Computer Vision · Models, Learning, and Inference by Prince, Simon J.D. -- Read -- Imperial Library of Trantor

Index

Cover Title Copyright Dedication Acknowledgements Foreword Preface Chapter 1: Introduction

Organization of the book Other books

Part I: Probability

Chapter 2: Introduction to probability

2.1 Random variables 2.2 Joint probability 2.3 Marginalization 2.4 Conditional probability 2.5 Bayes’ rule 2.6 Independence 2.7 Expectation

Chapter 3: Common probability distributions

3.1 Bernoulli distribution 3.2 Beta distribution 3.3 Categorical distribution 3.4 Dirichlet distribution 3.5 Univariate normal distribution 3.6 Normal-scaled inverse gamma distribution 3.7 Multivariate normal distribution 3.8 Normal inverse Wishart distribution 3.9 Conjugacy

Chapter 4: Fitting probability models

4.1 Maximum likelihood 4.2 Maximum a posteriori 4.3 The Bayesian approach 4.4 Worked example 1: Univariate normal 4.5 Worked example 2: Categorical distribution

Chapter 5: The normal distribution

5.1 Types of covariance matrix 5.2 Decomposition of covariance 5.3 Linear transformations of variables 5.4 Marginal distributions 5.5 Conditional distributions 5.6 Product of two normals 5.7 Change of variable

Part II: Machine learning for machine vision

Chapter 6: Learning and inference in vision

6.1 Computer vision problems 6.2 Types of model 6.3 Example 1: Regression 6.4 Example 2: Binary classification 6.5 Which type of model should we use? 6.6 Applications

Chapter 7: Modeling complex data densities

7.1 Normal classification model 7.2 Hidden variables 7.3 Expectation maximization 7.4 Mixture of Gaussians 7.5 The t-distribution 7.6 Factor analysis 7.7 Combining models 7.8 Expectation maximization in detail 7.9 Applications

Chapter 8: Regression models

8.1 Linear regression 8.2 Bayesian linear regression 8.3 Nonlinear regression 8.4 Kernels and the kernel trick 8.5 Gaussian process regression 8.6 Sparse linear regression 8.7 Dual linear regression 8.8 Relevance vector regression 8.9 Regression to multivariate data 8.10 Applications

Chapter 9: Classification models

9.1 Logistic regression 9.2 Bayesian logistic regression 9.3 Nonlinear logistic regression 9.4 Dual logistic regression 9.5 Kernel logistic regression 9.6 Relevance vector classification 9.7 Incremental fitting and boosting 9.8 Classification trees 9.9 Multiclass logistic regression 9.10 Random trees, forests, and ferns 9.11 Relation to non-probabilistic models 9.12 Applications

Part III: Connecting local models

Chapter 10: Graphical models

10.1 Conditional independence 10.2 Directed graphical models 10.3 Undirected graphical models 10.4 Comparing directed and undirected graphical models 10.5 Graphical models in computer vision 10.6 Inference in models with many unknowns 10.7 Drawing samples 10.8 Learning

Chapter 11: Models for chains and trees

11.1 Models for chains 11.2 MAP inference for chains 11.3 MAP inference for trees 11.4 Marginal posterior inference for chains 11.5 Marginal posterior inference for trees 11.6 Learning in chains and trees 11.7 Beyond chains and trees 11.8 Applications

Chapter 12: Models for grids

12.1 Markov random fields 12.2 MAP inference for binary pairwise MRFs 12.3 MAP inference for multilabel pairwise MRFs 12.4 Multilabel MRFs with non-convex potentials 12.5 Conditional random fields 12.6 Higher order models 12.7 Directed models for grids 12.8 Applications

Part IV: Preprocessing

Chapter 13: Image preprocessing and feature extraction

13.1 Per-pixel transformations 13.2 Edges, corners, and interest points 13.3 Descriptors 13.4 Dimensionality reduction

Part V: Models for geometry

Chapter 14: The pinhole camera

14.1 The pinhole camera 14.2 Three geometric problems 14.3 Homogeneous coordinates 14.4 Learning extrinsic parameters 14.5 Learning intrinsic parameters 14.6 Inferring three-dimensional world points 14.7 Applications

Chapter 15: Models for transformations

15.1 Two-dimensional transformation models 15.2 Learning in transformation models 15.3 Inference in transformation models 15.4 Three geometric problems for planes 15.5 Transformations between images 15.6 Robust learning of transformations 15.7 Applications

Chapter 16: Multiple cameras

16.1 Two-view geometry 16.2 The essential matrix 16.3 The fundamental matrix 16.4 Two-view reconstruction pipeline 16.5 Rectification 16.6 Multiview reconstruction 16.7 Applications

Part VI: Models for vision

Chapter 17: Models for shape

17.1 Shape and its representation 17.2 Snakes 17.3 Shape templates 17.4 Statistical shape models 17.5 Subspace shape models 17.6 Three-dimensional shape models 17.7 Statistical models for shape and appearance 17.8 Non-Gaussian statistical shape models 17.9 Articulated models 17.10 Applications

Chapter 18: Models for style and identity

18.1 Subspace identity model 18.2 Probabilistic linear discriminant analysis 18.3 Nonlinear identity models 18.4 Asymmetric bilinear models 18.5 Symmetric bilinear and multilinear models 18.6 Applications

Chapter 19: Temporal models

19.1 Temporal estimation framework 19.2 Kalman filter 19.3 Extended Kalman filter 19.4 Unscented Kalman filter 19.5 Particle filtering 19.6 Applications

Chapter 20: Models for visual words

20.1 Images as collections of visual words 20.2 Bag of words 20.3 Latent Dirichlet allocation 20.4 Single author–topic model 20.5 Constellation models 20.6 Scene models 20.7 Applications

Part VII: Appendices

Appendix A: Notation Appendix B: Optimization

B.1 Problem statement B.2 Choosing a search direction B.3 Line search B.4 Reparameterization

Appendix C: Liner algebra

C.1 Vectors C.2 Matrices C.3 Tensors C.4 Linear transformations C.5 Singular value decomposition C.6 Matrix calculus C.7 Common problems C.8 Tricks for inverting large matrices

Bibliography Index

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