Image Registration: Demons Algorithm

JOJO

2011.2.23

Outline

BackgroundDemons Maxwell’s Demons Thirion’s Demons Diffeomorphic Demons

ExperimentsConclusions

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

Outline

BackgroundDemons Maxwell’s Demons Thirion’s Demons Diffeomorphic Demons

ExperimentConclusion

Demons: Maxwell’s Demons

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• 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

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

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’

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

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

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

Demons: Thirion’s Demons

Disadvantage:

The topology of the image may be changed (determined by Jacobian determinant)

The transformation may be nonreversible

Outline

BackgroundDemons Maxwell’s Demons Thirion’s Demons Diffeomorphic Demons

ApplicationConclusion

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

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

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

Outline

BackgroundDemons Maxwell’s Demons Original Demons Diffeomorphic Demons

ExperimentsConclusions

Experiment

First experiments (design):

100 experiments with random images to compare Thirion’s demons and diffeomorphic demons

Experiment

First experiments (results):

Experiment

Second experiment (design):

Use synthetic T1 MR images from two different anatomies available from BrainWeb

ExperimentSecond experiments (results):

Experiment

Third experiment:

Try to apply the demons algorithm to automatic unsupervised classification of MR images in AD

Outline

BackgroundDemons Maxwell’s Demons Original Demons Diffeomorphic Demons

ExperimentsConclusions

Conclusion

Advantages:

Realize automation

Good performance on non_rigid registration

Relatively fast speedDisadvantage:

The segmentation accuracy based on demons need to be improved

Thank you!