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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.
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.
This book treats the latest developments in the theory of
order-restricted inference, with special attention to nonparametric
methods and algorithmic aspects. Among the topics treated are
current status and interval censoring models, competing risk
models, and deconvolution. Methods of order restricted inference
are used in computing maximum likelihood estimators and developing
distribution theory for inverse problems of this type. The authors
have been active in developing these tools and present the state of
the art and the open problems in the field. The earlier chapters
provide an introduction to the subject, while the later chapters
are written with graduate students and researchers in mathematical
statistics in mind. Each chapter ends with a set of exercises of
varying difficulty. The theory is illustrated with the analysis of
real-life data, which are mostly medical in nature.
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