Series: The IMA Volumes in Mathematics and
its Applications ,
Vol. 133
2003, Approx. 168 p. 86 illus., Hardcover
ISBN: 0-387-00497-1
About this book
This volume comprises some of the key work
presented at two IMA
Workshops on Computer Vision during fall
of 2000. Recent years
have seen significant advances in the application
of
sophisticated mathematical theories to the
problems arising in
image processing. Basic issues include image
smoothing and
denoising, image enhancement, morphology,
image compression, and
segmentation (determining boundaries of objectsuincluding
problems of camera distortion and partial
occlusion). Several
mathematical approaches have emerged, including
methods based on
nonlinear partial differential equations,
stochastic and
statistical methods, and signal processing
techniques, including
wavelets and other transform theories. Shape
theory is of
fundamental importance since it is the bottleneck
between high
and low level vision, and formed the bridge
between the two
workshops on vision. The recent geometric
partial differential
equation methods have been essential in throwing
new light on
this very difficult problem area. Further,
stochastic processes,
including Markov random fields, have been
used in a Bayesian
framework to incorporate prior constraints
on smoothness and the
regularities of discontinuities into algorithms
for image
restoration and reconstruction. A number
of applications are
considered including optical character and
handwriting
recognizers, printed-circuit board inspection
systems and quality
control devices, motion detection, robotic
control by visual
feedback, reconstruction of objects from
stereoscopic view and/or
motion, autonomous road vehicles, and many
others.
Table of contents
A large deviation theory analysis of Bayesian
tree search *
Expectation-based, multi-focal, saccadic
vision * Statistical
shape analysis in high-level vision * Maximal
entropy for
reconstruction of back projection images
* On the Monge-Kantorovich
problem and image warping * Analysis and
synthesis of visual
images in the brain: evidence for pattern
theory * Nonlinear
diffusions and optimal estimation * The Mumford-Shah
functional:
from segmentation to stereo
Written for:
Researchers, graduate students
Series: Lecture Notes in Mathematics , Vol.
1471
, 2003, VIII, 196 p., Softcover
ISBN: 3-540-40729-4
Due: December 1, 2003
About this book
This book, now in its 2nd edition, is devoted
to the arithmetical
theory of Siegel modular forms and their
L-functions. The central
object are L-functions of classical Siegel
modular forms whose
special values are studied using the Rankin-Selberg
method and
the action of certain differential operators
on modular forms
which have nice arithmetical properties.
A new method of p-adic
interpolation of these critical values is
presented. An important
class of p-adic L-functions treated in the
present book are p-adic
L-functions of Siegel modular forms having
logarithmic growth.
The given construction of these p-adic L-functions
uses precise
algebraic properties of the arithmetical
Shimura differential
operator. The book will be very useful for
postgraduate students
and for non-experts looking for a quick approach
to a rapidly
developing domain of algebraic number theory.
This new edition is
substantially revised to account for the
new explanations that
have emerged in the past 10 years of the
main formulas for
special L-values in terms of arithmetical
theory of nearly
holomorphic modular forms.
Table of contents
Introduction.- Non-Archimedean analytic functions,
measures and
distributions.- Siegel modular forms and
the holomorphic
projection operator.- Arithmetical differential
operators on
nearly holomorphic Siegel modular forms.-
Admissible measures for
standard L-functions and nearly holomorphic
Siegel modular forms.
Written for:
Graduate students and researchers in algebraic
number theory
Keywords: modular forms
Series: Lecture Notes in Mathematics, Vol.
1822
2003, XII, 345 p., Softcover
ISBN: 3-540-40786-3
Due: October 24, 2003
About this book
The C.I.M.E. session on Dynamical Systems,
held in Cetraro (Italy),
June 19-26, 2000, focused on the latest developments
in several
important areas in dynamical systems, with
full development and
historical context. The lectures of Chow
and Mallet-Paret focus
on the area of lattice differential systems,
the lectures of
Conto and Galleotti treat the classical problem
of classification
of orbits for two-dimensional autonomous
systems with polynomial
right sides, the lectures of Nussbaum focus
on applications of
fixed point theorems to the problem of limiting
profiles for the
solutions of singular perturbations of delay
differential
equations, and the lectures of Johnson and
Mantellini deal with
the existence of periodic and quasi-periodic
orbits to non-autonomous
systems. The volume will be of interest to
researchers and
graduate students working in these areas.
Table of contents
Preface.- S.-N. Chow: Lattice Dynamical Systems.-
R. Conti, M.
Galeotti: Totally bounded cubic systems in
R2.- R. Johnson, F.
Mantellini: Non-Autonomous Differential Equations.-
J. Mallet-Paret:
Traveling Waves in Spatially Discrete Dynamical
Systems of
Diffuse Type.- R.D. Nussbaum: Limiting Profiles
For Solutions of
Differential-Delay Equations
Written for:
Researchers and advanced students
Keywords: dynamical systems, differential
equations
2004, XVI, 382 p., Hardcover
ISBN: 3-540-40682-4
Due: October 7, 2003
About this book
In inverse problems, the aim is to obtain,
via a mathematical
model, information on quantities that are
not directly observable
but rather depend on other observable quantities.
Inverse
problems are encountered in such diverse
areas of application as
medical imaging, remote sensing, material
testing, geosciences
and financing. It has become evident that
new ideas coming from
differential geometry and modern analysis
are needed to tackle
even some of the most classical inverse problems.
This book
contains a collection of presentations, written
by leading
specialists, aiming to give the reader up-to-date
tools for
understanding the current developments in
the field.
Written for: Mathematicians, physicists
Keywords:
Inverse Problems for partial differential
equations
Differential geometry
Integral geometry
Carleman estimates
Elements of Mathematics
2004, XVI, 472 p., Hardcover
ISBN: 3-540-41129-1
About this book
Integration is the sixth and last of the
Books that form the core
of the Bourbaki series; it draws abundantly
on the preceding five
Books, especially General Topology and Topological
Vector Spaces,
making it a culmination of the core six.
The power of the tool
thus fashioned is strikingly displayed in
Chapter II of the
author's Theories Spectrales [MR 35 #4725],
an exposition, in a
mere 38 pages, of abstract harmonic analysis
and the structure of
locally compact abelian groups. The present
volume comprises
Chapters 1-6 in English translation (a second
volume will contain
the remaining Chapters 7-9). The individual
fascicles of the
original French edition have been extensively
reviewed [Chs. 1--4,
MR 14, 960, 2e edn. MR 36 #2763; Ch. 5, MR
18, 881, 2e edn. MR 35
#322; Ch.6, MR 23 #A2033; Chs. 7-8, MR 31
#3539; Ch. 9, MR 43 #2183].
Chapters 1-5 received very substantial revisions
in a second
edition, including changes to some fundamental
definitions.
Chapters 6-8 are based on the first editions
of Chs. 1-5. The
English edition has given the author the
opportunity to correct
misprints, update references, clarify the
concordance of Chapter
6 with the second editions of Chapters 1-5,
and revise the
definition of a key concept in Chapter 6
(measurable equivalence
relations).
Written for: Mathematicians and graduate
students