Deformable Density Matching for 3D Non rigid Registration of Shapes 1st Edition by Arunabha S Roy, Ajay Gopinath, Anand Rangarajan ISBN 9783540757573

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ISBN 10: 
ISBN 13: 9783540757573
Author: Arunabha S Roy, Ajay Gopinath, Anand Rangarajan

There exists a large body of literature on shape matching and registration in medical image analysis. However, most of the previous work is focused on matching particular sets of features—point-sets, lines, curves and surfaces. In this work, we forsake specific geometric shape representations and instead seek probabilistic representations—specifically Gaussian mixture models—of shapes. We evaluate a closed-form distance between two probabilistic shape representations for the general case where the mixture models differ in variance and the number of components. We then cast non-rigid registration as a deformable density matching problem. In our approach, we take one mixture density onto another by deforming the component centroids via a thin-plate spline (TPS) and also minimizing the distance with respect to the variance parameters. We validate our approach on synthetic and 3D arterial tree data and evaluate it on 3D hippocampal shapes.

 Deformable Density Matching for 3D Non-rigid Registration of Shapes 1st Table of contents:

• Preliminaries
  2.1 3D Shape Registration: Overview and Definitions
  2.2 Non-rigid Registration Techniques
  2.3 Deformable Models in Shape Matching
  2.4 Density Matching and Its Relevance in Registration

• Deformable Density Matching
  3.1 Overview of Deformable Models
  3.2 Mathematical Formulation of Density Matching
  3.3 Energy Functionals and Optimization in Deformable Models
  3.4 Comparison with Other Non-rigid Registration Methods

• Methodology for 3D Non-rigid Registration
  4.1 Problem Setup and Assumptions
  4.2 Step-by-Step Approach to Deformable Density Matching
  4.3 Model Representation and Data Structures
  4.4 Optimization Strategies for Non-rigid Registration

• Challenges in 3D Non-rigid Registration
  5.1 Handling Local Deformations and Topological Changes
  5.2 Addressing Noise and Inaccuracies in 3D Data
  5.3 Computational Complexity and Scalability
  5.4 Initial Alignment and Global Consistency

• Evaluation and Experimental Results
  6.1 Experimental Setup and Data Collection
  6.2 Quantitative Metrics for Registration Accuracy
  6.3 Performance Comparison with Existing Methods
  6.4 Case Studies: Applications in Medical Imaging and Computer Vision

• Applications of Deformable Density Matching
  7.1 Medical Imaging: Registration of Organs and Tissues
  7.2 Computer-Aided Design (CAD) and 3D Modeling
  7.3 Robotics: Shape Matching for Object Recognition
  7.4 Archaeology and Cultural Heritage Preservation

• Discussion
  8.1 Insights from Deformable Density Matching for 3D Registration
  8.2 Limitations and Open Problems
  8.3 Potential Improvements in Model Accuracy and Efficiency
  8.4 Directions for Future Research in Non-rigid Registration

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