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Mathematical Problems in Image Processing
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更新于2023-03-16
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供了各种图像分析的应用程序,并展示了如何离散化这些精确的数学。《MathematicalProblemsinImageProcessing》展示了它对数学领域的贡献,并突出了未解决的理论问题。而对于计算机视觉社区,此书提出了一个清晰、自洽的涉及数学的图像处理问题。值得一提的是,第二版《Mathematical Problems in Image Processing》提供了对PDE框架所涵盖的图像处理应用程序进展的回顾,并更新了现有的材料,同时,本书还提供了用于以最小的努力创建模拟的编程工具,十分难得。
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Applied Mathematical Sciences
Volume 147
Editors
S.S. Antman J.E. Marsden L. Sirovich
Advisors
J.K. Hale P. Holmes J. Keener
J. Keller B.J. Matkowsky A. Mielke
C.S. Peskin K.R. Sreenivasan
Applied Mathematical Sciences
1. John: Partial Differential Equations, 4th ed.
2. Sirovich: Techniques of Asymptotic Analysis.
3. Hale: Theory of Functional Differential
Equations, 2nd ed.
4. Percus: Combinatorial Methods.
5. von Mises/Friedrichs: Fluid Dynamics.
6. Freiberger/Grenander: A Short Course in
Computational Probability and Statistics.
7. Pipkin: Lectures on Viscoelasticity Theory.
8. Giacaglia: Perturbation Methods in Non-
linear Systems.
9. Friedrichs: Spectral Theory of Operators in
Hilbert Space.
10. Stroud: Numerical Quadrature and Solution
of Ordinary Differential Equations.
11. Wolovich: Linear Multivariable Systems.
12. Berkovitz: Optimal Control Theory.
13. Bluman/Cole: Similarity Methods for
Differential Equations.
14. Yoshizawa: Stability Theory and the
Existence of Periodic Solution and Almost
Periodic Solutions.
15. Braun: Differential Equations and Their
Applications, Fourth Edition.
16. Lefschetz: Applications of Algebraic
Topology.
17. Collatz/Wetterling: Optimization Problems.
18. Grenander: Pattern Synthesis: Lectures in
Pattern Theory, Vol. I.
19. Marsden/McCracken: Hopf Bifurcation and
Its Applications.
20. Driver: Ordinary and Delay Differential
Equations.
21. Courant/Friedrichs: Supersonic Flow and
Shock Waves.
22. Rouche/Habets/Laloy: Stability Theory by
Liapunov’s Direct Method.
23. Lamperti: Stochastic Processes: A Survey of
the Mathematical Theory.
24: Grenander: Pattern Analysis: Lectures in
Pattern Theory, Vol. II.
25. Davies: Integral Transforms and Their
Applications, Third Edition.
26. Kushner/Clark: Stochastic Approximation
Methods for Constrained and
Unconstrained Systems.
27. de Boor: A Practical Guide to Splines,
Revised Edition.
28.
Keilson: Markov Chain Models-Rarity and
Exponentiality.
29. de Veubeke: A Course in Elasticity.
30. Sniatycki: Geometric Quantization and
Quantum Mechanics.
31: Reid: Sturmian Theory for Ordinary
Differential Equations.
32. Meis/Markowitz: Numerical Solution of
Partial Differential Equations.
33. Grenander: Regular Structures: Lectures in
Pattern Theory, Vol. III.
34. Kevorkian/Cole: Perturbation Methods in
Applied Mathematics.
35: Carr: Applications of Centre Manifold
Theory.
36. Bengtsson/Ghil/Källén: Dynamic
Meteorology: Data Assimilation Methods.
37. Saperstone: Semidynamical Systems in
Infinite Dimensional Spaces.
38. Lichtenberg/Lieberman: Regular and Chaotic
Dynamics, 2nd ed.
39. Piccini/Stampacchia/Vidossich: Ordinary
Differential Equations in R
n
.
40. Naylor/Sell: Linear Operator Theory in
Engineering and Science.
41. Sparrow: The Lorenz Equations:
Bifurcations, Chaos, and Strange Attractors.
42. Guckenheimer/Holmes: Nonlinear
Oscillations, Dynamical Systems, and
Bifurcations of Vector Fields.
43. Ockendon/Taylor: Inviscid Fluid Flows.
44. Pazy: Semigroups of Linear Operators and
Applications to Partial Differential
Equations.
45. Glashoff/Gustafson: Linear Operations and
Approximation: An Introduction to the
Theoretical Analysis and Numerical
Treatment of Semi-Infinite Programs.
46. Wilcox: Scattering Theory for Diffraction
Gratings.
47. Hale et al.: Dynamics in Infinite
Dimensions.
48. Murray: Asymptotic Analysis.
49. Ladyzhenskaya: The Boundary-Value
Problems of Mathematical Physics.
50. Wilcox: Sound Propagation in Stratified
Fluids.
51. Golubitsky/Schaeffer: Bifurcation and
Groups in Bifurcation Theory, Vol. I.
52. Chipot: Variational Inequalities and Flow in
Porous Media.
53. Majda: Compressible Fluid Flow and
System of Conservation Laws in Several
Space Variables.
54. Wasow: Linear Turning Point Theory.
55. Yosida: Operational Calculus: A Theory of
Hyperfunctions.
56. Chang/Howes: Nonlinear Singular
Perturbation Phenomena: Theory and
Applications.
57. Reinhardt: Analysis of Approximation
Methods for Differential and Integral
Equations.
58. Dwoyer/Hussaini/Voigt (eds): Theoretical
Approaches to Turbulence.
(continued after index)
Gilles Aubert Pierre Kornprobst
Mathematical Problems in
Image Processing
Partial Differential Equations and the
Calculus of Variations
Second Edition
Gilles Aubert Pierre Kornprobst
Université de Nice Sophia-Antipolis INRIA, Projet Odyssée
CNRS UMR 6621 2004 route des lucioles - BP 93
Laboratoire J.A. Dieudonné 06902 SOPHIA ANTIPOLIS
Parc Valrose France
06108 NICE CX 2 Pierre.Kornprobst@sophia.inria.fr
France
gaubert@math.unice.fr
Editors:
S.S. Antman J.E. Marsden L. Sirovic
Department of Mathematics Control and Dynamical Laboratory of Applied
and Systems, 107-81 Mathematics
Institute for Physical Science California Institute of Department of
and Technology Technology Biomathematical
University of Maryland Pasadena, CA 91125 Sciences
College Park, MD 20742-4015 USA Mount Sinai School
USA marsden@cds.caltech.edu of Medicine
ssa@math.umd.edu New York, NY 10029-6574
USA
chico@camelot.mssm.edu
Mathematics Subject Classification (2000): 35J, 35L, 35Q, 49J, 49N
Library of Congress Control Number: 2006926450
ISBN-10: 0-387-32200-0 e-ISBN 0-387-21766-5
ISBN-13: 978-0387-32200-1
Printed on acid-free paper.
© 2006 Springer Science + Business Media, LLC
All rights reserved. This work may not be translated or copied in whole or in part without the
written permission of the publisher (Springer Science + Business Media, LLC, 233 Spring Street,
New York, NY 10013, USA), except for brief excerpts in connection with reviews or scholarly
analysis. Use in connection with any form of information storage and retrieval, electronic
adaptation, computer software, or by similar or dissimilar methodology now known or hereafter
developed is forbidden.
The use in this publication of trade names, trademarks, service marks, and similar terms, even if
they are not identified as such, is not to be taken as an expression of opinion as to whether or
not they are subject to proprietary rights.
Printed in the United States of America. (EB)
987654321
springer.com
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