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Table of contents
1 Introduction
1.1 Goals
1.2 Motivation
1.3 Challenges
1.3.1 3D local descriptors
1.3.2 Instance-level 2D-3D alignment
1.3.3 Category-level 2D-3D object recognition
1.4 Contributions
1.4.1 Wave Kernel Signature
1.4.2 3D discriminative visual elements
1.5 Thesis outline
1.6 Publications
2 Background
2.1 3D shape analysis
2.1.1 From the ideal shapes to discrete 3D models
2.1.2 3D point descriptors
2.1.3 3D shape alignment methods
2.2 Instance-level 2D-3D alignment
2.2.1 Contour-based methods
2.2.2 Local features for alignment
2.2.3 Global features for alignment
2.2.4 Relationship to our method
2.3 Category-level 2D-3D alignment
2.3.1 2D methods
2.3.2 3D methods
2.3.3 Relationship to our method
3 Wave Kernel Signature
3.1 Introduction
3.1.1 Motivation
3.1.2 From Quantum Mechanics to shape analysis
3.1.3 Spectral Methods for shape analysis
3.2 The Wave Kernel Signature
3.2.1 From heat diffusion to Quantum Mechanics
3.2.2 Schr¨odinger equation on a surface
3.2.3 A spectral signature for shapes
3.2.4 Global vs. local WKS
3.3 Mathematical Analysis of the WKS
3.3.1 Stability analysis
3.3.2 Spectral analysis
3.3.3 Invariance and discrimination
3.4 Experimental Results
3.4.1 Qualitative analysis
3.4.2 Quantitative evaluation
3.5 Applications
3.6 Conclusion
4 Painting-to-3D Alignment
4.1 Introduction
4.1.1 Motivation
4.1.2 From locally invariant to discriminatively trained features
4.1.3 Overview
4.2 3D discriminative visual elements
4.2.1 Learning 3D discriminative visual elements
4.2.2 Matching as classification
4.3 Discriminative visual elements for painting-to-3D alignment
4.3.1 View selection and representation
4.3.2 Least squares model for visual element selection and matching
4.3.3 Calibrated discriminative matching
4.3.4 Filtering elements unstable across viewpoint
4.3.5 Robust matching
4.3.6 Recovering viewpoint
4.3.7 Summary
4.4 Results and validation
4.4.1 Dataset for painting-to-3D alignment
4.4.2 Qualitative results
4.4.3 Quantitative evaluation
4.4.4 Algorithm analysis
4.5 Conclusion
5 Seeing 3D Chairs
5.1 Introduction
5.1.1 Motivation
5.1.2 From instance-level to category-level alignment
5.1.3 Approach Overview
5.2 Discriminative visual elements for category-level 3D-2D alignment
5.2.1 Representing a 3D shape collection
5.2.2 Calibrating visual element detectors
5.2.3 Matching spatial configurations of visual elements
5.3 Experiments and results
5.3.1 Large dataset of 3D chairs
5.3.2 Qualitative results
5.3.3 Quantitative evaluation
5.3.4 Algorithm analysis
5.4 Conclusion
6 Discusion
6.1 Contributions
6.2 Future work
6.2.1 Anisotropic Laplace-Beltrami operators
6.2.2 Object compositing
6.2.3 Use of 3D shape collection analysis
6.2.4 Synthetic data for deep convolutional network training
6.2.5 Exemplar based approach with CNN features
