| Preface | 5 |
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| Part I: Manifold Learning and Clustering/Segmentation | 6 |
| Part II: Tracking | 7 |
| Part III: Motion Analysis and Behavior Modeling | 9 |
| Part IV: Gesture and Action Recognition | 10 |
| Acknowledgements | 11 |
| Contents | 12 |
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| Manifold Learning and Clustering/Segmentation | 14 |
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| Practical Algorithms of Spectral Clustering: Toward Large-Scale Vision-Based Motion Analysis | 15 |
| Introduction | 15 |
| Spectral Clustering | 16 |
| Principle | 16 |
| Algorithm | 18 |
| Related Work | 18 |
| Dimensionality Reduction by Random Projection | 19 |
| Random Projection | 19 |
| Acceleration of Kernel Computation | 20 |
| Random Sampling as Random Projection | 20 |
| Using a Minority of Image Pixels | 21 |
| Efficient Random Projection | 21 |
| Size Reduction of Affinity Matrix by Sampling | 23 |
| Random Subsampling | 24 |
| Pre-clustering | 25 |
| Practical Ncut Algorithms | 26 |
| Randomized Ncut Algorithm | 26 |
| Invocation of Dimensionality Reduction | 27 |
| Relation to the Original Algorithm | 27 |
| Scale Selection | 27 |
| Number of Clusters | 28 |
| Ncut Algorithm with Pre-clustering | 28 |
| Experiments | 29 |
| Performance Tests | 29 |
| Error Analysis | 29 |
| Computational Cost | 30 |
| Image Segmentation | 31 |
| Motion Segmentation | 32 |
| Video Shot Segmentation | 33 |
| Segmentation Using Appearance-Based Similarities | 33 |
| Segmentation with Local Scaling | 33 |
| Conclusions | 35 |
| Appendix: Clustering Scores | 37 |
| References | 37 |
| Riemannian Manifold Clustering and Dimensionality Reduction for Vision-Based Analysis | 39 |
| Introduction | 40 |
| Chapter summary | 42 |
| Review of Local Nonlinear Dimensionality Reduction Methods in Euclidean Spaces | 43 |
| NLDR for a Nonlinear Manifold | 43 |
| Calculation of M in LLE | 44 |
| Calculation of M in LE | 44 |
| Calculation of M in HLLE | 45 |
| NLDR for a Single Subspace | 45 |
| Manifold Clustering and Dimensionality Reduction Using the Euclidean Metric | 47 |
| Manifold Clustering and Dimensionality Reduction for a k-Separated Union of k-Connected Nonlinear Manifolds | 47 |
| Degeneracies for a k-Separated Union of k-Connected Linear Manifolds | 48 |
| Manifold Clustering and Dimensionality Reduction Using the Riemannian Metric | 50 |
| Review of Riemannian Manifolds | 50 |
| Extending Manifold Clustering and Dimensionality Reduction to Riemannian Manifolds | 53 |
| Selection of the Riemannian kNN | 53 |
| Riemannian Calculation of M for LLE | 53 |
| Riemannian Calculation of M for LE | 54 |
| Riemannian Calculation of M for HLLE | 54 |
| Calculation of the Embedding Coordinates | 54 |
| Extending Manifold Clustering to Riemannian Manifolds | 55 |
| Experiments | 55 |
| Application and Experiments on SPSD(3) | 55 |
| Application and Experiments on the Space of Probability Density Functions | 58 |
| Conclusion and Open Research Problems | 62 |
| References | 63 |
| Manifold Learning for Multi-dimensional Auto-regressive Dynamical Models | 66 |
| Introduction | 66 |
| Learning Pullback Metrics for Linear Models | 68 |
| Pullback Metrics | 68 |
| Fisher Metric for Linear Models | 69 |
| General Framework | 69 |
| Objective Functions: Classification Performance and Inverse Volume | 71 |
| Pullback Metrics for Multidimensional Autoregressive Models | 72 |
| The Basis Manifold | 72 |
| The Basis Manifold AR(2,1) in the Scalar Case | 72 |
| The Multidimensional Case | 73 |
| Product Metric | 73 |
| Geodesics | 74 |
| An Automorphism for the Scalar Case | 75 |
| Product and Global Automorphisms for AR(2,p) | 75 |