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Table of Contents
Intro
Preface
Contents
An Overview of Some Mathematical Techniques and Problems Linking 3D Vision to 3D Printing
1 Introduction
2 Modeling with a Single Input Image
2.1 Modelization of the Surface Reflectance
2.2 Some Hints on Theoretical Issues: Viscosity Solutions and Boundary Conditions
2.3 Modelization of the Camera and the Light
3 Modeling with More Input Images
3.1 Photometric Stereo Technique
3.2 Multi-View SfS
4 An Example of Numerical Resolution
5 Moving from 3D Vision to 3D Printing
5.1 Overview
5.2 Front Propagation Problem, Level-set Method and the Eikonal Equation
5.3 Computation of the Signed Distance Function from a Surface
6 Handling Overhangs
6.1 Detecting Overhangs via Front Propagation
6.2 Fixing Overhangs via Level-set Method 1: A Direct Approach
6.3 Fixing Overhangs via Level-set Method 2: Topological Optimization with Shape Derivatives
7 Building Object-Dependent Infill Structures
8 Conclusions
Appendix A: The STL Format
Appendix B: The G-code Format
References
Photometric Stereo with Non-Lambertian Preprocessing and Hayakawa Lighting Estimation for Highly Detailed ShapeReconstruction
1 Introduction
2 Mathematical Setup
3 Photometric Stereo with Known Lighting
4 Hayakawa's Lighting Estimation Setup
5 The Oren-Nayar Model
6 Numerical Results
7 Summary and Conclusion
References
Shape-from-Template with Camera Focal Length Estimation
1 Introduction
1.1 Shape-from-Template (SfT)
1.2 Chapter Innovations
1.3 Chapter Organization
2 Related Works
2.1 SfT Approaches
2.1.1 Closed-Form Solutions
2.1.2 Optimization-Based Solutions
2.1.3 CNN-Based Solutions
2.2 fSfT Solutions
3 Methodology
3.1 Problem Modeling
3.1.1 Template Geometry and Deformation Parameterization
3.1.2 Cost Function
3.1.3 Cost Normalization Summary and Weight Hyper-parameters
3.2 Optimization
3.2.1 Approach Overview
3.2.2 Generating the Initialization Set
3.2.3 Optimization Process and Pseudocode
4 Experimental Results
4.1 Datasets
4.2 Evaluation Metrics
4.3 Success Rates
4.4 FLPE and SE Results
4.5 Results Visualizations
4.6 Convergence Basin
4.7 Results Summary
4.8 Additional Initialization Sensitivity Experiments
4.9 Isometric Weight Sensitivity
5 Conclusion
Appendix
1 Overview
2 Discrete Quasi-isometric Cost Implementation
2.1 Triangle Geometry and Embedding Functions
2.2 Cost
3 Optimization Termination Conditions
4 SfT Implementation Details
4.1 MDH
4.2 PnP
5 Dataset Descriptions
6 Additional Initialization Sensitivity Experiments
6.1 Initialization Policies
6.2 Dataset Versions
6.3 Results
7 Computation Cost Analysis
References
Reconstruction of a Botanical Tree from a 3D Point Cloud
Preface
Contents
An Overview of Some Mathematical Techniques and Problems Linking 3D Vision to 3D Printing
1 Introduction
2 Modeling with a Single Input Image
2.1 Modelization of the Surface Reflectance
2.2 Some Hints on Theoretical Issues: Viscosity Solutions and Boundary Conditions
2.3 Modelization of the Camera and the Light
3 Modeling with More Input Images
3.1 Photometric Stereo Technique
3.2 Multi-View SfS
4 An Example of Numerical Resolution
5 Moving from 3D Vision to 3D Printing
5.1 Overview
5.2 Front Propagation Problem, Level-set Method and the Eikonal Equation
5.3 Computation of the Signed Distance Function from a Surface
6 Handling Overhangs
6.1 Detecting Overhangs via Front Propagation
6.2 Fixing Overhangs via Level-set Method 1: A Direct Approach
6.3 Fixing Overhangs via Level-set Method 2: Topological Optimization with Shape Derivatives
7 Building Object-Dependent Infill Structures
8 Conclusions
Appendix A: The STL Format
Appendix B: The G-code Format
References
Photometric Stereo with Non-Lambertian Preprocessing and Hayakawa Lighting Estimation for Highly Detailed ShapeReconstruction
1 Introduction
2 Mathematical Setup
3 Photometric Stereo with Known Lighting
4 Hayakawa's Lighting Estimation Setup
5 The Oren-Nayar Model
6 Numerical Results
7 Summary and Conclusion
References
Shape-from-Template with Camera Focal Length Estimation
1 Introduction
1.1 Shape-from-Template (SfT)
1.2 Chapter Innovations
1.3 Chapter Organization
2 Related Works
2.1 SfT Approaches
2.1.1 Closed-Form Solutions
2.1.2 Optimization-Based Solutions
2.1.3 CNN-Based Solutions
2.2 fSfT Solutions
3 Methodology
3.1 Problem Modeling
3.1.1 Template Geometry and Deformation Parameterization
3.1.2 Cost Function
3.1.3 Cost Normalization Summary and Weight Hyper-parameters
3.2 Optimization
3.2.1 Approach Overview
3.2.2 Generating the Initialization Set
3.2.3 Optimization Process and Pseudocode
4 Experimental Results
4.1 Datasets
4.2 Evaluation Metrics
4.3 Success Rates
4.4 FLPE and SE Results
4.5 Results Visualizations
4.6 Convergence Basin
4.7 Results Summary
4.8 Additional Initialization Sensitivity Experiments
4.9 Isometric Weight Sensitivity
5 Conclusion
Appendix
1 Overview
2 Discrete Quasi-isometric Cost Implementation
2.1 Triangle Geometry and Embedding Functions
2.2 Cost
3 Optimization Termination Conditions
4 SfT Implementation Details
4.1 MDH
4.2 PnP
5 Dataset Descriptions
6 Additional Initialization Sensitivity Experiments
6.1 Initialization Policies
6.2 Dataset Versions
6.3 Results
7 Computation Cost Analysis
References
Reconstruction of a Botanical Tree from a 3D Point Cloud