Riemannian Geometric Statistics In Medical Image Analysis

Over the past 15 years, there has been a growing need in the medical image computing community for principled methods to process nonlinear geometric data. Riemannian geometry has emerged as one of the most powerful mathematical and computational frameworks for analyzing such data. Riemannian Geometric Statistics in Medical Image Analysis is a complete reference on statistics on Riemannian manifolds and more general nonlinear spaces with applications in medical image analysis. It provides an introduction to the core methodology followed by a presentation of state-of-the-art methods. Beyond medical image computing, the methods described in this book may also apply to other domains such as signal processing, computer vision, geometric deep learning, and other domains where statistics on geometric features appear. As such, the presented core methodology takes its place in the field of geometric statistics, the statistical analysis of data being elements of nonlinear geometric spaces. The foundational material and the advanced techniques presented in the later parts of the book can be useful in domains outside medical imaging and present important applications of geometric statistics methodology Content includes: The foundations of Riemannian geometric methods for statistics on manifolds with emphasis on concepts rather than on proofs Applications of statistics on manifolds and shape spaces in medical image computing Diffeomorphic deformations and their applications As the methods described apply to domains such as signal processing (radar signal processing and brain computer interaction), computer vision (object and face recognition), and other domains where statistics of geometric features appear, this book is suitable for researchers and graduate students in medical imaging, engineering and computer science. A complete reference covering both the foundations and state-of-the-art methods Edited and authored by leading researchers in the field Contains theory, examples, applications, and algorithms Gives an overview of current research challenges and future applications

Over the past 15 years, there has been a growing need in the medical image computing community for principled methods to process nonlinear geometric data. Riemannian geometry has emerged as one of the most powerful mathematical and computational frameworks for analyzing such data. Riemannian Geometric Statistics in Medical Image Analysis is a complete reference on statistics on Riemannian manifolds and more general nonlinear spaces with applications in medical image analysis. It provides an introduction to the core methodology followed by a presentation of state-of-the-art methods. Content includes: - The foundations of Riemannian geometric methods for statistics on manifolds with emphasis on concepts rather than on proofs - Applications of statistics on manifolds and shape spaces in medical image computing - Diffeomorphic deformations and their applications As the methods described apply to domains such as signal processing (radar signal processing and brain computer interaction), computer vision (object and face recognition), and other domains where statistics of geometric features appear, this book is suitable for researchers and graduate students in medical imaging, engineering and computer science. - A complete reference covering both the foundations and state-of-the-art methods - Edited and authored by leading researchers in the field - Contains theory, examples, applications, and algorithms - Gives an overview of current research challenges and future applications

Medical Image Analysis presents practical knowledge on medical image computing and analysis as written by top educators and experts. This text is a modern, practical, self-contained reference that conveys a mix of fundamental methodological concepts within different medical domains. Sections cover core representations and properties of digital images and image enhancement techniques, advanced image computing methods (including segmentation, registration, motion and shape analysis), machine learning, how medical image computing (MIC) is used in clinical and medical research, and how to identify alternative strategies and employ software tools to solve typical problems in MIC. Provides an authoritative description of key concepts and methods Includes tutorial-based sections that clearly explain principles and their application to different medical domains Presents a representative selection of topics to match a modern and relevant approach to medical image computing

Deep Learning for Medical Image Analysis, Second Edition is a great learning resource for academic and industry researchers and graduate students taking courses on machine learning and deep learning for computer vision and medical image computing and analysis. Deep learning provides exciting solutions for medical image analysis problems and is a key method for future applications. This book gives a clear understanding of the principles and methods of neural network and deep learning concepts, showing how the algorithms that integrate deep learning as a core component are applied to medical image detection, segmentation, registration, and computer-aided analysis. · Covers common research problems in medical image analysis and their challenges · Describes the latest deep learning methods and the theories behind approaches for medical image analysis · Teaches how algorithms are applied to a broad range of application areas including cardiac, neural and functional, colonoscopy, OCTA applications and model assessment · Includes a Foreword written by Nicholas Ayache

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 offers readers fresh insights on applying Extended Reality to Digital Anatomy, a novel emerging discipline. Indeed, the way professors teach anatomy in classrooms is changing rapidly as novel technology-based approaches become ever more accessible. Recent studies show that Virtual (VR), Augmented (AR), and Mixed-Reality (MR) can improve both retention and learning outcomes. Readers will find relevant tutorials about three-dimensional reconstruction techniques to perform virtual dissections. Several chapters serve as practical manuals for students and trainers in anatomy to refresh or develop their Digital Anatomy skills. We developed this book as a support tool for collaborative efforts around Digital Anatomy, especially in distance learning, international and interdisciplinary contexts. We aim to leverage source material in this book to support new Digital Anatomy courses and syllabi in interdepartmental, interdisciplinary collaborations. Digital Anatomy – Applications of Virtual, Mixed and Augmented Reality provides a valuable tool to foster cross-disciplinary dialogues between anatomists, surgeons, radiologists, clinicians, computer scientists, course designers, and industry practitioners. It is the result of a multidisciplinary exercise and will undoubtedly catalyze new specialties and collaborative Master and Doctoral level courses world-wide. In this perspective, the UNESCO Chair in digital anatomy was created at the Paris Descartes University in 2015 (www.anatomieunesco.org). It aims to federate the education of anatomy around university partners from all over the world, wishing to use these new 3D modeling techniques of the human body.

Geometry and Statistics, Volume 46 in the Handbook of Statistics series, highlights new advances in the field, with this new volume presenting interesting chapters written by an international board of authors. Provides the authority and expertise of leading contributors from an international board of authors Presents the latest release in the Handbook of Statistics series Updated release includes the latest information on Geometry and Statistics

This book constitutes the proceedings of the International Workshop on Shape in Medical Imaging, ShapeMI 2020, which was held in conjunction with the 23rd International Conference on Medical Image Computing and Computer Assistend Intervention, MICCAI 2020, in October 2020. The conference was planned to take place in Lima, Peru, but changed to a virtual format due to the COVID-19 pandemic. The 12 full papers included in this volume were carefully reviewed and selected from 18 submissions. They were organized in topical sections named: methods; learning; and applications.

Deep Network Design for Medical Image Computing: Principles and Applications covers a range of MIC tasks and discusses design principles of these tasks for deep learning approaches in medicine. These include skin disease classification, vertebrae identification and localization, cardiac ultrasound image segmentation, 2D/3D medical image registration for intervention, metal artifact reduction, sparse-view artifact reduction, etc. For each topic, the book provides a deep learning-based solution that takes into account the medical or biological aspect of the problem and how the solution addresses a variety of important questions surrounding architecture, the design of deep learning techniques, when to introduce adversarial learning, and more. This book will help graduate students and researchers develop a better understanding of the deep learning design principles for MIC and to apply them to their medical problems. Explains design principles of deep learning techniques for MIC Contains cutting-edge deep learning research on MIC Covers a broad range of MIC tasks, including the classification, detection, segmentation, registration, reconstruction and synthesis of medical images

Object Oriented Data Analysis is a framework that facilitates inter-disciplinary research through new terminology for discussing the often many possible approaches to the analysis of complex data. Such data are naturally arising in a wide variety of areas. This book aims to provide ways of thinking that enable the making of sensible choices. The main points are illustrated with many real data examples, based on the authors' personal experiences, which have motivated the invention of a wide array of analytic methods. While the mathematics go far beyond the usual in statistics (including differential geometry and even topology), the book is aimed at accessibility by graduate students. There is deliberate focus on ideas over mathematical formulas. J. S. Marron is the Amos Hawley Distinguished Professor of Statistics, Professor of Biostatistics, Adjunct Professor of Computer Science, Faculty Member of the Bioinformatics and Computational Biology Curriculum and Research Member of the Lineberger Cancer Center and the Computational Medicine Program, at the University of North Carolina, Chapel Hill. Ian L. Dryden is a Professor in the Department of Mathematics and Statistics at Florida International University in Miami, has served as Head of School of Mathematical Sciences at the University of Nottingham, and is joint author of the acclaimed book Statistical Shape Analysis.