MultiResolution Parameterization of Meshes for Improved Surface Based Registration

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Multi-Resolution Parameterization of Meshes for
Improved Surface Based Registration
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• Sylvain Jaume - Matthieu Ferrant - Simon Warfield
  - Benoît Macq
• TELE - Université catholique de Louvain (Belgium)
• SPL - Harvard Medical School (USA)

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Surface Based Registration

• Surface Registration Matching a surface onto
  object in 3D image

Applications

• brain atlas matching for automatic

labeling of sulci

• tracking heart boundary in real-time

MRI

• segmenting anatomical structures

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Common Approach Active Surface

• Active surface surface model deformed to the
  object

boundary under some forces
(Cohen Cohen 93)

• Image force to attract the surface to the object

• Balloon force to increase capture range

• Internal force to limit bending

Limitation
Trade-off local accuracy
global smoothness
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Our Approach Multi-Resolution (M-R) Surface
Matching

• Build a Multi-Resolution reference surface of
  the object

• Re-use the parameters of this surface to match a
  new object

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Building M-R Reference Surface (I)

• External force move nodes x to minimize distance

x
2
T
2
Dist(x,T )
Area(T )
...

T
?
i
i
1
Dist(x)
x

x
?
1
Area(T )
T
i
0
j
j
x
distance to object 3D euclidean distance map
0

• Internal force smooth nodes to keep regularity

?
(x - x )
x
x
?


i
j
i1
i
j
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Building M-R Reference Surface (II)

• External force along surface normal or opposite
  direction

Image gradient
Surface normal

• Internal force along this normal axis

.
x - x
i
j
(x - x )
x
x
n
n


i
j
i1
i
Parameters length of the deformation vector
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Building M-R Reference Surface (III)

• Refine by triangle quadrisection from resolution
  i to i1

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Cuts through the Reference Surface
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Matching Surface onto a New Target Image
i1
Refine by
Surface at
Deform at res. i
Matched Surface
onto target
at resolution in
quadrisection
resolution i0
Reference
Extract parameters
Model
at resolution i
Potential function distance map of segmented
target image
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Cuts through the Matched Surface
Morphological closing was needed to avoid
flattening
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Conclusions of our M-R Surface Matching

• internal external forces are more more
  localized

• convergence and accuracy of matched surface

• matching imperfectly segmented images

• difficult balance between int. ext. forces

• better potential function needed

• oversampling in smooth areas

Other benefits

• shape characterization

• progressive transmission of the mesh