Mathematical Methods In Time Series Analysis And Digital Image Processing

This coherent and articulate volume summarizes work carried out in the field of theoretical signal and image processing. It focuses on non-linear and non-parametric models for time series as well as on adaptive methods in image processing. The aim of this volume is to bring together research directions in theoretical signal and imaging processing developed rather independently in electrical engineering, theoretical physics, mathematics and the computer sciences.

Digital image processing technology has developed markedly over the last ten years, and more and more information is being conveyed through its display and analysis. The way in which image data is stored and processed is fundamental to all aspects of information technology. Examples include remote sensing using digital satellites; making diagnoses using conventional X-ray computed tomography; and research into the behavior of the human brain using magnetic resonance imaging. This book consists of twenty-one papers that collectively cover a broad range of image processing problems and the way in which their solutions are used in different areas of science and technology. The papers present details of the ways computers of varying processing power can be programmed to store images efficiently, resolve features and patterns that are either time consuming or impossible for humans to interpret, and develop machines that can "see" like humans. They also discuss a wide range of applications, including the use of lasers for studying dynamic behavior of mechanical components, and fractal geometry for recognizing patterns. The book will be useful to any engineer, scientist, and technologist interested in current research issues in image processing.

Change Detection and Image Time Series Analysis 1 presents a wide range of unsupervised methods for temporal evolution analysis through the use of image time series associated with optical and/or synthetic aperture radar acquisition modalities. Chapter 1 introduces two unsupervised approaches to multiple-change detection in bi-temporal multivariate images, with Chapters 2 and 3 addressing change detection in image time series in the context of the statistical analysis of covariance matrices. Chapter 4 focuses on wavelets and convolutional-neural filters for feature extraction and entropy-based anomaly detection, and Chapter 5 deals with a number of metrics such as cross correlation ratios and the Hausdorff distance for variational analysis of the state of snow. Chapter 6 presents a fractional dynamic stochastic field model for spatio temporal forecasting and for monitoring fast-moving meteorological events such as cyclones. Chapter 7 proposes an analysis based on characteristic points for texture modeling, in the context of graph theory, and Chapter 8 focuses on detecting new land cover types by classification-based change detection or feature/pixel based change detection. Chapter 9 focuses on the modeling of classes in the difference image and derives a multiclass model for this difference image in the context of change vector analysis.

Change Detection and Image Time Series Analysis 2 presents supervised machine-learning-based methods for temporal evolution analysis by using image time series associated with Earth observation data. Chapter 1 addresses the fusion of multisensor, multiresolution and multitemporal data. It proposes two supervised solutions that are based on a Markov random field: the first relies on a quad-tree and the second is specifically designed to deal with multimission, multifrequency and multiresolution time series. Chapter 2 provides an overview of pixel based methods for time series classification, from the earliest shallow learning methods to the most recent deep-learning-based approaches. Chapter 3 focuses on very high spatial resolution data time series and on the use of semantic information for modeling spatio-temporal evolution patterns. Chapter 4 centers on the challenges of dense time series analysis, including pre processing aspects and a taxonomy of existing methodologies. Finally, since the evaluation of a learning system can be subject to multiple considerations, Chapters 5 and 6 offer extensive evaluations of the methodologies and learning frameworks used to produce change maps, in the context of multiclass and/or multilabel change classification issues.

Developed in this book are several deep connections between time-frequency (Fourier/Gabor) analysis and time-scale (wavelet) analysis, emphasizing the powerful adaptive methods that emerge when separate techniques from each area are properly assembled in a larger context. While researchers at the forefront of these areas are well aware of the benefits of such a unified approach, there remains a knowledge gap in the larger community of practitioners about the precise strengths and limitations of Fourier/Gabor analysis versus wavelets. This book fills that gap by presenting the interface of time-frequency and time-scale methods as a rich area of work. "Foundations of Time-Frequency and Time-Scale Methods" will be suitable for applied mathematicians and engineers in signal/image processing and communication theory, as well as researchers and students in mathematical analysis, signal analysis, and mathematical physics.

Computer vision and image analysis require interdisciplinary collaboration between mathematics and engineering. This book addresses the area of high-accuracy measurements of length, curvature, motion parameters and other geometrical quantities from acquired image data. It is a common problem that these measurements are incomplete or noisy, such that considerable efforts are necessary to regularise the data, to fill in missing information, and to judge the accuracy and reliability of these results. This monograph brings together contributions from researchers in computer vision, engineering and mathematics who are working in this area. The book can be read both by specialists and graduate students in computer science, electrical engineering or mathematics who take an interest in data evaluations by approximation or interpolation, in particular data obtained in an image analysis context.

With the rise of advanced computerized data collection systems, monitoring devices, and instrumentation technologies, large and complex datasets accrue as an inevitable part of biomedical enterprise. The availability of these massive amounts of data offers unprecedented opportunities to advance our understanding of underlying biological and physiol

At no other time in human history have the influence and impact of image processing on modern society, science, and technology been so explosive. Image processing has become a critical component in contemporary science and technology and has many important applications. This book develops the mathematical foundation of modern image processing and low-level computer vision, and presents a general framework from the analysis of image structures and patterns to their processing. The core mathematical and computational ingredients of several important image processing tasks are investigated. The book bridges contemporary mathematics with state-of-the-art methodologies in modern image processing while organizing the vast contemporary literature into a coherent and logical structure.