Consistency Conditions on the Medial Axis 1st edition by Anthony Pollitt, Peter GibliN, Benjamin Kimia ISBN 3540219835 9783540219835

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ISBN 10:       3540219835
ISBN 13: 978-3540219835
Author:         Anthony Pollitt, Peter GibliN, Benjamin Kimia
 

Consistency Conditions on the Medial Axis 1st Table of contents:

• Introduction

  • 1.1 Background and Motivation
  • 1.2 The Medial Axis: Definition and Significance
  • 1.3 Applications of the Medial Axis in Computational Geometry
  • 1.4 Consistency Conditions: Why They Matter
  • 1.5 Objectives and Contributions of the Paper
  • 1.6 Structure of the Paper

• Related Work

  • 2.1 Historical Overview of the Medial Axis
  • 2.2 Computational Approaches to the Medial Axis
  • 2.3 Previous Studies on Consistency Conditions
  • 2.4 The Role of Medial Axis in Shape Representation and Analysis
  • 2.5 Limitations and Open Questions in Medial Axis Consistency

• Mathematical Foundations of the Medial Axis

  • 3.1 Geometric Definition of the Medial Axis
  • 3.2 Properties of the Medial Axis in Simple and Complex Shapes
  • 3.3 The Relationship Between the Medial Axis and Voronoi Diagram
  • 3.4 Mathematical Formulation of Distance Functions
  • 3.5 Medial Axis in 2D and 3D Spaces

• Consistency Conditions for the Medial Axis

  • 4.1 The Concept of Consistency in Geometric Models
  • 4.2 Necessary and Sufficient Conditions for Medial Axis Consistency
  • 4.3 Geometric Interpretation of Consistency Conditions
  • 4.4 Stability and Robustness of the Medial Axis Under Perturbations
  • 4.5 Consistency Conditions in Different Topological Settings

• Geometric Algorithms for Computing the Medial Axis

  • 5.1 Overview of Medial Axis Extraction Techniques
  • 5.2 Exact and Approximate Algorithms for Medial Axis Computation
  • 5.3 Ensuring Consistency in Medial Axis Algorithms
  • 5.4 Computational Complexity of Medial Axis Extraction
  • 5.5 Numerical Stability and Error Analysis in Medial Axis Computation

• Applications of Consistent Medial Axis

  • 6.1 Shape Reconstruction and Simplification
  • 6.2 Path Planning and Motion Analysis
  • 6.3 Object Recognition and Matching Using the Medial Axis
  • 6.4 Topological and Geometrical Data Analysis
  • 6.5 Medical Imaging: Use of Medial Axis for Anatomical Shape Analysis

• Experimental Setup and Evaluation

  • 7.1 Datasets and Test Cases for Medial Axis Computation
  • 7.2 Evaluating Medial Axis Consistency in Real-World Shapes
  • 7.3 Performance Metrics: Accuracy, Stability, and Robustness
  • 7.4 Benchmarking Medial Axis Consistency Algorithms
  • 7.5 Results of Consistent Medial Axis Computations

• Results and Discussion

  • 8.1 Visual Results: Medial Axis Consistency in Different Shapes
  • 8.2 Impact of Consistency Conditions on Algorithm Performance
  • 8.3 Comparison with Inconsistent Medial Axis Algorithms
  • 8.4 Error Analysis: Handling Perturbations and Inaccuracies
  • 8.5 Insights from Experimental Results

• Challenges and Future Directions

  • 9.1 Handling Complex Shapes and Non-Smooth Boundaries
  • 9.2 Generalizing Consistency Conditions for Higher-Dimensional Spaces
  • 9.3 Real-Time Medial Axis Computation and Consistency Checking
  • 9.4 Integrating Medial Axis Consistency with Other Shape Analysis Tools
  • 9.5 Future Research on Medial Axis Applications in Computational Biology and Robotics

• Conclusion

  • 10.1 Summary of Key Findings
  • 10.2 Contributions to Medial Axis Theory and Computation
  • 10.3 Practical Implications of Medial Axis Consistency
  • 10.4 Final Remarks and Future Work

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