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Riemannian Geometric Statistics In Medical Image Analysis

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Riemannian Geometric Statistics in Medical Image Analysis

Riemannian Geometric Statistics in Medical Image Analysis Book
Author : Xavier Pennec,Stefan Sommer,Tom Fletcher
Publisher : Academic Press
Release : 2019-09-02
ISBN : 0128147261
Language : En, Es, Fr & De

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Book Description :

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

Elastic Shape Analysis of Three Dimensional Objects

Elastic Shape Analysis of Three Dimensional Objects Book
Author : Ian H. Jermyn,Sebastian Kurtek,Hamid Laga,Anuj Srivastava
Publisher : Morgan & Claypool Publishers
Release : 2017-09-15
ISBN : 1681730286
Language : En, Es, Fr & De

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Book Description :

Statistical analysis of shapes of 3D objects is an important problem with a wide range of applications. This analysis is difficult for many reasons, including the fact that objects differ in both geometry and topology. In this manuscript, we narrow the problem by focusing on objects with fixed topology, say objects that are diffeomorphic to unit spheres, and develop tools for analyzing their geometries. The main challenges in this problem are to register points across objects and to perform analysis while being invariant to certain shape-preserving transformations. We develop a comprehensive framework for analyzing shapes of spherical objects, i.e., objects that are embeddings of a unit sphere in R, including tools for: quantifying shape differences, optimally deforming shapes into each other, summarizing shape samples, extracting principal modes of shape variability, and modeling shape variability associated with populations. An important strength of this framework is that it is elastic: it performs alignment, registration, and comparison in a single unified framework, while being invariant to shape-preserving transformations. The approach is essentially Riemannian in the following sense. We specify natural mathematical representations of surfaces of interest, and impose Riemannian metrics that are invariant to the actions of the shape-preserving transformations. In particular, they are invariant to reparameterizations of surfaces. While these metrics are too complicated to allow broad usage in practical applications, we introduce a novel representation, termed square-root normal fields (SRNFs), that transform a particular invariant elastic metric into the standard L2 metric. As a result, one can use standard techniques from functional data analysis for registering, comparing, and summarizing shapes. Specifically, this results in: pairwise registration of surfaces; computation of geodesic paths encoding optimal deformations; computation of Karcher means and covariances under the shape metric; tangent Principal Component Analysis (PCA) and extraction of dominant modes of variability; and finally, modeling of shape variability using wrapped normal densities. These ideas are demonstrated using two case studies: the analysis of surfaces denoting human bodies in terms of shape and pose variability; and the clustering and classification of the shapes of subcortical brain structures for use in medical diagnosis. This book develops these ideas without assuming advanced knowledge in differential geometry and statistics. We summarize some basic tools from differential geometry in the appendices, and introduce additional concepts and terminology as needed in the individual chapters.

Medical Image Computing and Computer Assisted Intervention MICCAI 2006

Medical Image Computing and Computer Assisted Intervention     MICCAI 2006 Book
Author : Rasmus Larsen,Mads Nielsen,Jon Sporring
Publisher : Springer
Release : 2006-09-29
ISBN : 3540447288
Language : En, Es, Fr & De

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Book Description :

The two-volume set LNCS 4190 and LNCS 4191 constitute the refereed proceedings of the 9th International Conference on Medical Image Computing and Computer-Assisted Intervention, MICCAI 2006. The program committee carefully selected 39 revised full papers and 193 revised poster papers for presentation in two volumes. This second volume collects 118 papers related to segmentation, validation and quantitative image analysis, brain image processing, and much more.

Visualization and Processing of Higher Order Descriptors for Multi Valued Data

Visualization and Processing of Higher Order Descriptors for Multi Valued Data Book
Author : Ingrid Hotz,Thomas Schultz
Publisher : Springer
Release : 2015-07-03
ISBN : 3319150901
Language : En, Es, Fr & De

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Book Description :

Modern imaging techniques and computational simulations yield complex multi-valued data that require higher-order mathematical descriptors. This book addresses topics of importance when dealing with such data, including frameworks for image processing, visualization and statistical analysis of higher-order descriptors. It also provides examples of the successful use of higher-order descriptors in specific applications and a glimpse of the next generation of diffusion MRI. To do so, it combines contributions on new developments, current challenges in this area and state-of-the-art surveys. Compared to the increasing importance of higher-order descriptors in a range of applications, tools for analysis and processing are still relatively hard to come by. Even though application areas such as medical imaging, fluid dynamics and structural mechanics are very different in nature they face many shared challenges. This book provides an interdisciplinary perspective on this topic with contributions from key researchers in disciplines ranging from visualization and image processing to applications. It is based on the 5th Dagstuhl seminar on Visualization and Processing of Higher Order Descriptors for Multi-Valued Data. This book will appeal to scientists who are working to develop new analysis methods in the areas of image processing and visualization, as well as those who work with applications that generate higher-order data or could benefit from higher-order models and are searching for novel analytical tools.

New Developments in the Visualization and Processing of Tensor Fields

New Developments in the Visualization and Processing of Tensor Fields Book
Author : David H. Laidlaw,Anna Vilanova
Publisher : Springer Science & Business Media
Release : 2012-09-14
ISBN : 3642273424
Language : En, Es, Fr & De

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Book Description :

Bringing together key researchers in disciplines ranging from visualization and image processing to applications in structural mechanics, fluid dynamics, elastography, and numerical mathematics, the workshop that generated this edited volume was the third in the successful Dagstuhl series. Its aim, reflected in the quality and relevance of the papers presented, was to foster collaboration and fresh lines of inquiry in the analysis and visualization of tensor fields, which offer a concise model for numerous physical phenomena. Despite their utility, there remains a dearth of methods for studying all but the simplest ones, a shortage the workshops aim to address. Documenting the latest progress and open research questions in tensor field analysis, the chapters reflect the excitement and inspiration generated by this latest Dagstuhl workshop, held in July 2009. The topics they address range from applications of the analysis of tensor fields to purer research into their mathematical and analytical properties. They show how cooperation and the sharing of ideas and data between those engaged in pure and applied research can open new vistas in the study of tensor fields.

Graphs in Biomedical Image Analysis Computational Anatomy and Imaging Genetics

Graphs in Biomedical Image Analysis  Computational Anatomy and Imaging Genetics Book
Author : M. Jorge Cardoso,Tal Arbel,Enzo Ferrante,Xavier Pennec,Adrian V. Dalca,Sarah Parisot,Sarang Joshi,Nematollah K. Batmanghelich,Aristeidis Sotiras,Mads Nielsen,Mert R. Sabuncu,Tom Fletcher,Li Shen,Stanley Durrleman,Stefan Sommer
Publisher : Springer
Release : 2017-09-06
ISBN : 331967675X
Language : En, Es, Fr & De

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Book Description :

This book constitutes the refereed joint proceedings of the First International Workshop on Graphs in Biomedical Image Analysis, GRAIL 2017, the 6th International Workshop on Mathematical Foundations of Computational Anatomy, MFCA 2017, and the Third International Workshop on Imaging Genetics, MICGen 2017, held in conjunction with the 20th International Conference on Medical Imaging and Computer-Assisted Intervention, MICCAI 2017, in Québec City, QC, Canada, in September 2017. The 7 full papers presented at GRAIL 2017, the 10 full papers presented at MFCA 2017, and the 5 full papers presented at MICGen 2017 were carefully reviewed and selected. The GRAIL papers cover a wide range of graph based medical image analysis methods and applications, including probabilistic graphical models, neuroimaging using graph representations, machine learning for diagnosis prediction, and shape modeling. The MFCA papers deal with theoretical developments in non-linear image and surface registration in the context of computational anatomy. The MICGen papers cover topics in the field of medical genetics, computational biology and medical imaging.

Medical Imaging

Medical Imaging Book
Author : Anonim
Publisher : Unknown
Release : 2004
ISBN : 0987650XXX
Language : En, Es, Fr & De

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Book Description :

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Mathematical Reviews

Mathematical Reviews Book
Author : Anonim
Publisher : Unknown
Release : 2007
ISBN : 0987650XXX
Language : En, Es, Fr & De

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Book Description :

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Dissertation Abstracts International

Dissertation Abstracts International Book
Author : Anonim
Publisher : Unknown
Release : 2005
ISBN : 0987650XXX
Language : En, Es, Fr & De

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Book Description :

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Medical Image Computing and Computer Assisted Intervention MICCAI 2016

Medical Image Computing and Computer Assisted Intervention     MICCAI 2016 Book
Author : Sebastien Ourselin,Leo Joskowicz,Mert R. Sabuncu,Gozde Unal,William Wells
Publisher : Springer
Release : 2016-10-17
ISBN : 3319467204
Language : En, Es, Fr & De

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Book Description :

The three-volume set LNCS 9900, 9901, and 9902 constitutes the refereed proceedings of the 19th International Conference on Medical Image Computing and Computer-Assisted Intervention, MICCAI 2016, held in Athens, Greece, in October 2016. Based on rigorous peer reviews, the program committee carefully selected 228 revised regular papers from 756 submissions for presentation in three volumes. The papers have been organized in the following topical sections: Part I: brain analysis; brain analysis - connectivity; brain analysis - cortical morphology; Alzheimer disease; surgical guidance and tracking; computer aided interventions; ultrasound image analysis; cancer image analysis; Part II: machine learning and feature selection; deep learning in medical imaging; applications of machine learning; segmentation; cell image analysis; Part III: registration and deformation estimation; shape modeling; cardiac and vascular image analysis; image reconstruction; and MR image analysis.

Statistics and Analysis of Shapes

Statistics and Analysis of Shapes Book
Author : Hamid Krim,Anthony Yezzi
Publisher : Springer Science & Business Media
Release : 2007-12-31
ISBN : 9780817644819
Language : En, Es, Fr & De

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Book Description :

The subject of pattern analysis and recognition pervades many aspects of our daily lives, including user authentication in banking, object retrieval from databases in the consumer sector, and the omnipresent surveillance and security measures around sensitive areas. Shape analysis, a fundamental building block in many approaches to these applications, is also used in statistics, biomedical applications (Magnetic Resonance Imaging), and many other related disciplines. With contributions from some of the leading experts and pioneers in the field, this self-contained, unified volume is the first comprehensive treatment of theory, methods, and algorithms available in a single resource. Developments are discussed from a rapidly increasing number of research papers in diverse fields, including the mathematical and physical sciences, engineering, and medicine.

Information Processing in Medical Imaging

Information Processing in Medical Imaging Book
Author : Anonim
Publisher : Unknown
Release : 1997
ISBN : 0987650XXX
Language : En, Es, Fr & De

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Book Description :

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Proceedings

Proceedings Book
Author : Anonim
Publisher : Unknown
Release : 2005
ISBN : 0987650XXX
Language : En, Es, Fr & De

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A Statistical Theory for Shape Analysis of Curves and Surfaces with Applications in Image Analysis Biometrics Bioinformatics and Medical Diagnostics

A Statistical Theory for Shape Analysis of Curves and Surfaces with Applications in Image Analysis  Biometrics  Bioinformatics and Medical Diagnostics Book
Author : Anonim
Publisher : Unknown
Release : 2010
ISBN : 0987650XXX
Language : En, Es, Fr & De

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Book Description :

Over the five year period, this project has mainly been concerned about developing a theory for statistical analysis of shapes of objects, both two and three-dimensional. Focusing on the boundaries of these objects, our framework is for shape analysis of curves and surfaces. The main achievements were development of tools for: (1) Quantifying Shape Differences: Given any two objects, we can quantify differences between their shapes. (2) Achieve Desired Invariance: Our notion of shape is invariant to certain transformations of curves - rigid motion, scaling and re-parameterization. (3) Compute Summary Statistics: Given a collection of shapes and shape classes we can generate summary statistics - mean, covariance, etc, to characterize a shape class. (4) Stochastic Modeling: We have developed probability models that capture observed variability in shape classes. These models form priors for Bayesian inferences. (5) Statistical Inferences: We have studied statistical evaluations, such as hypothesis testing, likelihood ratios, performance bounds, etc, for shape analysis. The salient components of this differential geometric framework are following. First, we define a space of curves or surfaces by choosing a mathematical representation for these objects and establish a Hilbert submanifold(s) for such representations. Then, we choose a Riemannian metric, usually an elastic metric for measuring distances on such manifolds. We arrive at a shape manifold by imposing remaining invariances in the representation. For these shape spaces, we have developed two numerical techniques for computing geodesic paths. Finally, we define and compute empirical statistics, and define probability models on tangent bundles. The resulting statistical models are then used to characterize objects in images according to shapes, for using in object detection, tracking and recognition. We have demonstrated these tools in different application understanding.

Geometric Methods in Signal and Image Analysis

Geometric Methods in Signal and Image Analysis Book
Author : Hamid Krim,Abdessamad Ben Hamza
Publisher : Cambridge University Press
Release : 2015-06-18
ISBN : 1316351963
Language : En, Es, Fr & De

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Book Description :

This comprehensive guide offers a new approach for developing and implementing robust computational methodologies that uncover the key geometric and topological information from signals and images. With the help of detailed real-world examples and applications, readers will learn how to solve complex signal and image processing problems in fields ranging from remote sensing to medical imaging, bioinformatics, robotics, security, and defence. With an emphasis on intuitive and application-driven arguments, this text covers not only a range of methods in use today, but also introduces promising new developments for the future, bringing the reader up-to-date with the state of the art in signal and image analysis. Covering basic principles as well as advanced concepts and applications, and with examples and homework exercises, this is an invaluable resource for graduate students, researchers, and industry practitioners in a range of fields including signal and image processing, biomedical engineering, and computer graphics.

Recent Applications of Harmonic Analysis to Function Spaces Differential Equations and Data Science

Recent Applications of Harmonic Analysis to Function Spaces  Differential Equations  and Data Science Book
Author : Isaac Pesenson,Quoc Thong Le Gia,Azita Mayeli,Hrushikesh Mhaskar,Ding-Xuan Zhou
Publisher : Birkhäuser
Release : 2017-08-09
ISBN : 3319555561
Language : En, Es, Fr & De

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Book Description :

The second of a two volume set on novel methods in harmonic analysis, this book draws on a number of original research and survey papers from well-known specialists detailing the latest innovations and recently discovered links between various fields. Along with many deep theoretical results, these volumes contain numerous applications to problems in signal processing, medical imaging, geodesy, statistics, and data science. The chapters within cover an impressive range of ideas from both traditional and modern harmonic analysis, such as: the Fourier transform, Shannon sampling, frames, wavelets, functions on Euclidean spaces, analysis on function spaces of Riemannian and sub-Riemannian manifolds, Fourier analysis on manifolds and Lie groups, analysis on combinatorial graphs, sheaves, co-sheaves, and persistent homologies on topological spaces. Volume II is organized around the theme of recent applications of harmonic analysis to function spaces, differential equations, and data science, covering topics such as: The classical Fourier transform, the non-linear Fourier transform (FBI transform), cardinal sampling series and translation invariant linear systems. Recent results concerning harmonic analysis on non-Euclidean spaces such as graphs and partially ordered sets. Applications of harmonic analysis to data science and statistics Boundary-value problems for PDE's including the Runge–Walsh theorem for the oblique derivative problem of physical geodesy.

Journal of the American Statistical Association

Journal of the American Statistical Association Book
Author : Anonim
Publisher : Unknown
Release : 2009
ISBN : 0987650XXX
Language : En, Es, Fr & De

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Estimation of Distance Functions and Geodesics and Its Use for Shape Comparison and Alignment

Estimation of Distance Functions and Geodesics and Its Use for Shape Comparison and Alignment Book
Author : Roberto Facundo Mémoli Techera
Publisher : Unknown
Release : 2005
ISBN : 0987650XXX
Language : En, Es, Fr & De

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Book Description :

Download Estimation of Distance Functions and Geodesics and Its Use for Shape Comparison and Alignment book written by Roberto Facundo Mémoli Techera, available in PDF, EPUB, and Kindle, or read full book online anywhere and anytime. Compatible with any devices.

Shapes and Diffeomorphisms

Shapes and Diffeomorphisms Book
Author : Laurent Younes
Publisher : Springer
Release : 2019-05-17
ISBN : 3662584964
Language : En, Es, Fr & De

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Book Description :

This book covers mathematical foundations and methods for the computerized analysis of shapes, providing the requisite background in geometry and functional analysis and introducing various algorithms and approaches to shape modeling, with a special focus on the interesting connections between shapes and their transformations by diffeomorphisms. A direct application is to computational anatomy, for which techniques such as large‒deformation diffeomorphic metric mapping and metamorphosis, among others, are presented. The appendices detail a series of classical topics (Hilbert spaces, differential equations, Riemannian manifolds, optimal control). The intended audience is applied mathematicians and mathematically inclined engineers interested in the topic of shape analysis and its possible applications in computer vision or medical imaging. The first part can be used for an advanced undergraduate course on differential geometry with a focus on applications while the later chapters are suitable for a graduate course on shape analysis through the action of diffeomorphisms. Several significant additions appear in the 2nd edition, most notably a new chapter on shape datasets, and a discussion of optimal control theory in an infinite-dimensional framework, which is then used to enrich the presentation of diffeomorphic matching.