Geodesic Loxodromes for Diffusion Tensor Interpolation and Difference Measurement 1st Edition by Gordon Kindlmann, Raul San Jose Estepar, Marc Niethammer, Steven Haker, Carl Fredrik Westin ISBN 9783540757573

Geodesic-Loxodromes for Diffusion Tensor Interpolation and Difference Measurement 1st Edition by Gordon Kindlmann, Raul San Jose Estepar, Marc Niethammer, Steven Haker, Carl Fredrik Westin – Ebook PDF Instant Download/Delivery. 9783540757573
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ISBN 13: 9783540757573
Author: Gordon Kindlmann, Raul San Jose Estepar, Marc Niethammer, Steven Haker, Carl Fredrik Westin

In algorithms for processing diffusion tensor images, two common ingredients are interpolating tensors, and measuring the distance between them. We propose a new class of interpolation paths for tensors, termed geodesic-loxodromes, which explicitly preserve clinically important tensor attributes, such as mean diffusivity or fractional anisotropy, while using basic differential geometry to interpolate tensor orientation. This contrasts with previous Riemannian and Log-Euclidean methods that preserve the determinant. Path integrals of tangents of geodesic-loxodromes generate novel measures of over-all difference between two tensors, and of difference in shape and in orientation.

Geodesic-Loxodromes for Diffusion Tensor Interpolation and Difference Measurement 1st Table of contents:

• Introduction
  1.1 Motivation and Background
  1.2 Diffusion Tensor Imaging (DTI) and Its Significance
  1.3 Geodesic-Loxodromes: Concept and Application
  1.4 Key Contributions and Objectives of the Paper
  1.5 Structure of the Paper

• Preliminaries
  2.1 Diffusion Tensor Fields in Imaging
  2.2 Mathematical Foundations of Geodesics and Loxodromes
  2.3 Interpolation Techniques for Diffusion Tensor Data
  2.4 Difference Measurement in Diffusion Tensor Fields
  2.5 Related Work on Diffusion Tensor Interpolation and Geodesics

• Geodesic-Loxodromes: Theory and Formulation
  3.1 Geodesic Curves and Their Role in Tensor Field Interpolation
  3.2 Loxodromes: Definition, Properties, and Applications
  3.3 Mathematical Representation of Geodesic-Loxodromes
  3.4 Geodesic-Loxodromes for Tensor Field Transport
  3.5 The Relationship Between Geodesic-Loxodromes and Diffusion Tensor Interpolation

• Diffusion Tensor Interpolation Using Geodesic-Loxodromes
  4.1 Interpolation Challenges in Diffusion Tensor Imaging
  4.2 Tensor Interpolation on Curved Spaces
  4.3 Applying Geodesic-Loxodromes to Diffusion Tensor Interpolation
  4.4 Computational Algorithms for Geodesic-Loxodrome-Based Interpolation
  4.5 Handling Noise and Inaccuracies in Tensor Data

• Measurement of Differences in Diffusion Tensor Fields
  5.1 Quantifying Differences in Diffusion Tensor Fields
  5.2 Methods for Comparing Tensor Fields: Distance Metrics
  5.3 Using Geodesic-Loxodromes to Measure Tensor Differences
  5.4 Computational Techniques for Difference Measurement
  5.5 Validation of Difference Measurement Techniques

• Methodology
  6.1 Overview of the Approach and Problem Setup
  6.2 Geodesic-Loxodrome-Based Interpolation and Difference Algorithms
  6.3 Data Preparation and Preprocessing
  6.4 Computational Framework and Tools Used

• Experimental Results
  7.1 Experimental Setup and Datasets
  7.2 Evaluation Metrics for Tensor Interpolation and Difference Measurement
  7.3 Performance Comparison with Other Interpolation Methods
  7.4 Case Studies and Applications in Medical Imaging
  7.5 Sensitivity to Noise and Distortion

• Applications in Diffusion Tensor Imaging
  8.1 Clinical Applications of Diffusion Tensor Imaging
  8.2 Diffusion Tensor Interpolation in Fiber Tracking and Reconstruction
  8.3 Geodesic-Loxodrome-Based Methods in Neuroimaging and Brain Studies
  8.4 Potential Applications in Cross-Subject and Longitudinal Studies

• Discussion
  9.1 Insights from Geodesic-Loxodrome-Based Interpolation
  9.2 Limitations and Challenges in Practical Implementation
  9.3 Opportunities for Further Research and Methodological Improvements
  9.4 Integration with Other Imaging Modalities

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