Curve Segmentation

1
Curve Segmentation

• Diffusion MRI tractography
• Eric Pichon
• Allen Tannenbaum

2

• This lecture is devoted to three people
• 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.

3
Introduction

• Artificial Intelligence (AI)
• Artificial Vision
• Segmentation determining structures in images

4
Active contours

• Edge detector
• Snakes
• Conformal active contours
• Segmentation output are E-optimal curves

5
Anisotropic active contours

• Add directionality

6
Curve minimization
Registration, Atlas-basedsegmentation

• Calculus of variations
• Start with initial curve
• Deform to minimize energy
• Steady state is locally optimum
• Dynamic programming
• Choose seed point s
• For any point t, determine globallyoptimal curve
  t ? s

Segmentation
7
Medical applications

• Any elongated structure
• bones, vessels, bronchi etc.
• Diffusion weighted MRI
• neural tracts

8
Synthetic example (2D)
9
Synthetic example (3D)
10
Synthetic example (3D)
11
Calculus of Variations
Minimized by
Compare to geodesic active contour.
12
Dynamic programming
Define the value function
13
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
14
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.