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Graphs in Biomedical Image Analysis, Computational Anatomy and Imaging Genetics

Author : M. Jorge Cardoso

Publisher : Springer

Page : 262 pages

File Size : 36,56 MB

Release : 2017-09-06

Category : Computers

ISBN : 331967675X

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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.



Riemannian Geometric Statistics in Medical Image Analysis

Author : Xavier Pennec

Publisher : Academic Press

Page : 636 pages

File Size : 17,11 MB

Release : 2019-09-02

Category : Computers

ISBN : 0128147261

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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



Handbook of Mathematical Models and Algorithms in Computer Vision and Imaging

Author : Ke Chen

Publisher : Springer Nature

Page : 1981 pages

File Size : 44,49 MB

Release : 2023-02-24

Category : Mathematics

ISBN : 3030986616

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Book Description

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.



Mathematics Of Shapes And Applications

Author : Sergey Kushnarev

Publisher : World Scientific

Page : 220 pages

File Size : 47,55 MB

Release : 2019-11-20

Category : Mathematics

ISBN : 9811200149

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Book Description

Understanding how a single shape can incur a complex range of transformations, while defining the same perceptually obvious figure, entails a rich and challenging collection of problems, at the interface between applied mathematics, statistics and computer science. The program on Mathematics of Shapes and Applications, was held at the Institute for Mathematical Sciences at the National University of Singapore in 2016. It provided discussions on theoretical developments and numerous applications in computer vision, object recognition and medical imaging.The analysis of shapes is an example of a mathematical problem directly connected with applications while offering deep open challenges to theoretical mathematicians. It has grown, over the past decades, into an interdisciplinary area in which researchers studying infinite-dimensional Riemannian manifolds (global analysis) interact with applied mathematicians, statisticians, computer scientists and biomedical engineers on a variety of problems involving shapes.The volume illustrates this wealth of subjects by providing new contributions on the metric structure of diffeomorphism groups and shape spaces, recent developments on deterministic and stochastic models of shape evolution, new computational methods manipulating shapes, and new statistical tools to analyze shape datasets. In addition to these contributions, applications of shape analysis to medical imaging and computational anatomy are discussed, leading, in particular, to improved understanding of the impact of cognitive diseases on the geometry of the brain.







Handbook of Variational Methods for Nonlinear Geometric Data

Author : Philipp Grohs

Publisher : Springer Nature

Page : 703 pages

File Size : 32,1 MB

Release : 2020-04-03

Category : Mathematics

ISBN : 3030313514

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Book Description

This book covers different, current research directions in the context of variational methods for non-linear geometric data. Each chapter is authored by leading experts in the respective discipline and provides an introduction, an overview and a description of the current state of the art. Non-linear geometric data arises in various applications in science and engineering. Examples of nonlinear data spaces are diverse and include, for instance, nonlinear spaces of matrices, spaces of curves, shapes as well as manifolds of probability measures. Applications can be found in biology, medicine, product engineering, geography and computer vision for instance. Variational methods on the other hand have evolved to being amongst the most powerful tools for applied mathematics. They involve techniques from various branches of mathematics such as statistics, modeling, optimization, numerical mathematics and analysis. The vast majority of research on variational methods, however, is focused on data in linear spaces. Variational methods for non-linear data is currently an emerging research topic. As a result, and since such methods involve various branches of mathematics, there is a plethora of different, recent approaches dealing with different aspects of variational methods for nonlinear geometric data. Research results are rather scattered and appear in journals of different mathematical communities. The main purpose of the book is to account for that by providing, for the first time, a comprehensive collection of different research directions and existing approaches in this context. It is organized in a way that leading researchers from the different fields provide an introductory overview of recent research directions in their respective discipline. As such, the book is a unique reference work for both newcomers in the field of variational methods for non-linear geometric data, as well as for established experts that aim at to exploit new research directions or collaborations. Chapter 9 of this book is available open access under a CC BY 4.0 license at link.springer.com.



Automatic Localization of Spatially Correlated Key Points in Medical Images

Author : Alexander Oliver Mader

Publisher : BoD – Books on Demand

Page : 252 pages

File Size : 48,86 MB

Release : 2021-04-15

Category : Medical

ISBN : 3753480061

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Book Description

The task of object localization in medical images is a corner stone of automatic image processing and a prerequisite for other medical imaging tasks. In this thesis, we present a general framework for the automatic detection and localization of spatially correlated key points in medical images based on a conditional random field (CRF). The problem of selecting suitable potential functions (knowledge sources) and defining a reasonable graph topology w.r.t. the dataset is automated by our proposed data-driven CRF optimization. We show how our fairly simple setup can be applied to different medical datasets involving different image dimensionalities (i.e., 2D and 3D), image modalities (i.e., X-ray, CT, MRI) and target objects ranging from 2 to 102 distinct key points by automatically adapting the CRF to the dataset. While the used general "default" configuration represents an easy to transfer setup, it already outperforms other state-of-the-art methods on three out of four datasets. By slightly gearing the proposed approach to the fourth dataset, we further illustrate that the approach is capable of reaching state-of-the-art performance of highly sophisticated and data-specific deep-learning-based approaches. Additionally, we suggest and evaluate solutions for common problems of graph-based approaches such as the reduced search space and thus the potential exclusion of the correct solution, better handling of spatial outliers using latent variables and the incorporation of invariant higher order potential functions. Each extension is evaluated in detail and the whole method is additionally compared to a rivaling convolutional-neural-network-based approach on a hard problem (i.e., the localization of many locally similar repetitive target key points) in terms of exploiting the spatial correlation. Finally, we illustrate how follow-up tasks, segmentation in this case, may benefit from a correct localization by reaching state-of-the-art performance using off-the-shelve methods in combination with our proposed method.



Topological Data Analysis

Author : Nils A. Baas

Publisher : Springer Nature

Page : 522 pages

File Size : 26,73 MB

Release : 2020-06-25

Category : Mathematics

ISBN : 3030434087

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Book Description

This book gathers the proceedings of the 2018 Abel Symposium, which was held in Geiranger, Norway, on June 4-8, 2018. The symposium offered an overview of the emerging field of "Topological Data Analysis". This volume presents papers on various research directions, notably including applications in neuroscience, materials science, cancer biology, and immune response. Providing an essential snapshot of the status quo, it represents a valuable asset for practitioners and those considering entering the field.



Network Algorithms, Data Mining, and Applications

Author : Ilya Bychkov

Publisher : Springer Nature

Page : 251 pages

File Size : 49,17 MB

Release : 2020-02-22

Category : Mathematics

ISBN : 3030371573

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Book Description

This proceedings presents the result of the 8th International Conference in Network Analysis, held at the Higher School of Economics, Moscow, in May 2018. The conference brought together scientists, engineers, and researchers from academia, industry, and government. Contributions in this book focus on the development of network algorithms for data mining and its applications. Researchers and students in mathematics, economics, statistics, computer science, and engineering find this collection a valuable resource filled with the latest research in network analysis. Computational aspects and applications of large-scale networks in market models, neural networks, social networks, power transmission grids, maximum clique problem, telecommunication networks, and complexity graphs are included with new tools for efficient network analysis of large-scale networks. Machine learning techniques in network settings including community detection, clustering, and biclustering algorithms are presented with applications to social network analysis.