Geometric Methods in Signal and Image Analysis
Geometric Methods in Signal and Image Analysis

Author: Hamid Krim

Publisher: Cambridge University Press

Published: 2015-06-18

Total Pages: 299

ISBN-13: 1316351963

DOWNLOAD EBOOK

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.

Computational Information Geometry
Computational Information Geometry

Author: Frank Nielsen

Publisher: Springer

Published: 2016-11-24

Total Pages: 312

ISBN-13: 3319470582

DOWNLOAD EBOOK

This book focuses on the application and development of information geometric methods in the analysis, classification and retrieval of images and signals. It provides introductory chapters to help those new to information geometry and applies the theory to several applications. This area has developed rapidly over recent years, propelled by the major theoretical developments in information geometry, efficient data and image acquisition and the desire to process and interpret large databases of digital information. The book addresses both the transfer of methodology to practitioners involved in database analysis and in its efficient computational implementation.

Riemannian Geometric Statistics in Medical Image Analysis
Riemannian Geometric Statistics in Medical Image Analysis

Author: Xavier Pennec

Publisher: Academic Press

Published: 2019-09-02

Total Pages: 636

ISBN-13: 0128147261

DOWNLOAD EBOOK

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

Geometric Methods in Signal and Image Analysis
Geometric Methods in Signal and Image Analysis

Author: Hamid Krim

Publisher: Cambridge University Press

Published: 2015-06-18

Total Pages: 299

ISBN-13: 110703390X

DOWNLOAD EBOOK

A comprehensive guide to modern geometric methods for signal and image analysis, from basic principles to state-of-the-art concepts and applications.

Image Processing and Analysis
Image Processing and Analysis

Author: Tony F. Chan

Publisher: SIAM

Published: 2005-09-01

Total Pages: 414

ISBN-13: 089871589X

DOWNLOAD EBOOK

This book develops the mathematical foundation of modern image processing and low-level computer vision, bridging contemporary mathematics with state-of-the-art methodologies in modern image processing, whilst organizing contemporary literature into a coherent and logical structure. The authors have integrated the diversity of modern image processing approaches by revealing the few common threads that connect them to Fourier and spectral analysis, the machinery that image processing has been traditionally built on. The text is systematic and well organized: the geometric, functional, and atomic structures of images are investigated, before moving to a rigorous development and analysis of several image processors. The book is comprehensive and integrative, covering the four most powerful classes of mathematical tools in contemporary image analysis and processing while exploring their intrinsic connections and integration. The material is balanced in theory and computation, following a solid theoretical analysis of model building and performance with computational implementation and numerical examples.

Geometric Level Set Methods in Imaging, Vision, and Graphics
Geometric Level Set Methods in Imaging, Vision, and Graphics

Author: Stanley Osher

Publisher: Springer Science & Business Media

Published: 2007-05-08

Total Pages: 523

ISBN-13: 0387218106

DOWNLOAD EBOOK

Here is, for the first time, a book that clearly explains and applies new level set methods to problems and applications in computer vision, graphics, and imaging. It is an essential compilation of survey chapters from the leading researchers in the field. The applications of the methods are emphasized.

Sparse Image and Signal Processing
Sparse Image and Signal Processing

Author: Jean-Luc Starck

Publisher: Cambridge University Press

Published: 2015-10-14

Total Pages: 449

ISBN-13: 1107088062

DOWNLOAD EBOOK

Presents state-of-the-art sparse and multiscale image and signal processing with applications in astronomy, biology, MRI, media, and forensics.

Mathematical Methods for Signal and Image Analysis and Representation
Mathematical Methods for Signal and Image Analysis and Representation

Author: Luc Florack

Publisher: Springer Science & Business Media

Published: 2012-01-13

Total Pages: 321

ISBN-13: 1447123522

DOWNLOAD EBOOK

Mathematical Methods for Signal and Image Analysis and Representation presents the mathematical methodology for generic image analysis tasks. In the context of this book an image may be any m-dimensional empirical signal living on an n-dimensional smooth manifold (typically, but not necessarily, a subset of spacetime). The existing literature on image methodology is rather scattered and often limited to either a deterministic or a statistical point of view. In contrast, this book brings together these seemingly different points of view in order to stress their conceptual relations and formal analogies. Furthermore, it does not focus on specific applications, although some are detailed for the sake of illustration, but on the methodological frameworks on which such applications are built, making it an ideal companion for those seeking a rigorous methodological basis for specific algorithms as well as for those interested in the fundamental methodology per se. Covering many topics at the forefront of current research, including anisotropic diffusion filtering of tensor fields, this book will be of particular interest to graduate and postgraduate students and researchers in the fields of computer vision, medical imaging and visual perception.

Geometric Methods in Bio-Medical Image Processing
Geometric Methods in Bio-Medical Image Processing

Author: Ravikanth Malladi

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 151

ISBN-13: 3642559875

DOWNLOAD EBOOK

The genesis of this book goes back to the conference held at the University of Bologna, June 1999, on collaborative work between the University of California at Berkeley and the University of Bologna. The book, in its present form, is a compilation of some of the recent work using geometric partial differential equations and the level set methodology in medical and biomedical image analysis. The book not only gives a good overview on some of the traditional applications in medical imagery such as, CT, MR, Ultrasound, but also shows some new and exciting applications in the area of Life Sciences, such as confocal microscope image understanding.

Geometry of Deep Learning
Geometry of Deep Learning

Author: Jong Chul Ye

Publisher: Springer Nature

Published: 2022-01-05

Total Pages: 338

ISBN-13: 9811660468

DOWNLOAD EBOOK

The focus of this book is on providing students with insights into geometry that can help them understand deep learning from a unified perspective. Rather than describing deep learning as an implementation technique, as is usually the case in many existing deep learning books, here, deep learning is explained as an ultimate form of signal processing techniques that can be imagined. To support this claim, an overview of classical kernel machine learning approaches is presented, and their advantages and limitations are explained. Following a detailed explanation of the basic building blocks of deep neural networks from a biological and algorithmic point of view, the latest tools such as attention, normalization, Transformer, BERT, GPT-3, and others are described. Here, too, the focus is on the fact that in these heuristic approaches, there is an important, beautiful geometric structure behind the intuition that enables a systematic understanding. A unified geometric analysis to understand the working mechanism of deep learning from high-dimensional geometry is offered. Then, different forms of generative models like GAN, VAE, normalizing flows, optimal transport, and so on are described from a unified geometric perspective, showing that they actually come from statistical distance-minimization problems. Because this book contains up-to-date information from both a practical and theoretical point of view, it can be used as an advanced deep learning textbook in universities or as a reference source for researchers interested in acquiring the latest deep learning algorithms and their underlying principles. In addition, the book has been prepared for a codeshare course for both engineering and mathematics students, thus much of the content is interdisciplinary and will appeal to students from both disciplines.