Curve Segmentation
Diffusion MRI tractography
Eric Pichon
Allen Tannenbaum
This lecture is devoted to three people:
(1)C-F Westin who pointed out that I had to lecture this
morning.
(2) William “Sandy” Wells for good company during
Dinner last night.
(3) And last but not least Eric Pichon who gave me these
slides.
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Introduction
• Artificial Intelligence (AI)
• Artificial Vision
• Segmentation: determining structures in images
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Active contours
• Edge detector
• Snakes
• Conformal active contours
• Segmentation output are E-optimal curves
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Anisotropic active contours
• Add directionality
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Curve minimization
• Calculus of variations
– Start with initial curve
– Deform to minimize energy
– Steady state is locally optimum
• Dynamic programming
Registration,
Atlas-based
segmentation
Segmentation
– Choose seed point s
– For any point t, determine globally
optimal curve t  s
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Medical applications
• Any elongated structure
– bones, vessels, bronchi etc.
• Diffusion weighted MRI
– neural tracts
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Synthetic example (2D)
QuickTime™ and a
Cinepak decompressor
are needed to see this picture.
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Synthetic example (3D)
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Synthetic example (3D)
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Calculus of Variations
Minimized by
Compare to geodesic active contour.
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Dynamic programming
Define the value function
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Dynamic programming
The value function satisfies the Hamilton-Jacobi-Bellman
equation
which can be solved numerically for
From any target point t , the optimal curve *(s,t) Is
obtained by following d* (i.e., minimizing E*).
Note: isotropic case reduces to the Eikonal equation
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Conclusions
• Pichon in doctoral thesis is now testing various
anisotropic conformal factors for DTI
tractography.
• Framework is very general and gives
directionality to geodesic (conformal) active
contour framework.
• Pichon will give more details during the level set
session on Tuesday.
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