Transcript Group-wise Registration in NAMIC-kit Serdar K Balci (MIT) Lilla Zöllei (MGH)

Group-wise Registration in
NAMIC-kit
Serdar K Balci (MIT)
Lilla Zöllei (MGH)
Kinh Tieu (BWH)
Mert R Sabuncu (MIT)
Polina Golland (MIT)
Robust Group-wise Registration
• Entropy based group-wise registration
• ITK implementation
• Empirical Evaluation
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Background: Groupwise Registration
• Images
I1 ,, I N 
Transforms
T1 ,, TN 
• Transforms:
– Affine
– Non-rigid using B-Splines
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Registering to the Mean of the
Population
max  MI I n (Tn ( x));  ( x) 
N
T1 ,,TN n 1
T6
T5
T4
T1
T2
T3
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Groupwise Registration: Congealing
min  H v I (T ( xv )) 
V
T1 ,,TN v 1
L . Zöllei, E. Learned-Miller, E. Grimson, W.M. Wells III.
"Efficient Population Registration of 3D Data."
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Congealing: Intuition
• If Gaussian
pv I (T ( xv ))  ~ N v ,  v 
max   log Ν I n Tn ( xv ) ; v ,  v 
V
N
T1 ,,TN v 1 n 1
 I n Tn ( xv )   v
min   
2
T1 ,,TN v 1 n 1

v

V
N




2
• If also pv  Nv v ,  
• Registering to the mean with LS metric
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Implementation
• ITK classes
– Group-wise registration using congealing
• Variance
• Entropy
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Results
Before
Affine
BS 4
BS 8
BS 16
Entropy
Variance
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Overlap Measures
 Ln Tn ( x) 
N
n 1
N
N   Ln Tn ( x) 
n 1
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Full Term Babies
Before
Affine
BS 4
BS 8
BS 16
BS 32
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Pre Term Babies
Before
BS 8
Affine
BS 4
BS 16
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Summary
• Implemented group-wise registration in ITK
– Congealing: Entropy based registration
– Affine and BSpline
– Multithreaded implementation
– *Bspline optimization
• Initial Evaluation
– A population of 50 subjects
– Used segmentation labels to evaluate
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Ongoing Work
• Finding optimal parameters
• B-Spline mesh size,
• # of hierarchical levels
• Subsampling
• Quantitative comparison to other methods
• Pair-wise registration to the mean using MI
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Congealing with Two Images
• Using Parzen windows
T1, T2   max
  log  GI n Tn ( xv )  I k Tk ( xv )
T ,T
1
v n
2
k
• As we only have two images
 max  log GI1 T1 ( xv )  I 2 T2 ( xv )
T1 ,T2
v
 max I1 T1 ( x)   I 2 T2 ( x) 
2
T1 ,T2
• Pairwise registration using LS metric
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Groupwise Reg. using Pairwise Reg.
• If we assume that images are independent given a
subject, representative of the population
arg max pI1 ,, I N T1 ,, TN   arg max  MI I i (Ti ( x)); I R (TR ( x)) 
T1 ,,TN
T1 ,,TN
iimages
TR
T1
TN
T2
T3
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Registering to the mean
• We assume independence over images
arg max pI1 ,, I N T1 ,, TN   arg max  pi I i (Ti ( x))  ( x) 
T1 ,,TN
T1 ,,TN
iimages
• and draw i.i.d. samples from each image
 arg max 
T1 ,,TN
iimages jspace
 arg max 
T1 ,,TN

 pi I i (Ti ( x j ))  ( x j )


 log pi I i (Ti ( x j ))  ( x j )
iimages jspace

 arg max  MI I i (Ti ( x));  ( x j )
T1 ,,TN
iimages
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Groupwise Registration using Joint
Entropy
• Assume i.i.d over space, but don’t make any
assumptions about images
T1 ,, TN   arg max
T1 ,,TN

 p I1 ( x j ), , I N ( x j ) T1 ( x j ), , TN ( x j )
jspace

 arg min H I1 (T1 ( x), , I N (TN ( x)) 
T1 ,,TN
• Estimating entropy of an N-dimensional distribution
is a challenging task
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Results: Congealing with Entropy
Before
After (B-Splines ~20mm)
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