Course

1
Spatial Preprocessing I
Chloe Hutton The Wellcome Department of Imaging
Neuroscience, London, UK
Slides from John Ashburner, Jesper Andersson and
Tina Good The Wellcome Department of Cognitive
Neurology, UCL London UK http//www.fil.ion.ucl
.ac.uk/spm
chutton_at_fil.ion.ucl.ac.uk
2
Overview
Statistical Parametric Map
Design matrix
fMRI time-series
kernel
Motion correction
smoothing
General Linear Model
Coregistration
Parameter Estimates
Spatial normalisation
Segmentation
anatomical reference
3
Movement Correction Why?

• Subjects move in scanner (can be related to the
  task)
• Sensitivity Large error variance may prevent us
  from finding activations.
• Specificity Task correlated motion may pose as
  activations.

Large Activation
Intensity in voxel
Scan
4
No movement
t190.40
t199.81
5
Movement uncorrelated to task
t190.62
t199.28
6
Movement correlated to task
t1911.52
t198.92
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How to do Motion Correction

• Within-subject, within modality can assume there
  is no shape change, so the motion is rigid-body.
• Registration
• Determine the 6 parameters that describe the
  rigid body transformation between each image and
  a reference image.
• Transformation
• Re-sample each image according to the determined
  transformation parameters.

3 translations
z
y
x
3 rotations
z
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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

Translations
Pitch about x axis
Roll about y axis
Yaw about z axis
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Registration what do we need to do?
f2
f1

• Find the rigid body transformation that best
  matches image f2 to image f1.
• For an fMRI time series, f1 is usually the first
  image in the run.

f2-f1
??x
?y
??
The way the difference image would have looked
had there been a 1mm x-translation
The way the difference image would have looked
had there been a 1mm y-translation
The way the difference image would have looked
had there been a 1 degree rotation
Observed difference
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Registration how do we do it?

• Determine the ?x, ? y, and ?? so that the mean
  squared difference between f1 and f2 is minimised.

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Transformation re-sampling the transformed
image
Transformed image

• Visit each voxel in space of the transformed
  image.
• Transform the voxel coordinate.
• Find the voxel in the original image.
• Calculate voxel values in transformed image using
  interpolation
• eg trilinear interpolation, bspline
  interpolation.

Original image
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Simple Interpolation

• Nearest neighbour
• Take the value of the closest voxel
• Tri-linear
• Just a weighted average of the neighbouring
  voxels
• f5 f1 x2 f2 x1
• f6 f3 x2 f4 x1
• f7 f5 y2 f6 y1

13
Residual Errors from fMRI

• Gaps between slices can cause aliasing artefacts.
  
• Re-sampling can introduce interpolation errors.
• especially tri-linear interpolation
• Slices are not acquired simultaneously
• rapid movements not accounted for by rigid body
  model.
• Image artefacts that do not move according to the
  rigid body model
• image distortion
• image dropout
• nyquist ghost
• Functions of the estimated motion parameters can
  be used as confounds in subsequent analyses.

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Coregistration between modality (within subject)

• Match images from same subject but different
  modalities
• anatomical localisation of single subject
  activations
• achieve a more precise spatial normalisation of
  functional image using detailed structure of
  anatomical image.
• Requires affine transformation to allow scaling
  between different image resolutions.

15
Affine Transforms

• Rigid-body transformations are a subset
• An affine transform is defined by 12 parameters
• 3 translations - in X, Y Z directions
• 3 rotations - about X, Y Z axes
• 3 zooms (scaling factors) in X, Y Z
  directions.
• 3 shears along X, Y Z axes.
• Parallel lines remain parallel

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Between Modality Coregistration using Mutual
Information

• Find the affine transformation that best
  matches the images.
• Images are matched so that the Mutual Information
  in the 2D histogram is maximised.
• For histograms normalised to integrate to unity,
  the Mutual Information is defined by
• SiSj hij log hij
• Sk hik Sl hlj

17
Segmentation

• Classification of brain tissues used for voxel
  based morphometry.
• Mixture Model cluster analysis to classify MR
  image (or images) as GM, WM CSF.
• Additional information is obtained from prior
  probability images which are matched to MR image
  using affine registration.
• Assumes that each MRI voxel is one of a number of
  distinct tissue types (clusters).
• Each cluster has a (multivariate) normal
  distribution.

.
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Segmentation - Bias Correction

• Image non-uniformity caused by radiofrequency
  coil.
• A smooth intensity modulating function can be
  modelled by a linear combination of DCT basis
  functions

19
Segmentation - Algorithm

• Results may contain some non-brain tissue
• These can be removed using morphologicaloperation
  s
• erosion
• conditional dilation

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Voxel-Based Morphometry
Preparation of images for each subject
Spatially normalised
Partitioned grey matter
Original image
Smoothed

• A voxel by voxel statistical analysis is used to
  detect regional differences in the amount of grey
  matter between populations.

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Smoothing

• Why Smooth?
• Potentially increase signal to noise.
• Inter-subject averaging.
• Validity of statistical inference in SPM.
• In SPM, smoothing is a convolution with a
  Gaussian kernel.
• Kernel defined in terms of FWHM (full width at
  half maximum).

Gaussian smoothing kernel
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Summary

• Motion correction of functional images is
  required to increase sensitivity and specificity
  of activation studies.
• Motion correction is within-subject, within
  modality, therefore can use a rigid body
  transformation.
• Residual effects may exist in fMRI after motion
  correction.
• Within subject, between modality coregistration
  uses an affine transformation.
• Segmentation of tissue classes can be used for
  voxel based morphometry.
• Gaussian smoothing for increased SNR, intersubjet
  averaging and validity of statistical inference
  in SPM.

23
References Ashburner Friston (1997)
Multimodal image coregistration and partitioning
- a unified framework. NeuroImage
6(3)209-217 Collignon et al (1995) Automated
multi-modality image registration based on
information theory. IPMI95 pp
263-274 Ashburner et al (1997) Incorporating
prior knowledge into image registration.
NeuroImage 6(4)344-352 Ashburner Friston
(2000) Voxel-based morphometry - the methods. To
appear in NeuroImage.