Download Realignment

Realignment – Motion Correction
(gif from FMRIB at Oxford)
Overview
fMRI time-series
kernel
Design matrix
Motion
correction
Smoothing
General Linear Model
Spatial
normalisation
Statistical Parametric Map
Parameter Estimates
Standard
template
Reasons for Motion Correction
• Subjects will always move in the scanner
• The sensitivity of the analysis depends on the residual
noise in the image series, so movement that is unrelated to
the subject’s task will add to this noise and hence
realignment will increase the sensitivity
• However, subject movement may also correlate with the
task…
• …in which case realignment may reduce sensitivity (and it
may not be possible to discount artefacts that owe to
motion)
Within-subject Registration
• Assumes there is no shape change, and motion
is rigid-body (i.e. translations/rotations)
• The steps are:
*Registration - i.e. Optimising the parameters that
describe a rigid body transformation between the
source and reference images
- Reference image can be mean image or first image in
session
*Transformation - i.e. Re-sampling according to the
determined transformation
1. Registration
Determine the rigid
body transformation
that minimises the sum
Squared Error
of squared difference
between images
Rigid body transformations parameterised by:
Translations
1

0
0

0
0
0
1
0
0
1
0
0
Xtrans
Pitch
1
 
Ytrans 0

Zt rans 0
 
1  0
Roll
0
0
cos()
sin()
sin()
cos()
0
0
0
 cos()
 
0  0

0 sin()
 
1  0
Yaw
0
sin()
1
0
0
cos()
0
0
0
 cos()
 
0 sin()

0  0
 
1  0
sin()
0
0
cos()
0
0
0
1
0
0
0
1


1. Registration – Mean Squared Difference
• Minimising mean-squared difference works
for intra-modal registration (realignment)
• Simple relationship between intensities in one
image, versus those in the other
– Assumes normally distributed differences
1. Registration
• Iterative procedure (GaussNewton ascent)
• Additional scaling parameter
• Nx6 matrix of realignment
parameters written to file (N is
number of scans)
• Orientation matrices in *.mat
file updated for each volume
(do not have to be resliced)
• Reslice now or later  each
time degrades the image
3D Rigid-body Transformations
• A 3D rigid body transform is defined by:
– 3 translations - in X, Y & Z directions
– 3 rotations - about X, Y & Z axes
• The order of the operations matters
1


0

0

0
0 0 Xtrans 
1 0
0 1
0 0
1

 
Ytrans   0

Ztrans   0
 
1   0
Translations
0
0
cosΦ
sinΦ
 sinΦ cosΦ
0
0
Pitch
about x axis
0 
 cosΘ

 
0  0

0    sinΘ
 
1   0
0 sinΘ 0 
1
0
0 cosΘ
0
0
Roll
about y axis
 cosΩ

 
0    sinΩ

0  0
 
1   0
sinΩ 0 0 
cosΩ 0 0 

0
1 0
0
0 1 
Yaw
about z axis

2. Transformation (reslicing)
Nearest Neighbour
• Application of registration parameters involves
re-sampling the image to create new voxels by
interpolation from existing voxels
• Interpolation can be nearest neighbour (0-order),
tri-linear (1st-order), (windowed) fourier/sinc, or
in SPM2, nth-order “b-splines”
Linear
Full sinc (no alias)
d1
v1
Windowed sinc
d2
v2
d3
d4
v4
v3
B-spline Interpolation
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.
Residual Errors after Realignment
• Interpolation errors, especially with tri-linear interpolation
and small-window sinc
• Ghosts (and other artefacts) in the image (which do not
move as a rigid body)
• Rapid movements within a scan (which cause non-rigid
image deformation)
• Spin excitation history effects (residual magnetisation effects
of previous scans)
• Interaction between movement and local field
inhomogeniety, giving non-rigid distortion
Sources & References & So On…
• Rik Henson’s SPM minicourse (where these
slides where mostly stolen from)
• John Ashburner’s lecture on spatial
preprocessing (SPM course USA 2005)
• Human Brain Function, 2nd Edition (Edited by J
Ashburner, K Friston, W Penny) – mostly
chapter 2.