PDE methods for DWMRI Analysis and Image Registration

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

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Outline

Geodesic Tractography Review

Cingulum Bundle Tractography--------------------------------------------- Fast Numerical Schemes

Applications to Image Registration

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Contributors

Georgia Tech- John Melonakos, Vandana

Mohan, Allen Tannenbaum BWH-

Marc Niethammer, Kate Smith, Marek Kubicki, Martha Shenton

UCI- Jim Fallon

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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.

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Directional Dependence

tangentdirection

the new length functional

This is a metric on a “Finsler” manifold if Ψ satisfies certain properties.

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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.

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Computing the first variation of the functional E, the L2-optimal E-minimizing deformation is:

Closed Curves:The Flow Derivation

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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:

Open Curves:The Value Function

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Numerics

Closed Curves Open Curves

Level Set Techniques Dynamic Programming(Fast Sweeping)

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Finsler vs Riemann vs Euclid

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Outline

Geodesic Tractography Review

Cingulum Bundle Tractography--------------------------------------------- Fast Numerical Schemes

Applications to Image Registration

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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.

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The Cingulum Bundle

5-7 mm in diameter

“ring-like belt” around CC

Involved in executive control and emotional processing

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The Data

24 datasets from BWH (Marek Kubicki)12 Schizophrenics12 Normal Controls

54 Sampling Directions

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The Algorithm Input

Locating the bundle endpoints (work done by Kate Smith)

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The Algorithm Input

How the ROIs were drawn

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Results

Anterior View

Posterior View

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Results

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Results

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Results – A Statistical Note

Attempt to sub-divide the tract to find FA significance

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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.

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Outline

Geodesic Tractography Review

Cingulum Bundle Tractography--------------------------------------------- Fast Numerical Schemes

Applications to Image Registration

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Contributors

Georgia Tech- Gallagher Pryor, Tauseef

Rehman, John Melonakos, Allen Tannenbaum

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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).

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Multigrid Numerical Schemes

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Parallel Computing

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Algorithms on the GPU

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Parallel Computing

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Parallel Computing

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Outline

Geodesic Tractography Review

Cingulum Bundle Tractography--------------------------------------------- Fast Numerical Schemes

Applications to Image Registration

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The Registration Problem

Synthetic Registration Problem

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Solution – The Warped Grid

Synthetic Registration Problem

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The Registration Problem

Brain Sag Registration Problem

Before After

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Solution – The Warped Grid

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Speedup

A 128^3 registration in less than 15 seconds

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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

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Questions?