image registration: demons algorithm jojo 2011.2.23
TRANSCRIPT
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Image Registration: Demons Algorithm
JOJO
2011.2.23
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Outline
BackgroundDemons Maxwell’s Demons Thirion’s Demons Diffeomorphic Demons
ExperimentsConclusions
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BackgroundDefinition:
Register the pixels or voxels of the same anatomical structure in two medical images
Reasons:
Different ways of obtaining images
Different peoples’ different anatomical structures
Current non_rigid registration methods:
Demons, LDDMM (Large Deformation Diffeomorphic Metric Mapping), Hammer
( )( )transformation TimageM image S
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Outline
BackgroundDemons Maxwell’s Demons Thirion’s Demons Diffeomorphic Demons
ExperimentConclusion
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Demons: Maxwell’s Demons
aa
• A gas composed of a mix of two types of particles and
• The semi-permeable membrane (半透膜 ) contains a set of ‘demons’ (distinguish the two types of particles)
• Allow particles only to side A and particles only to side B
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Outline
BackgroundDemons Maxwell’s Demons Thirion’s Demons Diffeomorphic Demons
ExperimentConclusion
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Demons: Thirion’s Demons
Purpose:
Assumption
membrane: the contour of an object O in S
demons (P): scatter along the membrane
particles: M is the deformable grid, vertices are particles
( )transformationimageM image S
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Demons: Thirion’s Demons
Process:
Push the Model M inside O if the corresponding point of M is labelled ‘inside’, and outside O if it is labelled ‘outside’
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Demons: Thirion’s Demons
Flow chart:
The selection of the demons positions Ds
The space of TThe interpolation method to get the valueTi(M)
The formula giving the force f of a demon
Simple addition or composition mapping
Different demons
( )( )transformation TimageM image S
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Demons: Thirion’s Demons
Demons 0:
Ds: sample points of the disc contour
T: rigid transformation
Ti(M): analytically defined
f: constant magnitude forces
from Ti to Ti+1: simple addition
( )transformationimageM image S
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Demons: Thirion’s Demons
Demons 1:
Ds: All pixels (P) of s where
T: free form transformation
Ti(M): trilinear interpolation
f: to get the displacement
from Ti to Ti+1: simple addition
0S
2 2
( )
( ) ( )
m s su v
s m s
1i iT T u
( )transformationimageM image S
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Demons: Thirion’s Demons
Disadvantage:
The topology of the image may be changed (determined by Jacobian determinant)
The transformation may be nonreversible
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Outline
BackgroundDemons Maxwell’s Demons Thirion’s Demons Diffeomorphic Demons
ApplicationConclusion
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Demons: Diffeomorphic Demons
Basic:The most obvious difference:
composition mapping not simple addition
New conceptions:
Lie group, Lie algebra
exponential map
1 exp( )i iT T u
1i iT T u
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Demons: Diffeomorphic Demons
How to calculate exponential map
1) Let and choose N such that is close enough to 0, i.e.
2) Do N times recursive squaring of :
exp( )N times
u v v
2 Nv u
v
max v
v
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Demons: Diffeomorphic Demons
Diffeomorphic demons algorithm:
1) Initialize the transformation T, generally Identical transformation, then
2) Calculate the new ,3) Get the new T
4) If not convergence, go back to 2), otherwise, T is the optimal transformation
* , exp( ), *u G u c T u T G c
22
2
( ) ( )( ) ( )
( )P t
P i
x
M P S T Pu P J
PJ
0u
u
( )transformationimageM image S
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Outline
BackgroundDemons Maxwell’s Demons Original Demons Diffeomorphic Demons
ExperimentsConclusions
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Experiment
First experiments (design):
100 experiments with random images to compare Thirion’s demons and diffeomorphic demons
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Experiment
First experiments (results):
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Experiment
Second experiment (design):
Use synthetic T1 MR images from two different anatomies available from BrainWeb
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ExperimentSecond experiments (results):
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Experiment
Third experiment:
Try to apply the demons algorithm to automatic unsupervised classification of MR images in AD
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Outline
BackgroundDemons Maxwell’s Demons Original Demons Diffeomorphic Demons
ExperimentsConclusions
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Conclusion
Advantages:
Realize automation
Good performance on non_rigid registration
Relatively fast speedDisadvantage:
The segmentation accuracy based on demons need to be improved
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Thank you!