## Structured Learning and Prediction in Computer VisionPowerful statistical models that can be learned efficiently from large amounts of data are currently revolutionizing computer vision. These models possess a rich internal structure reflecting task-specific relations and constraints. Structured Learning and Prediction in Computer Vision introduces the reader to the most popular classes of structured models in computer vision. The focus is on discrete undirected graphical models which are covered in detail together with a description of algorithms for both probabilistic inference and maximum a posteriori inference. It also discusses separately recently successful techniques for prediction in general structured models. The second part of Structured Learning and Prediction in Computer Vision describes methods for parameter learning, distinguishing the classic maximum likelihood based methods from the more recent prediction-based parameter learning methods. It highlights developments to enhance current models and discusses kernelized models and latent variable models. Throughout Structured Learning and Prediction in Computer Vision the main text is interleaved with successful computer vision applications of the explained techniques. For convenience the reader can find a summary of the notation used at the end of the book. |

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### Contents

Introduction | 1 |

Inference in Graphical Models | 21 |

Structured Prediction | 53 |

Conditional Random Fields | 127 |

Structured Support Vector Machines | 149 |

Conclusion | 171 |

### Common terms and phrases

approximate argmax binary computer vision conditional likelihood Conditional Random Fields constraints convergence convex defined discrete discuss dual edge efficiently energy function Equation estimate evaluate factor graph feasible set foreground Gibbs sampler given global gradient descent graph cut graphical models guaranteed image segmentation Input integer interactions iteration kernel label Lagrangian decomposition Lagrangian relaxation latent variables learned weight vector linear programming relaxation loopy belief propagation loss function loss-augmented prediction lower bound MAP inference marginal distributions Markov chain maximization mean field neighborhood objective function obtain optimal solution optimization problem pairwise energies parameter learning parameterized pixel prediction function prediction problem primal probabilistic inference probability distribution S-SVM training sample sb.t shown in Figure simulated annealing solve step structured perceptron structured prediction subgradient method subset support vector machine task techniques Theorem tion tractable tree-structured typically unary factors upper bound variable-to-factor messages wcur