Analysis Of Variance In Statistical Image Processing

A key problem in practical image processing is the detection of specific features in a noisy image. Analysis of variance (ANOVA) techniques can be very effective in such situations, and this book gives a detailed account of the use of ANOVA in statistical image processing. The book begins by describing the statistical representation of images in the various ANOVA models. The authors present a number of computationally efficient algorithms and techniques to deal with such problems as line, edge, and object detection, as well as image restoration and enhancement. By describing the basic principles of these techniques, and showing their use in specific situations, the book will facilitate the design of new algorithms for particular applications. It will be of great interest to graduate students and engineers in the field of image processing and pattern recognition.

Spatial statistics is one of the most rapidly growing areas of statistics, rife with fascinating research opportunities. Yet many statisticians are unaware of those opportunities, and most students in the United States are never exposed to any course work in spatial statistics. Written to be accessible to the nonspecialist, this volume surveys the applications of spatial statistics to a wide range of areas, including image analysis, geosciences, physical chemistry, and ecology. The book describes the contributions of the mathematical sciences, summarizes the current state of knowledge, and identifies directions for research.

Images are all around us! The proliferation of low-cost, high-quality imaging devices has led to an explosion in acquired images. When these images are acquired from a microscope, telescope, satellite, or medical imaging device, there is a statistical image processing task: the inference of something—an artery, a road, a DNA marker, an oil spill—from imagery, possibly noisy, blurry, or incomplete. A great many textbooks have been written on image processing. However this book does not so much focus on images, per se, but rather on spatial data sets, with one or more measurements taken over a two or higher dimensional space, and to which standard image-processing algorithms may not apply. There are many important data analysis methods developed in this text for such statistical image problems. Examples abound throughout remote sensing (satellite data mapping, data assimilation, climate-change studies, land use), medical imaging (organ segmentation, anomaly detection), computer vision (image classification, segmentation), and other 2D/3D problems (biological imaging, porous media). The goal, then, of this text is to address methods for solving multidimensional statistical problems. The text strikes a balance between mathematics and theory on the one hand, versus applications and algorithms on the other, by deliberately developing the basic theory (Part I), the mathematical modeling (Part II), and the algorithmic and numerical methods (Part III) of solving a given problem. The particular emphases of the book include inverse problems, multidimensional modeling, random fields, and hierarchical methods.

Statistical Processing Techniques for Noisy Images presents a statistical framework to design algorithms for target detection, tracking, segmentation and classification (identification). Its main goal is to provide the reader with efficient tools for developing algorithms that solve his/her own image processing applications. In particular, such topics as hypothesis test-based detection, fast active contour segmentation and algorithm design for non-conventional imaging systems are comprehensively treated, from theoretical foundations to practical implementations. With a large number of illustrations and practical examples, this book serves as an excellent textbook or reference book for senior or graduate level courses on statistical signal/image processing, as well as a reference for researchers in related fields.

This book introduces the statistical software R to the image processing community in an intuitive and practical manner. R brings interesting statistical and graphical tools which are important and necessary for image processing techniques. Furthermore, it has been proved in the literature that R is among the most reliable, accurate and portable statistical software available. Both the theory and practice of R code concepts and techniques are presented and explained, and the reader is encouraged to try their own implementation to develop faster, optimized programs. Those who are new to the field of image processing and to R software will find this work a useful introduction. By reading the book alongside an active R session, the reader will experience an exciting journey of learning and programming.

Statistical image processing; application of the gibbs distribution to image segmentation; A model for orginal filtering of digital images; Spatial domain filtering of digital images; Spatial domain filters forimage processing; Edge detection by partitioning; A syntactic approach for SAR image nalysis; Parametric techniques for SAR image compression; Data compression of a first order intermittently excited AR process; A modular software for image information systems; A space-efficient hough transform implementation for object detection; New computing methods in image processing displays; Statistical graphics; Visualizing two-dimensional phenomena in four-dimensional space: A computer grahphics approach; The man-machine-graphics interface for statistical data analysis; Interactive color display methods for multivariate data; Interactive computer graphics in statistics; Illustrations of model diagnosis by means of three-dimensional biplots; Multivariate thin plate spline smoothing with positivity and other linear; Data analysis in three and four dimensions with nonparametric; Dimensionality reduction in density estimation; Volumetric 3-D displays and spatial perception; Index.

A rigorous, self-contained examination of mixed model theory and application Mixed modeling is one of the most promising and exciting areas of statistical analysis, enabling the analysis of nontraditional, clustered data that may come in the form of shapes or images. This book provides in-depth mathematical coverage of mixed models’ statistical properties and numerical algorithms, as well as applications such as the analysis of tumor regrowth, shape, and image. Paying special attention to algorithms and their implementations, the book discusses: Modeling of complex clustered or longitudinal data Modeling data with multiple sources of variation Modeling biological variety and heterogeneity Mixed model as a compromise between the frequentist and Bayesian approaches Mixed model for the penalized log-likelihood Healthy Akaike Information Criterion (HAIC) How to cope with parameter multidimensionality How to solve ill-posed problems including image reconstruction problems Modeling of ensemble shapes and images Statistics of image processing Major results and points of discussion at the end of each chapter along with "Summary Points" sections make this reference not only comprehensive but also highly accessible for professionals and students alike in a broad range of fields such as cancer research, computer science, engineering, and industry.

Comprehensive and thorough development of both probability and statistics for serious computer scientists; goal-oriented: "to present the mathematical analysis underlying probability results" Special emphases on simulation and discrete decision theory Mathematically-rich, but self-contained text, at a gentle pace Review of calculus and linear algebra in an appendix Mathematical interludes (in each chapter) which examine mathematical techniques in the context of probabilistic or statistical importance Numerous section exercises, summaries, historical notes, and Further Readings for reinforcement of content