Matching Tensors for Automatic Correspondence and Registration 1st edition by Ajmal Mian, Mohammed Bennamoun, Robyn Owens ISBN 3540219835 9783540219835
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Authors:Ajmal S. Mian, Mohammed Bennamoun; Robyn Owens , Tags:Computer Vision – ECCV 2004 , Author sort:Ajmal S. Mian, Mohammed Bennamoun & Owens, Robyn , Languages:Languages:eng , Published:Published:Mar 2004
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ISBN 10: 3540219835
ISBN 13: 978-3540219835
Author: Ajmal S. Mian, Mohammed Bennamoun, Robyn Owens
Complete 3-D modeling of a free-form object requires acquisition from multiple view-points. These views are then required to be registered in a common coordinate system by establishing correspondence between them in their regions of overlap. In this paper, we present an automatic correspondence technique for pair-wise registration of different views of a free-form object. The technique is based upon a novel robust representation scheme reported in this paper. Our representation scheme defines local 3-D grids over the object’s surface and represents the surface inside each grid by a fourth order tensor. Multiple tensors are built for the views which are then matched, using a correlation and verification technique to establish correspondence between a model and a scene tensor. This correspondence is then used to derive a rigid transformation that aligns the two views. The transformation is verified and refined using a variant of ICP. Our correspondence technique is fully automatic and does not assume any knowledge of the viewpoints or regions of overlap of the data sets. Our results show that our technique is accurate, robust, efficient and independent of the resolution of the views.
Matching Tensors for Automatic Correspondence and Registration 1st Table of contents:
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Introduction
- 1.1 Background and Motivation
- 1.2 Correspondence and Registration Problems
- 1.3 The Role of Tensors in Correspondence and Registration
- 1.4 Objectives and Contributions of the Paper
- 1.5 Structure of the Paper
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Related Work
- 2.1 Overview of Correspondence and Registration Methods
- 2.2 Techniques Based on Geometric Matching
- 2.3 Tensor Decompositions and Their Applications
- 2.4 Tensor-Based Approaches to Correspondence and Registration
- 2.5 Limitations and Open Challenges in Existing Methods
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Mathematical Foundations of Tensors
- 3.1 Definition and Basic Properties of Tensors
- 3.2 Tensor Notation and Operations
- 3.3 Tensor Decomposition and Factorization Techniques
- 3.4 Eigenvalues and Eigenvectors of Tensors
- 3.5 Applications of Tensors in Geometry and Image Analysis
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Tensor Matching for Correspondence
- 4.1 Defining Correspondence in Multidimensional Spaces
- 4.2 Tensor-Based Matching Algorithms
- 4.3 Constructing Correspondence Metrics Using Tensors
- 4.4 Matching Features Across Multiple Datasets Using Tensors
- 4.5 Challenges in Handling Noisy and Incomplete Data
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Tensor Registration Techniques
- 5.1 Overview of Registration Problem
- 5.2 Tensor-Based Approaches to Image and Shape Registration
- 5.3 Optimal Alignment of Tensors: Minimization Strategies
- 5.4 Global vs. Local Registration Techniques Using Tensors
- 5.5 Robustness to Deformations and Variations in Data
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Algorithm Design and Implementation
- 6.1 Overview of the Proposed Algorithm for Tensor Matching and Registration
- 6.2 Tensor Representation of Data for Registration and Correspondence
- 6.3 Key Steps in the Algorithm: Initialization, Matching, and Registration
- 6.4 Computational Complexity and Optimization Considerations
- 6.5 Software Implementation and Tools Used
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Experimental Setup and Evaluation
- 7.1 Datasets for Testing: Shape, Image, and Volumetric Data
- 7.2 Performance Metrics: Accuracy, Precision, and Recall
- 7.3 Experimental Protocols: Cross-validation and Benchmarking
- 7.4 Comparative Evaluation with Traditional Registration Methods
- 7.5 Results from Synthetic and Real-World Data
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Results and Discussion
- 8.1 Performance of Tensor-Based Matching and Registration
- 8.2 Handling Variations in Scale, Rotation, and Noise
- 8.3 Qualitative and Quantitative Evaluation of Results
- 8.4 Discussion of Error Analysis and Limitations
- 8.5 Insights into the Practical Utility of Tensor Matching
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Applications of Tensor Matching and Registration
- 9.1 Medical Imaging and Anatomical Registration
- 9.2 3D Shape Matching for Computer Vision and Graphics
- 9.3 Image Registration in Remote Sensing and Satellite Imaging
- 9.4 Robotics: Matching Sensor Data for Object Recognition
- 9.5 Cross-Modality Registration: Multi-View and Multi-Sensor Data
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Challenges and Future Directions
- 10.1 Handling Large-Scale Datasets and Real-Time Processing
- 10.2 Improving Robustness to Occlusions and Missing Data
- 10.3 Integrating Deep Learning with Tensor Matching Techniques
- 10.4 Generalizing Tensor Matching to Higher Dimensions
- 10.5 Future Research Directions in Tensor-Based Registration and Correspondence
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Conclusion
- 11.1 Summary of Key Contributions and Findings
- 11.2 Practical Implications of Tensor Matching and Registration
- 11.3 Limitations and Open Problems
- 11.4 Final Remarks and Future Work
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