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

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.

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 graduated from the Institute for Mathematics, University of Salzburg (Austria) in 2004, and received her PhD degree from the University of Cambridge (UK) in 2009, where she is a Professor in Applied Mathematics at the Department of Applied Mathematics and Theoretical Physics. There, she is head of the Cambridge Image Analysis group, Director of the Cantab Capital Institute for Mathematics of Information, Co-Director of the EPSRC Centre for Mathematical and Statistical Analysis of Multimodal Clinical Imaging, and since 2011 a fellow of Jesus College Cambridge. Dr. Schönlieb’s research interests focus on variational methods and partial differential equations for image analysis, image processing and inverse imaging problems. Her research has been acknowledged by scientific prizes, among them the LMS Whitehead Prize 2016, 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 IMA Conference on Challenges of Big Data in 2016, the SIAM Annual Meeting in 2017 and the Applied Inverse Problems Conference in 2019.
Xue-Cheng Tai is a Professor at the Department of Mathematics at Hong Kong Baptist University (China) since 2017 and before 2017 a Professor at the Department of Mathematics at Bergen University (Norway). His research interests include Numerical PDEs, optimization techniques, inverse problems and image processing. Dr. Tai has done significant research work his research areas and published over 80 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.

Laurent Younes is a Professor and chair of the Department of Applied Mathematics and Statistics, Johns Hopkins University (USA). He received the Bachelor’s degree from Ecole Normale Superieure (France) in 1984, and the master’s degree and doctorate from University of Paris 11 in 1985 and 1988, respectively. His research interests in Computer Vision and Imaging are wide and include statistical properties of Markov random fields, image analysis, deformation analysis, and shape recognition.