Wang, Huan. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2007. / Includes bibliographical references (leaves 113-119). / Abstracts in English and Chinese. / Contents / Abstract --- p.i / Acknowledgement --- p.iii / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Learning Frameworks --- p.1 / Chapter 1.2 --- Sample Representation --- p.3 / Chapter 2 --- Background Study --- p.5 / Chapter 2.1 --- Tensor Algebra --- p.5 / Chapter 2.1.1 --- Tensor Unfolding (Flattening) --- p.6 / Chapter 2.1.2 --- Tensor Product --- p.6 / Chapter 2.2 --- Manifold Embedding and Dimensionality Reduction --- p.8 / Chapter 2.2.1 --- Principal Component Analysis (PCA) --- p.9 / Chapter 2.2.2 --- Metric Multidimensional Scaling (MDS) --- p.10 / Chapter 2.2.3 --- Isomap --- p.10 / Chapter 2.2.4 --- Locally Linear Embedding (LLE) --- p.11 / Chapter 2.2.5 --- Discriminant Analysis --- p.11 / Chapter 2.2.6 --- Laplacian Eigenmap --- p.14 / Chapter 2.2.7 --- Graph Embedding: A General Framework --- p.15 / Chapter 2.2.8 --- Maximum Variance Unfolding --- p.16 / Chapter 3 --- The Trace Ratio Optimization --- p.17 / Chapter 3.1 --- Introduction --- p.17 / Chapter 3.2 --- Dimensionality Reduction Formulations: Trace Ratio vs. Ratio Trace --- p.19 / Chapter 3.3 --- Efficient Solution of Trace Ratio Problem --- p.22 / Chapter 3.4 --- Proof of Convergency to Global Optimum --- p.23 / Chapter 3.4.1 --- Proof of the monotonic increase of λn --- p.23 / Chapter 3.4.2 --- Proof of Vn convergence and global optimum for λ --- p.24 / Chapter 3.5 --- Extension and Discussion --- p.27 / Chapter 3.5.1 --- Extension to General Constraints --- p.27 / Chapter 3.5.2 --- Discussion --- p.28 / Chapter 3.6 --- Experiments --- p.29 / Chapter 3.6.1 --- Dataset Preparation --- p.30 / Chapter 3.6.2 --- Convergence Speed --- p.31 / Chapter 3.6.3 --- Visualization of Projection Matrix --- p.31 / Chapter 3.6.4 --- Classification by Linear Trace Ratio Algorithms with Orthogonal Constraints --- p.33 / Chapter 3.6.5 --- Classification by Kernel Trace Ratio algorithms with General Constraints --- p.36 / Chapter 3.7 --- Conclusion --- p.36 / Chapter 4 --- A Convergent Solution to Tensor Subspace Learning --- p.40 / Chapter 4.1 --- Introduction --- p.40 / Chapter 4.2 --- Subspace Learning with Tensor Data --- p.43 / Chapter 4.2.1 --- Graph Embedding with Tensor Representation --- p.43 / Chapter 4.2.2 --- Computational Issues --- p.46 / Chapter 4.3 --- Solution Procedure and Convergency Proof --- p.46 / Chapter 4.3.1 --- Analysis of Monotonous Increase Property --- p.47 / Chapter 4.3.2 --- Proof of Convergency --- p.48 / Chapter 4.4 --- Experiments --- p.50 / Chapter 4.4.1 --- Data Sets --- p.50 / Chapter 4.4.2 --- Monotonicity of Objective Function Value --- p.51 / Chapter 4.4.3 --- Convergency of the Projection Matrices . . --- p.52 / Chapter 4.4.4 --- Face Recognition --- p.52 / Chapter 4.5 --- Conclusions --- p.54 / Chapter 5 --- Maximum Unfolded Embedding --- p.57 / Chapter 5.1 --- Introduction --- p.57 / Chapter 5.2 --- Maximum Unfolded Embedding --- p.59 / Chapter 5.3 --- Optimize Trace Ratio --- p.60 / Chapter 5.4 --- Another Justification: Maximum Variance Em- bedding --- p.60 / Chapter 5.5 --- Linear Extension: Maximum Unfolded Projection --- p.61 / Chapter 5.6 --- Experiments --- p.62 / Chapter 5.6.1 --- Data set --- p.62 / Chapter 5.6.2 --- Evaluation Metric --- p.63 / Chapter 5.6.3 --- Performance Comparison --- p.64 / Chapter 5.6.4 --- Generalization Capability --- p.65 / Chapter 5.7 --- Conclusion --- p.67 / Chapter 6 --- Regression on MultiClass Data --- p.68 / Chapter 6.1 --- Introduction --- p.68 / Chapter 6.2 --- Background --- p.70 / Chapter 6.2.1 --- Intuitive Motivations --- p.70 / Chapter 6.2.2 --- Related Work --- p.72 / Chapter 6.3 --- Problem Formulation --- p.73 / Chapter 6.3.1 --- Notations --- p.73 / Chapter 6.3.2 --- Regularization along Data Manifold --- p.74 / Chapter 6.3.3 --- Cross Manifold Label Propagation --- p.75 / Chapter 6.3.4 --- Inter-Manifold Regularization --- p.78 / Chapter 6.4 --- Regression on Reproducing Kernel Hilbert Space (RKHS) --- p.79 / Chapter 6.5 --- Experiments --- p.82 / Chapter 6.5.1 --- Synthetic Data: Nonlinear Two Moons . . --- p.82 / Chapter 6.5.2 --- Synthetic Data: Three-class Cyclones --- p.83 / Chapter 6.5.3 --- Human Age Estimation --- p.84 / Chapter 6.6 --- Conclusions --- p.86 / Chapter 7 --- Correspondence Propagation --- p.88 / Chapter 7.1 --- Introduction --- p.88 / Chapter 7.2 --- Problem Formulation and Solution --- p.92 / Chapter 7.2.1 --- Graph Construction --- p.92 / Chapter 7.2.2 --- Regularization on categorical Product Graph --- p.93 / Chapter 7.2.3 --- Consistency in Feature Domain and Soft Constraints --- p.96 / Chapter 7.2.4 --- Inhomogeneous Pair Labeling . --- p.97 / Chapter 7.2.5 --- Reliable Correspondence Propagation --- p.98 / Chapter 7.2.6 --- Rearrangement and Discretizing --- p.100 / Chapter 7.3 --- Algorithmic Analysis --- p.100 / Chapter 7.3.1 --- Selection of Reliable Correspondences . . . --- p.100 / Chapter 7.3.2 --- Computational Complexity --- p.102 / Chapter 7.4 --- Applications and Experiments --- p.102 / Chapter 7.4.1 --- Matching Demonstration on Object Recognition Databases --- p.103 / Chapter 7.4.2 --- Automatic Feature Matching on Oxford Image Transformation Database . --- p.104 / Chapter 7.4.3 --- Influence of Reliable Correspondence Number --- p.106 / Chapter 7.5 --- Conclusion and Future Works --- p.106 / Chapter 8 --- Conclusion and Future Work --- p.110 / Bibliography --- p.113

1 / Maclyn Le Bourgeois Hickey

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The aim of this study was to add to our understanding of interocular interactions in normally sighted children (Group I, N=20), normal adults (Group II, N=20) and adults with anisometropic amblyopia (N=12) by investigating responses to a range of visual functions under three kinds of viewing condition. Visual functions tested were visual acuity, contrast sensitivity and alignment sensitivity. Stimuli were generated on a Cambridge VSG card driving a high resolution monitor and FE liquid crystal goggles, enabling three kinds of viewing conditions: 1. Monocular (non-tested eye occluded), used as a baseline for most functions. 2. Dichoptic (uniform field presented to the non-tested eye but with a binocular fusion lock). 3. Binocular. In general, binocular performance was better than monocular (binocular summation) but so too was dichoptic performance (dichoptic advantage). However there was much variation within individuals (the three functions showing different summation/advantage pattern) and between individuals. Significant conclusions include: (a) Maturational windows for interocular interactions differ for different spatial visual functions. (b) Interpretations of results from one visual function cannot be applied automatically to other functions. (c) Care must be taken in interpreting results based on 5 or fewer subjects.

This thesis presents a new and powerful approach to the development of a general purpose machine vision system. The approach is inspired from anatomical considerations of the primate's vision system. The geometrical arrangement of cones on a primate's retina can be described in terms of a hexagonal grid. The importance of the hexagonal grid is that it possesses special computational features that are pertinent to the vision process. The fundamental thrust of this thesis emanates from the observation that this hexagonal grid can be described in terms of the mathematical object known as a Euclidean ring. The Euclidean ring is employed to generate an algebra of linear transformations which are appropriate for the processing of multidimensional vision data. A parallel autonomous segmentation algorithm for multidimensional vision data is described. The algebra and segmentation algorithm are implemented on a network of transputers. The implementation is discussed in the context of the outline of a general purpose machine vision system's design.