Line Geometry for 3D Shape Understanding and Reconstruction 1st edition by Helmut Pottmann, Michael Hofer, Boris Odehnal, Johannes Wallner ISBN 3540219842 9783540219842

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Product details:

ISBN 10:       3540219842
ISBN 13: 978-3540219842
Author:       Helmut Pottmann, Michael Hofer, Boris Odehnal, Johannes Wallner  
 

Line Geometry for 3D Shape Understanding and Reconstruction 1st Table of contents:

1. Introduction

   • 1.1 Background and Motivation
   • 1.2 The Role of Line Geometry in 3D Shape Understanding
   • 1.3 Challenges in 3D Shape Reconstruction
   • 1.4 Objectives and Contributions of the Paper
   • 1.5 Structure of the Paper

2. Fundamentals of Line Geometry

   • 2.1 Basics of Line Geometry in 2D and 3D
   • 2.2 Geometrical Properties of Lines and Curves
   • 2.3 Line-Based Representations for 3D Shapes
   • 2.4 Differential Geometry and Line Geometry
   • 2.5 Overview of Line-Based Approaches in Computer Vision

3. 3D Shape Understanding Using Line Geometry

   • 3.1 Representation of 3D Shapes through Line Features
   • 3.2 Understanding Surface and Shape Structure via Lines
   • 3.3 Line Intersections and Their Role in Shape Understanding
   • 3.4 Detecting and Extracting Line Features from 3D Data
   • 3.5 Applications in Shape Recognition and Object Detection

4. Line-Based Reconstruction Techniques

   • 4.1 Overview of 3D Shape Reconstruction Methods
   • 4.2 Line-Based Approaches to 3D Surface Reconstruction
   • 4.3 Using Line Geometry for Edge Detection in 3D Models
   • 4.4 Curve and Surface Fitting Techniques with Line Geometry
   • 4.5 Integrating Line Features with Point Cloud Data

5. Methodology for 3D Shape Reconstruction

   • 5.1 Overview of the Proposed Line Geometry-Based Approach
   • 5.2 Step 1: Feature Extraction from 3D Data (Lines, Edges, and Curves)
   • 5.3 Step 2: Line-Based Geometry Modeling and Fitting
   • 5.4 Step 3: Surface Reconstruction from Line Features
   • 5.5 Step 4: Refining and Optimizing the 3D Reconstruction
   • 5.6 Handling Noisy and Incomplete Data

6. Algorithms for Line Geometry in 3D Shape Reconstruction

   • 6.1 Line Extraction Algorithms from 3D Point Clouds
   • 6.2 Algorithms for Line Fitting and Curve Reconstruction
   • 6.3 Geometric Processing Algorithms for Line-Based Reconstruction
   • 6.4 Optimizing Line-Based Approaches for Computational Efficiency
   • 6.5 Robustness and Accuracy of Line Geometry Methods

7. Experimental Setup and Evaluation

   • 7.1 Dataset Description and Sources of 3D Data (e.g., LiDAR, Stereo Images)
   • 7.2 Evaluation Metrics for 3D Reconstruction Accuracy
   • 7.3 Setup for Line Feature Extraction and Testing
   • 7.4 Performance of Line-Based Reconstruction Methods
   • 7.5 Comparison with Traditional 3D Reconstruction Techniques

8. Results and Discussion

   • 8.1 Visual Results: Line Geometry-Based 3D Reconstructions
   • 8.2 Quantitative Analysis: Reconstruction Accuracy and Efficiency
   • 8.3 Comparison with Other 3D Shape Understanding Methods
   • 8.4 Impact of Line Geometry on Reconstruction Quality
   • 8.5 Case Studies and Real-World Applications

9. Applications of Line Geometry in 3D Shape Understanding

   • 9.1 Applications in Robotics and Object Manipulation
   • 9.2 3D Reconstruction for Augmented Reality and Virtual Reality
   • 9.3 Architectural and Engineering Design
   • 9.4 Medical Imaging and 3D Visualization
   • 9.5 Cultural Heritage Preservation and Digital Archiving

10. Challenges and Future Directions

    • 10.1 Handling Complex Geometries and Non-Linear Shapes
    • 10.2 Improving Robustness Against Noise and Data Incompleteness
    • 10.3 Real-Time Line-Based 3D Reconstruction Techniques
    • 10.4 Integration with Other 3D Data Representation Methods (e.g., Meshes, Volumes)
    • 10.5 Expanding Applications to Dynamic and Moving Objects

11. Conclusion

    • 11.1 Summary of Key Findings
    • 11.2 Contributions to 3D Shape Understanding and Reconstruction
    • 11.3 Practical Implications for Real-World Applications
    • 11.4 Future Research Directions
12.  

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