Realignment – Motion CorrectionRealignment – Motion CorrectionRealignment – Motion CorrectionRealignment – Motion Correction

(gif from FMRIB at Oxford)

OverviewOverviewOverviewOverview

Motioncorrection

Smoothing

kernel

Spatialnormalisation

Standardtemplate

fMRI time-series Statistical Parametric Map

General Linear Model

Design matrix

Parameter Estimates

Reasons for Motion CorrectionReasons for Motion CorrectionReasons for Motion CorrectionReasons for Motion Correction

• Subjects will always move in the scannerSubjects will always move in the scanner

• The sensitivity of the analysis depends on the residual The sensitivity of the analysis depends on the residual noise in the image series, so movement that is unrelated to noise in the image series, so movement that is unrelated to the subject’s task will add to this noise and hence the subject’s task will add to this noise and hence realignment will increase the sensitivity realignment will increase the sensitivity

• However, subject movement may also correlate with the However, subject movement may also correlate with the task…task…

• ……in which case realignment may reduce sensitivity (and it in which case realignment may reduce sensitivity (and it may not be possible to discount artefacts that owe to may not be possible to discount artefacts that owe to motion)motion)

• Subjects will always move in the scannerSubjects will always move in the scanner

• The sensitivity of the analysis depends on the residual The sensitivity of the analysis depends on the residual noise in the image series, so movement that is unrelated to noise in the image series, so movement that is unrelated to the subject’s task will add to this noise and hence the subject’s task will add to this noise and hence realignment will increase the sensitivity realignment will increase the sensitivity

• However, subject movement may also correlate with the However, subject movement may also correlate with the task…task…

• ……in which case realignment may reduce sensitivity (and it in which case realignment may reduce sensitivity (and it may not be possible to discount artefacts that owe to may not be possible to discount artefacts that owe to motion)motion)

Within-subject RegistrationWithin-subject RegistrationWithin-subject RegistrationWithin-subject Registration

• Assumes there is no shape change, and motion Assumes there is no shape change, and motion is rigid-body (i.e. translations/rotations)is rigid-body (i.e. translations/rotations)

• The steps are:The steps are:**RegistrationRegistration - i.e. Optimising the parameters that - i.e. Optimising the parameters that

describe a rigid body transformation between the describe a rigid body transformation between the source and reference imagessource and reference images

- - Reference image can be mean image or first image in Reference image can be mean image or first image in sessionsession

**TransformationTransformation - i.e. Re-sampling according to the - i.e. Re-sampling according to the determined transformationdetermined transformation

• Assumes there is no shape change, and motion Assumes there is no shape change, and motion is rigid-body (i.e. translations/rotations)is rigid-body (i.e. translations/rotations)

• The steps are:The steps are:**RegistrationRegistration - i.e. Optimising the parameters that - i.e. Optimising the parameters that

describe a rigid body transformation between the describe a rigid body transformation between the source and reference imagessource and reference images

- - Reference image can be mean image or first image in Reference image can be mean image or first image in sessionsession

**TransformationTransformation - i.e. Re-sampling according to the - i.e. Re-sampling according to the determined transformationdetermined transformation

1. Registration1. Registration1. Registration1. Registration

Determine the Determine the rigidrigid

body transformationbody transformation

that minimises the sum that minimises the sum

of squared differenceof squared difference

between imagesbetween images

Determine the Determine the rigidrigid

body transformationbody transformation

that minimises the sum that minimises the sum

of squared differenceof squared difference

between imagesbetween images

1 0 0 Xtrans

0 1 0 Ytrans

0 0 1 Ztrans

0 0 0 1

1 0 0 0

0 cos() sin() 0

0 sin() cos() 0

0 0 0 1

cos() 0 sin() 0

0 1 0 0

sin() 0 cos() 0

0 0 0 1

cos() sin() 0 0

sin() cos() 0 0

0 0 1 0

0 0 0 1

Translations Pitch Roll Yaw

Rigid body transformations parameterised by:

Squared Error

1. Registration – Mean Squared Difference1. Registration – Mean Squared Difference1. Registration – Mean Squared Difference1. Registration – Mean Squared Difference

• Minimising mean-squared difference works Minimising mean-squared difference works for intra-modal registration (realignment)for intra-modal registration (realignment)

• Simple relationship between Simple relationship between intensitiesintensities in one in one image, versus those in the otherimage, versus those in the other– Assumes normally distributed differencesAssumes normally distributed differences

1. Registration1. Registration1. Registration1. Registration

• Iterative procedure (Gauss-Iterative procedure (Gauss-Newton ascent)Newton ascent)

• Additional scaling parameterAdditional scaling parameter

• Nx6 matrix of realignment Nx6 matrix of realignment parameters written to file (N is parameters written to file (N is number of scans)number of scans)

• Orientation matrices in *.mat Orientation matrices in *.mat file updated for each volume file updated for each volume (do not have to be resliced) (do not have to be resliced)

• Reslice now or later Reslice now or later each each time degrades the imagetime degrades the image

• Iterative procedure (Gauss-Iterative procedure (Gauss-Newton ascent)Newton ascent)

• Additional scaling parameterAdditional scaling parameter

• Nx6 matrix of realignment Nx6 matrix of realignment parameters written to file (N is parameters written to file (N is number of scans)number of scans)

• Orientation matrices in *.mat Orientation matrices in *.mat file updated for each volume file updated for each volume (do not have to be resliced) (do not have to be resliced)

• Reslice now or later Reslice now or later each each time degrades the imagetime degrades the image

3D Rigid-body Transformations3D Rigid-body Transformations3D Rigid-body Transformations3D Rigid-body Transformations

• A 3D rigid body transform is defined by:A 3D rigid body transform is defined by:– 3 translations - in X, Y & Z directions3 translations - in X, Y & Z directions– 3 rotations - about X, Y & Z axes3 rotations - about X, Y & Z axes

• The order of the operations mattersThe order of the operations matters

• A 3D rigid body transform is defined by:A 3D rigid body transform is defined by:– 3 translations - in X, Y & Z directions3 translations - in X, Y & Z directions– 3 rotations - about X, Y & Z axes3 rotations - about X, Y & Z axes

• The order of the operations mattersThe order of the operations matters

1000

0100

00cossin

00sincos

1000

0cos0sin

0010

0sin0cos

1000

0cossin0

0sincos0

0001

1000

Zt100

Y010

X001

rans

trans

trans

ΩΩ

ΩΩ

ΘΘ

ΘΘ

ΦΦ

ΦΦ

Translations Pitchabout x axis

Rollabout y axis

Yawabout z axis

• Application of registration parameters involves Application of registration parameters involves re-samplingre-sampling the image to create new voxels by the image to create new voxels by interpolation from existing voxelsinterpolation from existing voxels

• InterpolationInterpolation can be nearest neighbour ( can be nearest neighbour (00-order), -order), tri-linear (tri-linear (11st-order), (windowed) fourier/sinc, or st-order), (windowed) fourier/sinc, or in SPM2, in SPM2, nnth-order “th-order “b-splines”b-splines”

• Application of registration parameters involves Application of registration parameters involves re-samplingre-sampling the image to create new voxels by the image to create new voxels by interpolation from existing voxelsinterpolation from existing voxels

• InterpolationInterpolation can be nearest neighbour ( can be nearest neighbour (00-order), -order), tri-linear (tri-linear (11st-order), (windowed) fourier/sinc, or st-order), (windowed) fourier/sinc, or in SPM2, in SPM2, nnth-order “th-order “b-splines”b-splines”

2. Transformation (reslicing)2. Transformation (reslicing)2. Transformation (reslicing)2. Transformation (reslicing)

d1 d2

d3

d4

v1

v4

v2

v3

Nearest Neighbour

Linear

Full sinc (no alias)

Windowed sinc

B-spline InterpolationB-spline InterpolationB-spline InterpolationB-spline Interpolation

A continuous function is represented

by a linear combination of basis

functions

A continuous function is represented

by a linear combination of basis

functions

Nearest neighbour and trilinear interpolation are the same as B-spline interpolation with degrees 0 and 1.

• Interpolation errors, especially with tri-linear interpolation Interpolation errors, especially with tri-linear interpolation and small-window sincand small-window sinc

• Ghosts (and other artefacts) in the image (which do not Ghosts (and other artefacts) in the image (which do not move as a rigid body)move as a rigid body)

• Rapid movements Rapid movements withinwithin a scan (which cause non-rigid a scan (which cause non-rigid image deformation)image deformation)

• Spin excitation history effects (residual magnetisation Spin excitation history effects (residual magnetisation effects of previous scans)effects of previous scans)

• Interaction between movement and local field Interaction between movement and local field inhomogeniety, giving non-rigid distortioninhomogeniety, giving non-rigid distortion

• Interpolation errors, especially with tri-linear interpolation Interpolation errors, especially with tri-linear interpolation and small-window sincand small-window sinc

• Ghosts (and other artefacts) in the image (which do not Ghosts (and other artefacts) in the image (which do not move as a rigid body)move as a rigid body)

• Rapid movements Rapid movements withinwithin a scan (which cause non-rigid a scan (which cause non-rigid image deformation)image deformation)

• Spin excitation history effects (residual magnetisation Spin excitation history effects (residual magnetisation effects of previous scans)effects of previous scans)

• Interaction between movement and local field Interaction between movement and local field inhomogeniety, giving non-rigid distortioninhomogeniety, giving non-rigid distortion

Residual Errors after RealignmentResidual Errors after RealignmentResidual Errors after RealignmentResidual Errors after Realignment

Sources & References & So On…Sources & References & So On…Sources & References & So On…Sources & References & So On…

• Rik Henson’s SPM minicourse (where these Rik Henson’s SPM minicourse (where these slides where mostly stolen from)slides where mostly stolen from)

• John Ashburner’s lecture on spatial John Ashburner’s lecture on spatial preprocessing (SPM course USA 2005)preprocessing (SPM course USA 2005)

• Human Brain Function, 2Human Brain Function, 2ndnd Edition (Edited by J Edition (Edited by J Ashburner, K Friston, W Penny) – mostly Ashburner, K Friston, W Penny) – mostly chapter 2.chapter 2.

• Rik Henson’s SPM minicourse (where these Rik Henson’s SPM minicourse (where these slides where mostly stolen from)slides where mostly stolen from)

• John Ashburner’s lecture on spatial John Ashburner’s lecture on spatial preprocessing (SPM course USA 2005)preprocessing (SPM course USA 2005)

• Human Brain Function, 2Human Brain Function, 2ndnd Edition (Edited by J Edition (Edited by J Ashburner, K Friston, W Penny) – mostly Ashburner, K Friston, W Penny) – mostly chapter 2.chapter 2.