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foreword by henri maitreacknowledgmentslist of figuresnotation and symbols1  introduction  1.1   about modeling    1.1.1  bayesian approach    1.1.2  inverse problem    1.1.3  energy-based formulation    1.1.4  models  1.2   structure of the book  spline models2  nonparametrie spline models  2.1   definition  2.2   optimization    2.2.1  bending spline    2.2.2  spline under tension    2.2.3  robustness  2.3   bayesian interpretation  2.4   choice of regularization parameter  2.5   approximation using a surface    2.5.1  l-spline surface    2.5.2  quadratic energy    2.5.3  finite element optimization3  parametric spline models  3.1   representation on a basis of b-splines    3.1.1  approximation spline    3.1.2  construction of b-splines  3.2   extensions    3.2.1  multidimensional case    3.2.2  heteroscedasticity  3.3   high-dimensional splines    3.3.1  revealing directions    3.3.2  projection pursuit regression4  auto-associative models  4.1   analysis of multidimensional data    4.1.1  a classical approach    4.1.2  toward an alternative approach  4.2   auto-associative composite models    4.2.1  model and algorithm    4.2.2  properties  4.3   projection pursuit and spline smoothing    4.3.1  projection index    4.3.2  spline smoothing  4.4   illustration¢¢  markov models5  fundamental aspects  5.1   definitions    5.1.1  finite markov fields    5.1.2  gibbs fields  5.2   markov-gibbs equivalence  5.3   examples    5.3.1  bending energy    5.3.2  bernoulli energy    5.3.3  gaussian energy  5.4   consistency problem6  bayesian estimation  6.1   principle  6.2   cost functions    6.2.1  cost b-hnction examples    6.2.2  calculation problems7  simulation and optimization  7.1   simulation    7.1.1  homogeneous markov chain    7.1.2  metropolis dynamic    7.1.3  simulated gibbs distribution  7.2   stochastic optimization  7.3   probabilistic aspects  7.4   deterministic optimization    7.4.1  icm algorithm    7.4.2  relaxation algorithms8  parameter estimation  8.1   complete data    8.1.1  maximum likelihood    8.1.2  maximum pseudolikelihood    8.1.3  logistic estimation  8.2   incomplete data    8.2.1  maximum likelihood    8.2.2  gibbsian em algorithm    8.2.3  bayesian calibration  ¢£  modeling in action9  model-building  9.1   multiple spline approximation    9.1.1  choice of data and image characteristics    9.1.2  definition of the hidden field    9.1.3  building an energy  9.2   markov modeling methodology    9.2.1  details for implementation10 degradation in imaging    10.1  denoising    10.1.1 models with explicit discontinuities    10.1.2 models with implicit discontinuities    10.2  deblurring    10.2.1 a particularly ill-posed problem    10.2.2 model with implicit discontinuities    10.3  scatter    10.3.1 direct problem    10.3.2 inverse problem  10.4  sensitivity functions and image fusion    10.4.1 a restoration problem    10.4.2 transfer function estimation    10.4.3 estimation of stained transfer function11 detection of filamentary entities  11.1  valley detection principle    11.1.1 definitions    11.1.2 bayes-markov formulation  11.2  building the prior energy    11.2.1 detection term    11.2.2 regularization term  11.3  optimization  11.4  extension to the case of an image pair12 reconstruction and projections  12.1  projection model    12.1.1 transmission tomography    12.1.2 emission tomography  12.2  regularized reconstruction    12.2.1 regularization with explicit discontinuities   12.2.2 three-dimensional reconstruction  12.3  reconstruction with a single view    12.3.1 generalized cylinder    12.3.2 training the deformations    12.3.3 reconstruction in the presence of occlusion13 matching  13.1  template and hidden outline    13.1.1 rigid transformations    13.1.2 spline model of a template  13.2  elastic deformations    13.2.1 continuous random fields    13.2.2 probabilistie aspectsreferencesauthor indexsubject index