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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.
Gaussian scale-space is one of the best understood multi-resolution
techniques available to the computer vision and image analysis
community. It is the purpose of this book to guide the reader
through some of its main aspects. During an intensive weekend in
May 1996 a workshop on Gaussian scale-space theory was held in
Copenhagen, which was attended by many of the leading experts in
the field. The bulk of this book originates from this workshop.
Presently there exist only two books on the subject. In contrast to
Lindeberg's monograph (Lindeberg, 1994e) this book collects
contributions from several scale space researchers, whereas it
complements the book edited by ter Haar Romeny (Haar Romeny, 1994)
on non-linear techniques by focusing on linear diffusion. This book
is divided into four parts. The reader not so familiar with
scale-space will find it instructive to first consider some
potential applications described in Part 1. Parts II and III both
address fundamental aspects of scale-space. Whereas scale is
treated as an essentially arbitrary constant in the former, the
latter em phasizes the deep structure, i.e. the structure that is
revealed by varying scale. Finally, Part IV is devoted to
non-linear extensions, notably non-linear diffusion techniques and
morphological scale-spaces, and their relation to the linear case.
The Danish National Science Research Council is gratefully
acknowledged for providing financial support for the workshop under
grant no. 9502164."
Despite the fact that images constitute the main objects in
computer vision and image analysis, there is remarkably little
concern about their actual definition. In this book a complete
account of image structure is proposed in terms of rigorously
defined machine concepts, using basic tools from algebra, analysis,
and differential geometry. Machine technicalities such as
discretisation and quantisation details are de-emphasised, and
robustness with respect to noise is manifest. From the foreword by
Jan Koenderink: It is my hope that the book will find a wide
audience, including physicists - who still are largely unaware of
the general importance and power of scale space theory,
mathematicians - who will find in it a principled and formally
tight exposition of a topic awaiting further development, and
computer scientists - who will find here a unified and conceptually
well founded framework for many apparently unrelated and largely
historically motivated methods they already know and love. The book
is suited for self-study and graduate courses, the carefully
formulated exercises are designed to get to grips with the subject
matter and prepare the reader for original research.'
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Deep Structure, Singularities, and Computer Vision - First International Workshop, DSSCV 2005, Maastricht, The Netherlands, June 9-10, 2005, Revised Selected Papers (Paperback, 2005 ed.)
Ole Fogh Olsen, Luc Florack, Arjan Kuijper
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R1,643
Discovery Miles 16 430
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Ships in 10 - 15 working days
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Whatisactuallytheinformationdirectlyrepresentedinthescale-space?Istarted
to wonder about this shortly after Peter Johansen, 15 years ago,
showed me his intriguing paper on how uniquely to reconstruct a
band-limited 1D signal from its scale-space toppoints. Still, I
have not fully understood its implications. Merely recording where
structure vanishes under blurring is su?cient to fully reconstruct
the details. Of course, technicalities exist, for example, you must
also know negative scale toppoints. Nevertheless, I ?nd it
surprising that we may trade the metric properties of a signal with
the positions of its inherent structure. The result has been
generalizedto analytic signals, shown also for the zero crossings
of the Laplacean, but has not yet been generalized to 2D. This
remains an open problem. In 2003, Peter Giblin, Liverpool
University, Luc Florack, Eindhoven Univ- sity of Technology, Jon
Sporring, University of Copenhagen, my colleague Ole Fogh Olsen,
and several others started the project collaborationDeep Structure
and Singularities in Computer Vision under the European Union, IST,
Future and Emerging Technologies program, trying to obtain further
knowledge about what informationis actuallycarriedby the
singularitiesof shapesand gray-scale images. In this project, we
probed from several directions the question of how much of the
metric information is actually encoded in the structure of shapes
and images. We, and many others, have given hints in this
direction.
Despite the fact that images constitute the main objects in
computer vision and image analysis, there is remarkably little
concern about their actual definition. In this book a complete
account of image structure is proposed in terms of rigorously
defined machine concepts, using basic tools from algebra, analysis,
and differential geometry. Machine technicalities such as
discretisation and quantisation details are de-emphasised, and
robustness with respect to noise is manifest. From the foreword by
Jan Koenderink: It is my hope that the book will find a wide
audience, including physicists - who still are largely unaware of
the general importance and power of scale space theory,
mathematicians - who will find in it a principled and formally
tight exposition of a topic awaiting further development, and
computer scientists - who will find here a unified and conceptually
well founded framework for many apparently unrelated and largely
historically motivated methods they already know and love. The book
is suited for self-study and graduate courses, the carefully
formulated exercises are designed to get to grips with the subject
matter and prepare the reader for original research.'
|
Scale-Space Theory in Computer Vision - First International Conference, Scale-Space '97, Utrecht, The Netherlands, July 2 - 4, 1997, Proceedings (Paperback, 1997 ed.)
Bart Ter Haar Romeny, Luc Florack, Jan Koenderink, Max Viergever
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R1,713
Discovery Miles 17 130
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Ships in 10 - 15 working days
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This book constitutes the refereed proceedings of the First
International Conference on Scale-Space Theory for Computer Vision,
Scale-Space '97, held in Utrecht, The Netherlands, in July
1997.
The volume presents 21 revised full papers selected from a total of
41 submissions. Also included are 2 invited papers and 13 poster
presentations. This book is the first comprehensive documentation
of the application of Scale-Space techniques in computer vision
and, in the broader context, in image processing and pattern
recognition.
Gaussian scale-space is one of the best understood multi-resolution
techniques available to the computer vision and image analysis
community. It is the purpose of this book to guide the reader
through some of its main aspects. During an intensive weekend in
May 1996 a workshop on Gaussian scale-space theory was held in
Copenhagen, which was attended by many of the leading experts in
the field. The bulk of this book originates from this workshop.
Presently there exist only two books on the subject. In contrast to
Lindeberg's monograph (Lindeberg, 1994e) this book collects
contributions from several scale space researchers, whereas it
complements the book edited by ter Haar Romeny (Haar Romeny, 1994)
on non-linear techniques by focusing on linear diffusion. This book
is divided into four parts. The reader not so familiar with
scale-space will find it instructive to first consider some
potential applications described in Part 1. Parts II and III both
address fundamental aspects of scale-space. Whereas scale is
treated as an essentially arbitrary constant in the former, the
latter em phasizes the deep structure, i.e. the structure that is
revealed by varying scale. Finally, Part IV is devoted to
non-linear extensions, notably non-linear diffusion techniques and
morphological scale-spaces, and their relation to the linear case.
The Danish National Science Research Council is gratefully
acknowledged for providing financial support for the workshop under
grant no. 9502164."
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