| Description |
1 online resource |
| Series |
Springer INdAM series ; v. 54 |
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Springer INdAM series ; v. 54.
|
| 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 |
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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 |
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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 |
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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 |
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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 |
| Summary |
The volume collects several contributions to the INDAM workshop Mathematical Methods for Objects Reconstruction: from 3D Vision to 3D Printing held in Rome, February, 2021. The goal of the workshop was to discuss new methods and conceptual structures for managing these challenging problems. The chapters reflect this goal and the authors are academic researchers and some experts from industry working in the areas of 3D modeling, computer vision, 3D printing and/or developing new mathematical methods for these problems. The contributions present methodologies and challenges raised by the emergence of large-scale 3D reconstruction applications and low-cost 3D printers. The volume collects complementary knowledges from different areas of mathematics, computer science and engineering on research topics related to 3D printing, which are, so far, widely unexplored. Young researchers and future scientific leaders in the field of 3D data acquisition, 3D scene reconstruction, and 3D printing software development will find an excellent introduction to these problems and to the mathematical techniques necessary to solve them |
| Notes |
Online resource; title from PDF title page (SpringerLink, viewed August 11, 2023) |
| Subject |
Three-dimensional printing -- Mathematics
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Three-dimensional imaging -- Mathematics
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| Form |
Electronic book
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| Author |
Cristiani, Emiliano
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Falcone, Maurizio.
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Tozza, Silvia
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| ISBN |
9789819907762 |
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9819907764 |
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