Handbook of Mathematical Models and Algorithms in Computer Vision and Imaging

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 Schoenlieb 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. Schoenlieb'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.

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 Eulers 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