Galilean Differential Geometry of Moving Images 1st edition by Daniel Fagerstrom ISBN 3540219811 9783540219811

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Product details:

ISBN 10:       3540219811
ISBN 13: 978-3540219811
Author:         Daniel Fagerström
 

Galilean Differential Geometry of Moving Images 1st Table of contents:

1. Introduction

   • 1.1 Motivation and Objectives
   • 1.2 Galilean Differential Geometry in the Context of Moving Images
   • 1.3 Relevance of Differential Geometry to Image Motion Analysis
   • 1.4 Contributions of the Paper
   • 1.5 Structure of the Paper

2. Related Work

   • 2.1 Overview of Differential Geometry in Image Processing
   • 2.2 Galilean Transformations and Their Role in Motion Analysis
   • 2.3 Moving Image Analysis: Optical Flow, Motion Field, and Deformation
   • 2.4 Previous Applications of Galilean Geometry to Image Sequences
   • 2.5 Limitations of Existing Approaches

3. Preliminaries

   • 3.1 Overview of Galilean Geometry
   • 3.2 Basic Concepts in Differential Geometry (Curvature, Metric, Geodesics)
   • 3.3 Mathematical Framework for Moving Images
   • 3.4 Galilean Transformations: Mathematical Definition and Properties
   • 3.5 Relation to Classical Geometry and Kinematics

4. Galilean Geometry Applied to Moving Images

   • 4.1 Definition of Moving Images in Galilean Terms
   • 4.2 Differential Geometry of Image Curves and Surfaces
   • 4.3 Representation of Motion Using Galilean Frames of Reference
   • 4.4 Image Flow and Galilean Symmetry
   • 4.5 Geometric Features of Moving Images (Curvature, Torsion, and Flow)
   • 4.6 Galilean Covariance in Image Sequences

5. Motion Analysis Using Galilean Differential Geometry

   • 5.1 Tracking Image Features in Galilean Coordinates
   • 5.2 Differential Operators in the Galilean Framework
   • 5.3 Galilean-Invariant Descriptors for Motion Detection
   • 5.4 Kinematic Analysis of Moving Objects in Image Sequences
   • 5.5 Analyzing Deformations and Flows in Moving Images
   • 5.6 Galilean-Differential Operators for Optical Flow Estimation

6. Algorithm Design and Implementation

   • 6.1 Numerical Methods for Computing Geometric Quantities
   • 6.2 Algorithm for Tracking Curves and Surfaces in Moving Images
   • 6.3 Real-Time Computation of Galilean Derivatives
   • 6.4 Integration with Existing Image Processing Tools
   • 6.5 Optimizing Motion Estimation Using Galilean Geometry
   • 6.6 Handling Noise and Uncertainty in Motion Estimation

7. Experimental Setup and Evaluation

   • 7.1 Datasets for Moving Image Analysis
   • 7.2 Performance Metrics for Motion Estimation (e.g., accuracy, robustness)
   • 7.3 Experimental Setup: Hardware and Software Platforms
   • 7.4 Benchmarking Galilean Methods Against Other Motion Models
   • 7.5 Sensitivity to Environmental Factors (lighting, occlusion, etc.)
   • 7.6 Visual and Quantitative Results

8. Results and Discussion

   • 8.1 Comparison of Galilean Differential Geometry with Traditional Methods
   • 8.2 Effectiveness of Galilean Geometry in Capturing Image Motion
   • 8.3 Handling Complex Motion Patterns and Deformations
   • 8.4 Robustness of the Method to Noise and Distortions
   • 8.5 Visual Qualitative Analysis of Motion Estimation
   • 8.6 Limitations and Future Improvements

9. Applications of Galilean Differential Geometry in Moving Images

   • 9.1 Motion Tracking and Object Detection
   • 9.2 Video Stabilization and Enhancement
   • 9.3 Optical Flow and Motion Segmentation
   • 9.4 Robotics and Autonomous Vehicles
   • 9.5 Medical Imaging and Biomechanics
   • 9.6 Augmented Reality and Virtual Reality

10. Challenges and Future Directions

• 10.1 Extending Galilean Geometry to Non-Rigid Motion
• 10.2 Real-Time Motion Analysis and Optimization
• 10.3 Multiview and 3D Motion Reconstruction Using Galilean Methods
• 10.4 Incorporating Deep Learning with Galilean Differential Geometry
• 10.5 Future Research Directions in Moving Image Analysis

11. Conclusion

• 11.1 Summary of Key Contributions
• 11.2 Impact of Galilean Differential Geometry on Moving Image Analysis
• 11.3 Final Thoughts and Outlook for Future Research

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