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PDE methods for DWMRI Analysis
and Image Registration
presented by John Melonakos – NAMIC Core 1 Workshop – 31/May/2007
Outline

Geodesic Tractography Review
Cingulum Bundle Tractography
-------------------------------------------- Fast Numerical Schemes


Applications to Image Registration
2
Contributors

Georgia Tech

BWH

John Melonakos, Vandana
Mohan, Allen Tannenbaum
Marc Niethammer, Kate Smith,
Marek Kubicki, Martha Shenton
UCI
Jim Fallon
3
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.
4
Directional Dependence
the new length functional
tangent
direction
This is a metric on a “Finsler” manifold
if Ψ satisfies certain properties.
5
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.
6
Closed Curves:
The Flow Derivation
Computing the first variation of the functional E,
the L2-optimal E-minimizing deformation is:
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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:
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Numerics
Closed Curves
Level Set Techniques
Open Curves
Dynamic Programming
(Fast Sweeping)
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Finsler vs Riemann vs Euclid
10
Outline

Geodesic Tractography Review
Cingulum Bundle Tractography
-------------------------------------------- Fast Numerical Schemes


Applications to Image Registration
11
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.
12
The Cingulum Bundle
 5-7
mm in diameter
 “ring-like
belt” around CC
 Involved
in executive
control and emotional
processing
13
The Data
 24
datasets from BWH
(Marek Kubicki)
 12
Schizophrenics
 12 Normal Controls
 54
Sampling Directions
14
The Algorithm Input

Locating the bundle endpoints

(work done by Kate Smith)
15
The Algorithm Input

How the ROIs were drawn
16
Results

Anterior View

Posterior View
17
Results
18
Results
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Results – A Statistical Note

Attempt to
sub-divide
the tract to
find FA
significance
20
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.
21
Outline

Geodesic Tractography Review
Cingulum Bundle Tractography
-------------------------------------------- Fast Numerical Schemes


Applications to Image Registration
22
Contributors

Georgia Tech
Gallagher Pryor, Tauseef
Rehman, John Melonakos,
Allen Tannenbaum
23
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
28
Parallel Computing
29
Outline

Geodesic Tractography Review
Cingulum Bundle Tractography
-------------------------------------------- Fast Numerical Schemes


Applications to Image Registration
30
The Registration Problem

Synthetic Registration Problem
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Solution – The Warped Grid

Synthetic Registration Problem
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The Registration Problem

Before

After
Brain Sag Registration Problem
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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

36
Questions?
37