Stochastic geometry; Bayesian analysis and computation; Structured CS optimal sampling; phase retrieval with random sensing; Multi-Frame Super-resolution Reconstruction; Spatial, semi-supervised, and machine learning

 

Part 3 --- Shape spaces and geometric flows 

Editors: L Younces / X C Tai / K Chen 

Geometry and learning in 3D correspondence problems; Shape priors for Single and Multiple Object Segmentation; Spectral approaches to 3D shape correspondences; 3D Shape Inference from Images using Deep Learning; Riemannian Diffeomorphic Mapping; monocular sequences; Efficient regularization of functional map computations; Compact Rank Models and Optimization; graphical models for shapes and hierarchies in segmentation; image registration with uncertainty; Soliton solutions for the elastic metric on spaces of curves; Compensated convexity; interpolating distance between Wasserstein and Fisher-Rao; Nonlinear elasticity and image processing

O autorze

Ke Chen received his B.Sc., M.Sc. and Ph.D. degrees in Applied Mathematics, respectively, from the Dalian University of Technology (China), University of Manchester (UK) and University of Plymouth (UK). Dr. Chen is a computational mathematician specialised in developing novel and fast numerical algorithms for various scientific computing (especially imaging) applications. He has been the Director of a Multidisciplinary Research Centre for Mathematical Imaging Techniques (CMIT) since 2007, and the Director of the EPSRC Liverpool Centre of Mathematics in Healthcare (LCMH) since 2015. He heads a large group of computational imagers, tackling novel analysis of real-life images. His group’s imaging work in variational modelling and algorithmic development is mostly interdisciplinary, strongly motivated by emerging real-life problems and their challenges: image restoration, image inpainting, tomography, image segmentation and registration.

Carola-Bibiane Schönlieb is Professor of Applied Mathematics at the University of Cambridge. There, she is head of the Cambridge Image Analysis group and co-Director of the EPSRC Cambridge Mathematics of Information in Healthcare Hub. Since 2011 she is a fellow of Jesus College Cambridge and since 2016 a fellow of the Alan Turing Institute, London. She also holds the Chair of the Committee for Applications and Interdisciplinary Relations (CAIR) of the EMS. Her current research interests focus on variational methods, partial differential equations and machine learning for image analysis, image processing and inverse imaging problems. She has active interdisciplinary collaborations with clinicians, biologists and physicists on biomedical imaging topics, chemical engineers and plant scientists on image sensing, as well as collaborations with artists and art conservators on digital art restoration.

Her research has been acknowledged by scientific prizes, among them the LMS Whitehead Prize 2016, the Philip Leverhulme Prize in 2017, the Calderon Prize 2019, a Royal Society Wolfson fellowship in 2020, a doctorate honoris causa from the University of Klagenfurt in 2022, and by invitations to give plenary lectures at several renowned applied mathematics conferences, among them the SIAM conference on Imaging Science in 2014, the SIAM conference on Partial Differential Equations in 2015, the SIAM annual meeting in 2017, the Applied Inverse Problems Conference in 2019, the FOCM 2020 and the GAMM 2021.

Carola graduated from the Institute for Mathematics, University of Salzburg (Austria) in 2004. From 2004 to 2005 she held a teaching position in Salzburg. She received her PhD degree from the University of Cambridge (UK) in 2009. After one year of postdoctoral activity at the University of Göttingen (Germany), she became a Lecturer at Cambridge in 2010, promoted to Reader in 2015 and promoted to Professor in 2018.

Prof. Xue-Cheng Tai is a Chief Research Scientist and Executive Program Director at Hong Kong Center for Cerebro-cardiovascular Health Engineering (COCHE), Hong Kong Science Park. He was a Professor and Head at the Department of Mathematics at Hong Kong Baptist University (China) since 2017.  Before 2017, hr served as Professor at the Department of Mathematics at Bergen University (Norway). His research interests include Numerical PDEs, optimization techniques, inverse problems and image processing. He has done significant research work his research areas and published over 250 top quality international conference and journal papers. He is the winner of the 8th Feng Kang Prize for scientific computing. He served as organizing and program committee members for a number of international conferences and has been often invited for international conferences. He has served as referee and reviewers for many premier conferences and journals. 

Prof. Laurent Younes is a professor in the Department Applied Mathematics and Statistics, Johns Hopkins University (USA), that he joined in 2003, after ten years as a researcher for the CNRS in France. He is a former student of the Ecole Normale Supérieure (Paris) and of the University of Paris 11 from which he received his Ph.D. in 1988. His work includes contributions to applied probability, statistics, graphical models, shape analysis and computational medicine. He is a fellow of the IMS and of the AMS.