Acknowledgements -- Contents -- Introduction -- Example Applications of Statistical Models -- Detecting Osteoporosis Using Dental Radiographs -- Detecting Vertebral Fractures -- Face Identification, Tracking, and Simulation of Ageing -- Overview -- Statistical Models of Shape and Appearance -- Finite-Dimensional Representations of Shape -- Shape Alignment -- Statistics of Shapes -- Principal Component Analysis -- Modelling Distributions of Sets of Shapes -- Gaussian Models -- Kernel Density Estimation -- Kernel Principal Component Analysis -- Using Principal Components to Constrain Shape -- Infinite-Dimensional Representations of Shape -- Parameterised Representations of Shape -- Applications of Shape Models -- Active Shape Models -- Active Appearance Models -- Establishing Correspondence -- The Correspondence Problem -- Approaches to Establishing Correspondence -- Manual Landmarking -- Automatic Methods of Establishing Correspondence -- Correspondence by Parameterisation -- Distance-Based Correspondence -- Feature-Based Correspondence -- Correspondence Based on Physical Properties -- Image-Based Correspondence -- Summary -- Correspondence by Optimisation -- Objective Function -- Manipulating Correspondence -- Optimisation -- Objective Functions -- Shape-Based Objective Functions -- Euclidian Distance and the Trace of the Model Covariance -- Bending Energy -- Curvature -- Shape Context -- Model-Based Objective Functions -- The Determinant of the Model Covariance -- Measuring Model Properties by Bootstrapping -- Specificity -- Generalization Ability -- An Information Theoretic Objective Function -- Shannon Codeword Length and Shannon Entropy -- Description Length for a Multivariate Gaussian Model -- Approximations to MDL -- Gradient of Simplified MDL Objective Functions -- Concluding Remarks -- Re-parameterisation of Open and Closed Curves.

Open Curves -- Piecewise-Linear Re-parameterisation -- Recursive Piecewise-Linear Re-parameterisation -- Localized Re-parameterisation -- Kernel-Based Representation of Re-parameterisation -- Cauchy Kernels -- Polynomial Re-parameterisation -- Differentiable Re-parameterisations for Closed Curves -- Wrapped Kernel Re-parameterisation for Closed Curves -- Use in Optimisation -- Parameterisation and Re-parameterisation of Surfaces -- Surface Parameterisation -- Initial Parameterisation for Open Surfaces -- Initial Parameterisation for Closed Surfaces -- Defining a Continuous Parameterisation -- Removing Area Distortion -- Consistent Parameterisation -- Re-parameterisation of Surfaces -- Re-parameterisation of Open Surfaces -- Recursive Piecewise Linear Re-parameterisation -- Localized Re-parameterisation -- Re-parameterisation of Closed Surfaces -- Recursive Piecewise-Linear Re-parameterisation -- Localized Re-parameterisation -- Cauchy Kernel Re-parameterisation -- Symmetric Theta Transformation -- Asymmetric Theta Transformations -- Shear Transformations -- Re-parameterisation of Other Topologies -- Use in Optimisation -- Optimisation -- A Tractable Optimisation Approach -- Optimising One Example at a Time -- Stochastic Selection of Values for Auxiliary Parameters -- Gradient Descent Optimisation -- Optimising Pose -- Tailoring Optimisation -- Closed Curves and Surfaces -- Open Surfaces -- Multi-part Objects -- Implementation Issues -- Calculating the Covariance Matrix by Numerical Integration -- Numerical Estimation of the Gradient -- Sampling the Set of Shapes -- Detecting Singularities in the Re-parameterisations -- Example Optimisation Routines -- Example 1: Open Curves -- Example 2: Open Surfaces -- Non-parametric Regularization -- Regularization -- Non-parametric Regularization -- Fluid Regularization -- The Shape Manifold -- The Induced Metric.

Tangent Space -- Covariant Derivatives -- Shape Images -- Implementation Issues -- Iterative Updating of Shape Images -- Dealing with Shapes with Spherical Topology -- Avoiding Singularities by Re-gridding -- Example Implementation of Non-parametric Regularization -- Example Optimisation Routines Using Iterative Updating of Shape Images -- Example 3: Open Surfaces Using Shape Images -- Example 4: Optimisation of Closed Surfaces Using Shape Images -- Evaluation of Statistical Models -- Evaluation Using Ground Truth -- Evaluation in the Absence of Ground Truth -- Specificity and Generalization: Quantitative Measures -- Specificity and Generalization as Graph-Based Estimators -- Evaluating the Coefficients n, -- Generalized Specificity -- Specificity and Generalization in Practice -- Discussion -- Appendix Thin-Plate and Clamped-Plate Splines -- Curvature and Bending Energy -- Variational Formulation -- Green's Functions -- Green's Functions for the Thin-Plate Spline -- Green's Functions for the Clamped-Plate Spline -- Appendix Differentiating the Objective Function -- Finite-Dimensional Shape Representations -- The Pseudo-Inverse -- Varying the Shape -- From PCA to Singular Value Decomposition -- Infinite Dimensional Shape Representations -- Glossary -- References -- Index.