图像分析中的模型和逆问题 内容简介

《图像分析中的模型和逆问题》，本书是一部十分优秀的讲述成像分析中的贝叶斯成像和样条模型的教材。随着更多数学家在新兴学科数字成像数理中参与地越来越多，并且在解决复杂问题的模型建立方面扮演越来越重要的角色，做出的贡献也日益呈现。这本书出现显得尤为重要。本书更多地强调基于能量的模型，这些模型大多源于作者参与的机器人视野和X光线照相术，如追踪3D线、射线图像处理、3D重组和X线断层摄影术、等等的工业项目。读者对象：该书的目标读者是想学习更多在成像处理应用的数理统计人员和想要将数学知识应用于自身研究的工程人员。

图像分析中的模型和逆问题 本书特色

this book fulfills a need in the field of computer science research and education. it is not intended for professional mathematicians, but it undoubtedly deals with applied mathematics. most of the expectations of the topic are fulfilled: precision, exactness, completeness, and excellent references to the original historical works. however, for the sake of read-ability, many demonstrations are omitted. it is not a book on practical image processing, of which so many abound, although all that it teaches is directly concerned with image analysis and image restoration. it is the perfect resource for any advanced scientist concerned with a better un-derstanding of the theoretical models underlying the methods that have efficiently solved numerous issues in robot vision and picture processing.

图像分析中的模型和逆问题 目录

foreword by henri maitreacknowledgmentslist of figuresnotation and symbols1introduction1.1 about modeling1.1.1bayesian approach1.1.2inverse problem1.1.3energy-based formulation1.1.4models1.2 structure of the bookspline models2nonparametrie spline models2.1 definition2.2 optimization2.2.1bending spline2.2.2spline under tension2.2.3robustness2.3 bayesian interpretation2.4 choice of regularization parameter2.5 approximation using a surface2.5.1l-spline surface2.5.2quadratic energy2.5.3finite element optimization3parametric spline models3.1 representation on a basis of b-splines3.1.1approximation spline3.1.2construction of b-splines3.2 extensions3.2.1multidimensional case3.2.2heteroscedasticity3.3 high-dimensional splines3.3.1revealing directions3.3.2projection pursuit regression4auto-associative models4.1 analysis of multidimensional data4.1.1a classical approach4.1.2toward an alternative approach4.2 auto-associative composite models4.2.1model and algorithm4.2.2properties4.3 projection pursuit and spline smoothing4.3.1projection index4.3.2spline smoothing4.4 illustrationⅱmarkov models5fundamental aspects5.1 definitions5.1.1finite markov fields5.1.2gibbs fields5.2 markov-gibbs equivalence5.3 examples5.3.1bending energy5.3.2bernoulli energy5.3.3gaussian energy5.4 consistency problem6bayesian estimation6.1 principle6.2 cost functions6.2.1cost b-hnction examples6.2.2calculation problems7simulation and optimization7.1 simulation7.1.1homogeneous markov chain7.1.2metropolis dynamic7.1.3simulated gibbs distribution7.2 stochastic optimization7.3 probabilistic aspects7.4 deterministic optimization7.4.1icm algorithm7.4.2relaxation algorithms8parameter estimation8.1 complete data8.1.1maximum likelihood8.1.2maximum pseudolikelihood8.1.3logistic estimation8.2 incomplete data8.2.1maximum likelihood8.2.2gibbsian em algorithm8.2.3bayesian calibrationⅲmodeling in action9model-building9.1 multiple spline approximation9.1.1choice of data and image characteristics9.1.2definition of the hidden field9.1.3building an energy9.2 markov modeling methodology9.2.1details for implementation10 degradation in imaging10.1denoising10.1.1 models with explicit discontinuities10.1.2 models with implicit discontinuities10.2deblurring10.2.1 a particularly ill-posed problem10.2.2 model with implicit discontinuities10.3scatter10.3.1 direct problem10.3.2 inverse problem10.4sensitivity functions and image fusion10.4.1 a restoration problem10.4.2 transfer function estimation10.4.3 estimation of stained transfer function11 detection of filamentary entities11.1valley detection principle11.1.1 definitions11.1.2 bayes-markov formulation11.2building the prior energy11.2.1 detection term11.2.2 regularization term11.3optimization11.4extension to the case of an image pair12 reconstruction and projections12.1projection model12.1.1 transmission tomography12.1.2 emission tomography12.2regularized reconstruction12.2.1 regularization with explicit discontinuities 12.2.2 three-dimensional reconstruction12.3reconstruction with a single view12.3.1 generalized cylinder12.3.2 training the deformations12.3.3 reconstruction in the presence of occlusion13 matching13.1template and hidden outline13.1.1 rigid transformations13.1.2 spline model of a template13.2elastic deformations13.2.1 continuous random fields13.2.2 probabilistie aspectsreferencesauthor indexsubject index

图像分析中的模型和逆问题 作者简介

Bernard Chalmond是国际知名学者，在数学和物理学界享有盛誉。本书凝聚了作者多年科研和教学成果，适用于科研工作者、高校教师和研究生。