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PDE methods for DWMRI Analysis and Image Registration

This workshop presentation by John Melonakos at NAMIC Core 1 offers insights into advanced methods for Diffusion-Weighted MRI (DWMRI) analysis and image registration. The topics covered include a review of geodesic tractography, specific tractography of the cingulum bundle, fast numerical schemes, and novel applications in image registration. The contributions from Georgia Tech and BWH emphasize computational techniques using Finsler geometry for optimal tract identification and analysis of brain structures, showcasing improvements in registration speed and accuracy.

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PDE methods for DWMRI Analysis and Image Registration

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  1. PDE methods for DWMRI Analysis and Image Registration presented by John Melonakos – NAMIC Core 1 Workshop – 31/May/2007

  2. Outline • Geodesic Tractography Review • Cingulum Bundle Tractography --------------------------------------------- • Fast Numerical Schemes • Applications to Image Registration

  3. Contributors • Georgia Tech- • John Melonakos, Vandana Mohan, Allen Tannenbaum • BWH- • Marc Niethammer, Kate Smith, Marek Kubicki, Martha Shenton • UCI- • Jim Fallon

  4. Publications • J. Melonakos, E. Pichon, S. Angenent, A. Tannenbaum. “Finsler Active Contours”. IEEE Transactions on Pattern Analysis and Machine Intelligence. (to appear 2007). • J. Melonakos, V. Mohan, M. Niethammer, K. Smith, M. Kubicki, A. Tannenbaum. “Finsler Tractography for White Matter Connectivity Analysis of the Cingulum Bundle”. MICCAI 2007. • V. Mohan, J. Melonakos, M. Niethammer, M. Kubicki, A. Tannenbaum. “Finsler Level Set Segmentation for Imagery in Oriented Domains”. BMVC 2007 (in submission). • Eric Pichon and Allen Tannenbaum. Curve segmentation using directional information, relation to pattern detection. In IEEE International Conference on Image Processing (ICIP), volume 2, pages 794-797, 2005. • Eric Pichon, Carl-Fredrik Westin, and Allen Tannenbaum. A Hamilton-Jacobi-Bellman approach to high angular resolution diffusion tractography. In International Conference on Medical Image Computing and Computer Assisted Intervention (MICCAI), pages 180-187, 2005.

  5. Directional Dependence the new length functional tangent direction This is a metric on a “Finsler” manifold if Ψ satisfies certain properties.

  6. Finsler Metrics • the Finsler properties: • Regularity • Positive homogeneity of degree one in the second variable • Strong Convexity Note: Finsler geometry is a generalization of Riemannian geometry.

  7. Closed Curves:The Flow Derivation Computing the first variation of the functional E, the L2-optimal E-minimizing deformation is:

  8. Open Curves:The Value Function Consider a seed region S½Rn, define for all target points t2Rn the value function: curves between S and t It satisfies the Hamilton-Jacobi-Bellman equation:

  9. Numerics Closed Curves Open Curves Level Set Techniques Dynamic Programming (Fast Sweeping)

  10. Finsler vs Riemann vs Euclid

  11. Outline • Geodesic Tractography Review • Cingulum Bundle Tractography --------------------------------------------- • Fast Numerical Schemes • Applications to Image Registration

  12. A Novel Approach • Use open curves to find the optimal “anchor tract” connecting two ROIs • Initialize a level set surface evolution on the anchor tract to capture the entire fiber bundle.

  13. The Cingulum Bundle • 5-7 mm in diameter • “ring-like belt” around CC • Involved in executive control and emotional processing

  14. The Data • 24 datasets from BWH (Marek Kubicki) • 12 Schizophrenics • 12 Normal Controls • 54 Sampling Directions

  15. The Algorithm Input • Locating the bundle endpoints • (work done by Kate Smith)

  16. The Algorithm Input • How the ROIs were drawn

  17. Results • Anterior View • Posterior View

  18. Results

  19. Results

  20. Results – A Statistical Note • Attempt to sub-divide the tract to find FA significance

  21. Work In Progress • Implemented a level set surface evolution to capture the entire bundle – preliminary results. • Working with Marek Kubicki and Jim Fallon to make informed subdivision of the bundle for statistical processing. • Linking the technique to segmentation work in order to connect brain structures.

  22. Outline • Geodesic Tractography Review • Cingulum Bundle Tractography --------------------------------------------- • Fast Numerical Schemes • Applications to Image Registration

  23. Contributors • Georgia Tech- • Gallagher Pryor, Tauseef Rehman, John Melonakos, Allen Tannenbaum

  24. Publications • T. Rehman, G. Pryor, J. Melonakos, I. Talos, A. Tannenbaum. “Multi-resolution 3D Nonrigid Registration via Optimal Mass Transport”. MICCAI 2007 workshop (in submission). • T. Rehman, G. Pryor, and A. Tannenbaum. Fast Optimal Mass Transport for Dynamic Active Contour Tracking on the GPU. In IEEE Conference on Decision and Control, 2007 (in submission). • G. Pryor, T. Rehman, A. Tannenbaum. BMVC 2007 (in submission).

  25. Multigrid Numerical Schemes

  26. Parallel Computing

  27. Algorithms on the GPU

  28. Parallel Computing

  29. Parallel Computing

  30. Outline • Geodesic Tractography Review • Cingulum Bundle Tractography --------------------------------------------- • Fast Numerical Schemes • Applications to Image Registration

  31. The Registration Problem • Synthetic Registration Problem

  32. Solution – The Warped Grid • Synthetic Registration Problem

  33. The Registration Problem Brain Sag Registration Problem • Before • After

  34. Solution – The Warped Grid

  35. Speedup A 128^3 registration in less than 15 seconds

  36. Key Conclusions • Multigrid algorithms on the GPU can dramatically increase performance • We used Optimal Mass Transport for registration, but other PDEs may also be implemented in this way

  37. Questions?

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