Statistical Parametric Mapping (SPM) 1. Talk I: Spatial Pre-processing 2. Talk II: General Linear...
Transcript of Statistical Parametric Mapping (SPM) 1. Talk I: Spatial Pre-processing 2. Talk II: General Linear...
Statistical ParametricMapping (SPM)
1. Talk I: Spatial Pre-processing
2. Talk II: General Linear Model
3. Talk III: Statistical Inference
3. Talk IV: Experimental Design
Statistical ParametricMapping (SPM)
1. Talk I: Spatial Pre-processing
2. Talk II: General Linear Model
3. Talk III: Statistical Inference
3. Talk IV: Experimental Design
Spatial Preprocessing & Computational Neuroanatomy
With thanks to: John Ashburner, Jesper Andersson
Spatial Preprocessing & Computational Neuroanatomy
With thanks to: John Ashburner, Jesper Andersson
OverviewOverviewOverviewOverview
Motioncorrection
Smoothing
kernel
Spatialnormalisation
Standardtemplate
fMRI time-series Statistical Parametric Map
General Linear Model
Design matrix
Parameter Estimates
1. Realignment (motion correction)
2. Normalisation (to stereotactic space)
3. Smoothing
4. Between-modality Coregistration
5. Segmentation (to gray/white/CSF)
6. Morphometry (VBM/DBM/TBM)
1. Realignment (motion correction)
2. Normalisation (to stereotactic space)
3. Smoothing
4. Between-modality Coregistration
5. Segmentation (to gray/white/CSF)
6. Morphometry (VBM/DBM/TBM)
OverviewOverviewOverviewOverview
1. Realignment (motion correction)
2. Normalisation (to stereotactic space)
3. Smoothing
4. Between-modality Coregistration
5. Segmentation (to gray/white/CSF)
6. Morphometry (VBM/DBM/TBM)
1. Realignment (motion correction)
2. Normalisation (to stereotactic space)
3. Smoothing
4. Between-modality Coregistration
5. Segmentation (to gray/white/CSF)
6. Morphometry (VBM/DBM/TBM)
OverviewOverviewOverviewOverview
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 noise in the image series, so 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 movement that is unrelated to 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 task…However, subject movement may also correlate with the task…
• ……in which case realignment may reduce sensitivity (and it may not be possible to in which case realignment may reduce sensitivity (and it may not be possible to discount artefacts that owe to motion)discount artefacts that owe to motion)
• Subjects will always move in the scannerSubjects will always move in the scanner
• The sensitivity of the analysis depends on the residual noise in the image series, so 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 movement that is unrelated to 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 task…However, subject movement may also correlate with the task…
• ……in which case realignment may reduce sensitivity (and it may not be possible to in which case realignment may reduce sensitivity (and it may not be possible to discount artefacts that owe to motion)discount artefacts that owe to motion)
• RealignmentRealignment (of (of same-modality same-modality images from images from same subjectsame subject) involves two stages:) involves two stages:
– 1. Registration1. Registration - determining the 6 parameters that describe the rigid body - determining the 6 parameters that describe the rigid body transformation between each image and a reference imagetransformation between each image and a reference image
– 2. Transformation (reslicing) 2. Transformation (reslicing) - re-sampling each image according to the - re-sampling each image according to the determined transformation parametersdetermined transformation parameters
• RealignmentRealignment (of (of same-modality same-modality images from images from same subjectsame subject) involves two stages:) involves two stages:
– 1. Registration1. Registration - determining the 6 parameters that describe the rigid body - determining the 6 parameters that describe the rigid body transformation between each image and a reference imagetransformation between each image and a reference image
– 2. Transformation (reslicing) 2. Transformation (reslicing) - re-sampling each image according to the - re-sampling each image according to the determined transformation parametersdetermined transformation parameters
1. Registration1. Registration1. Registration1. Registration
• Determine the Determine the rigid body transformationrigid body transformation that minimises the sum of squared that minimises the sum of squared difference between imagesdifference between images
• Rigid body transformation is defined by:Rigid body transformation is defined by:– 3 3 translationstranslations - in X, Y & Z directions - in X, Y & Z directions
– 3 3 rotationsrotations - about X, Y & Z axes - about X, Y & Z axes
• Operations can be represented as Operations can be represented as affineaffine transformation matrices: transformation matrices:
xx11 = m = m1,11,1xx00 + m + m1,21,2yy00 + m + m1,31,3zz00 + m + m1,41,4
yy11 = m = m2,12,1xx00 + m + m2,22,2yy00 + m + m2,32,3zz00 + m + m2,42,4
zz11 = m = m3,13,1xx00 + m + m3,23,2yy00 + m + m3,33,3zz00 + m + m3,43,4
• Determine the Determine the rigid body transformationrigid body transformation that minimises the sum of squared that minimises the sum of squared difference between imagesdifference between images
• Rigid body transformation is defined by:Rigid body transformation is defined by:– 3 3 translationstranslations - in X, Y & Z directions - in X, Y & Z directions
– 3 3 rotationsrotations - about X, Y & Z axes - about X, Y & Z axes
• Operations can be represented as Operations can be represented as affineaffine transformation matrices: transformation matrices:
xx11 = m = m1,11,1xx00 + m + m1,21,2yy00 + m + m1,31,3zz00 + m + m1,41,4
yy11 = m = m2,12,1xx00 + m + m2,22,2yy00 + m + m2,32,3zz00 + m + m2,42,4
zz11 = m = m3,13,1xx00 + m + m3,23,2yy00 + m + m3,33,3zz00 + m + m3,43,4
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. 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)
• Slice-timing correction can be Slice-timing correction can be performed before or after performed before or after realignment (depending on realignment (depending on acquisition)acquisition)
• 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)
• Slice-timing correction can be Slice-timing correction can be performed before or after performed before or after realignment (depending on realignment (depending on acquisition)acquisition)
• 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
• Interpolation errors, especially with tri-linear interpolation and small-window sincInterpolation errors, especially with tri-linear interpolation and small-window sinc
• PET: PET:
– Incorrect attenuation correction because scans are no longer aligned with transmission Incorrect attenuation correction because scans are no longer aligned with transmission scan (a transmission scan is often acquired to give a map of local positron attenuation)scan (a transmission scan is often acquired to give a map of local positron attenuation)
• fMRI (EPI): fMRI (EPI):
– Ghosts (and other artefacts) in the image (which do not move as a rigid body)Ghosts (and other artefacts) in the image (which do not move as a rigid body)
– Rapid movements Rapid movements withinwithin a scan (which cause non-rigid image deformation) a scan (which cause non-rigid image deformation)
– Spin excitation history effects (residual magnetisation effects of previous scans)Spin excitation history effects (residual magnetisation effects of previous scans)
– Interaction between movement and local field inhomogeniety, giving non-rigid distortionInteraction between movement and local field inhomogeniety, giving non-rigid distortion
• Interpolation errors, especially with tri-linear interpolation and small-window sincInterpolation errors, especially with tri-linear interpolation and small-window sinc
• PET: PET:
– Incorrect attenuation correction because scans are no longer aligned with transmission Incorrect attenuation correction because scans are no longer aligned with transmission scan (a transmission scan is often acquired to give a map of local positron attenuation)scan (a transmission scan is often acquired to give a map of local positron attenuation)
• fMRI (EPI): fMRI (EPI):
– Ghosts (and other artefacts) in the image (which do not move as a rigid body)Ghosts (and other artefacts) in the image (which do not move as a rigid body)
– Rapid movements Rapid movements withinwithin a scan (which cause non-rigid image deformation) a scan (which cause non-rigid image deformation)
– Spin excitation history effects (residual magnetisation effects of previous scans)Spin excitation history effects (residual magnetisation effects of previous scans)
– Interaction between movement and local field inhomogeniety, giving non-rigid distortionInteraction between movement and local field inhomogeniety, giving non-rigid distortion
Residual Errors after RealignmentResidual Errors after RealignmentResidual Errors after RealignmentResidual Errors after Realignment
• Echo-planar images (EPI) contain Echo-planar images (EPI) contain distortionsdistortions owing to owing to field inhomogenieties (susceptibility artifacts, field inhomogenieties (susceptibility artifacts, particularly in phase-encoding direction)particularly in phase-encoding direction)
• They can be “undistorted” by use of a They can be “undistorted” by use of a field-map field-map (available in the “FieldMap” SPM toolbox)(available in the “FieldMap” SPM toolbox)
• (Note that susceptibility artifacts that cause (Note that susceptibility artifacts that cause drop-out drop-out are more difficult to correct)are more difficult to correct)
• However, movement interacts with the field However, movement interacts with the field inhomogeniety (presence of object affects Binhomogeniety (presence of object affects B00), ie ), ie
distortions change with position of object in fielddistortions change with position of object in field
• This movement-by-distortion can be accommodated This movement-by-distortion can be accommodated during realignment using “unwarp”during realignment using “unwarp”
• Echo-planar images (EPI) contain Echo-planar images (EPI) contain distortionsdistortions owing to owing to field inhomogenieties (susceptibility artifacts, field inhomogenieties (susceptibility artifacts, particularly in phase-encoding direction)particularly in phase-encoding direction)
• They can be “undistorted” by use of a They can be “undistorted” by use of a field-map field-map (available in the “FieldMap” SPM toolbox)(available in the “FieldMap” SPM toolbox)
• (Note that susceptibility artifacts that cause (Note that susceptibility artifacts that cause drop-out drop-out are more difficult to correct)are more difficult to correct)
• However, movement interacts with the field However, movement interacts with the field inhomogeniety (presence of object affects Binhomogeniety (presence of object affects B00), ie ), ie
distortions change with position of object in fielddistortions change with position of object in field
• This movement-by-distortion can be accommodated This movement-by-distortion can be accommodated during realignment using “unwarp”during realignment using “unwarp”
UnwarpUnwarpUnwarpUnwarpNew inSPM2
Distorted image
Corrected image
Field-map
• One could include the movement parameters as confounds One could include the movement parameters as confounds in the statistical model of activationsin the statistical model of activations
• However, this may remove activations of interest if they However, this may remove activations of interest if they are correlated with the movementare correlated with the movement
• Better is to incorporate physics knowledge, eg to model Better is to incorporate physics knowledge, eg to model how field changes as function of how field changes as function of pitchpitch and and rollroll (assuming (assuming phase-encoding is in y-direction)…phase-encoding is in y-direction)…
• … … using Taylor expansion (about mean realigned image):using Taylor expansion (about mean realigned image):
• Iterate: 1) estimate movement parameters (Iterate: 1) estimate movement parameters (, ), 2) ), 2) estimate deformation fields, 1) re-estimate movement …estimate deformation fields, 1) re-estimate movement …
• Fields expressed by spatial basis functions (3D discrete Fields expressed by spatial basis functions (3D discrete cosine set)…cosine set)…
• One could include the movement parameters as confounds One could include the movement parameters as confounds in the statistical model of activationsin the statistical model of activations
• However, this may remove activations of interest if they However, this may remove activations of interest if they are correlated with the movementare correlated with the movement
• Better is to incorporate physics knowledge, eg to model Better is to incorporate physics knowledge, eg to model how field changes as function of how field changes as function of pitchpitch and and rollroll (assuming (assuming phase-encoding is in y-direction)…phase-encoding is in y-direction)…
• … … using Taylor expansion (about mean realigned image):using Taylor expansion (about mean realigned image):
• Iterate: 1) estimate movement parameters (Iterate: 1) estimate movement parameters (, ), 2) ), 2) estimate deformation fields, 1) re-estimate movement …estimate deformation fields, 1) re-estimate movement …
• Fields expressed by spatial basis functions (3D discrete Fields expressed by spatial basis functions (3D discrete cosine set)…cosine set)…
UnwarpUnwarpUnwarpUnwarpNew inSPM2
Roll
Pitch
Estimated derivative fields
0B 0B + B0
UnwarpUnwarpUnwarpUnwarp
B0{i} B0 0B 0B
= + + + error(0th-order term
can be determined from fieldmap)
-f1 fi
1 +2 + ... +5 + ...1 y f 0 1
B
i 0 2
B 1 y f
i 0 5
B 1 y f
i
5
i
f
3
i
f
1
i
f
New inSPM2
UnwarpUnwarpUnwarpUnwarpNew inSPM2
Example: Movement correlated with design
tmax=13.38
No correction
tmax=5.06
Correction by covariation
tmax=9.57
Correction by Unwarp
1. Realignment (motion correction)
2. Normalisation (to stereotactic space)
3. Smoothing
4. Between-modality Coregistration
5. Segmentation (to gray/white/CSF)
6. Morphometry (VBM/DBM/TBM)
1. Realignment (motion correction)
2. Normalisation (to stereotactic space)
3. Smoothing
4. Between-modality Coregistration
5. Segmentation (to gray/white/CSF)
6. Morphometry (VBM/DBM/TBM)
OverviewOverviewOverviewOverview
Reasons for NormalisationReasons for NormalisationReasons for NormalisationReasons for Normalisation
• Inter-subject averagingInter-subject averaging
– extrapolate findings to the population as a wholeextrapolate findings to the population as a whole
– increase statistical power above that obtained from single subjectincrease statistical power above that obtained from single subject
• Reporting of activations as co-ordinates within a standard stereotactic spaceReporting of activations as co-ordinates within a standard stereotactic space
– e.g. the space described by e.g. the space described by Talairach & TournouxTalairach & Tournoux
• Inter-subject averagingInter-subject averaging
– extrapolate findings to the population as a wholeextrapolate findings to the population as a whole
– increase statistical power above that obtained from single subjectincrease statistical power above that obtained from single subject
• Reporting of activations as co-ordinates within a standard stereotactic spaceReporting of activations as co-ordinates within a standard stereotactic space
– e.g. the space described by e.g. the space described by Talairach & TournouxTalairach & Tournoux
• Label-basedLabel-based approaches: Warp the images such that defined landmarks approaches: Warp the images such that defined landmarks (points/lines/surfaces) are aligned(points/lines/surfaces) are aligned
– but few readily identifiable landmarks (and manually defined?)but few readily identifiable landmarks (and manually defined?)
• Intensity-basedIntensity-based approaches: Warp to images to maximise some voxel-wise approaches: Warp to images to maximise some voxel-wise similarity measuresimilarity measure
– eg, squared error, assuming intensity correspondence (within-modality)eg, squared error, assuming intensity correspondence (within-modality)
• Normalisation constrained to correct for only gross differences; residual Normalisation constrained to correct for only gross differences; residual variabilility accommodated by subsequent spatial smoothingvariabilility accommodated by subsequent spatial smoothing
• Label-basedLabel-based approaches: Warp the images such that defined landmarks approaches: Warp the images such that defined landmarks (points/lines/surfaces) are aligned(points/lines/surfaces) are aligned
– but few readily identifiable landmarks (and manually defined?)but few readily identifiable landmarks (and manually defined?)
• Intensity-basedIntensity-based approaches: Warp to images to maximise some voxel-wise approaches: Warp to images to maximise some voxel-wise similarity measuresimilarity measure
– eg, squared error, assuming intensity correspondence (within-modality)eg, squared error, assuming intensity correspondence (within-modality)
• Normalisation constrained to correct for only gross differences; residual Normalisation constrained to correct for only gross differences; residual variabilility accommodated by subsequent spatial smoothingvariabilility accommodated by subsequent spatial smoothing
SummarySummarySummarySummary
Spatial Normalisation
Original image
Templateimage
Spatially normalised
Deformation field
• Determine transformation that minimises the sum of squared difference between an image and a (combination of) template image(s)
• Two stages:
1. affine registration to match size and position of the images
2. non-linear warping to match the overall brain shape
• Uses a Bayesian framework to constrain affine and warps
• Determine transformation that minimises the sum of squared difference between an image and a (combination of) template image(s)
• Two stages:
1. affine registration to match size and position of the images
2. non-linear warping to match the overall brain shape
• Uses a Bayesian framework to constrain affine and warps
Stage 1. Full Affine TransformationStage 1. Full Affine Transformation
• The first part of normalisation is a The first part of normalisation is a 12 parameter affine transformation12 parameter affine transformation
– 3 translations3 translations
– 3 rotations3 rotations
– 3 zooms3 zooms
– 3 shears3 shears
• Better if template image in same Better if template image in same modality (eg because of image modality (eg because of image distortions in EPI but not T1)distortions in EPI but not T1)
1000
0100
00)cos()sin(
00)sin()cos(
1000
0)cos(0)sin(
0010
0)sin(0)cos(
1000
0)cos()sin(0
0)sin()cos(0
0001
1000
Z100
Y010
X001
trans
trans
trans
1000
0100
0YZ10
0XZXY1
1000
0Z00
00Y0
000X
shear
shearshear
zoom
zoom
zoom
Rotation
Translation Zoom
Shear
Rigid body
Six affine registered imagesSix affine registered imagesSix affine registered imagesSix affine registered images Six affine + nonlinear registeredSix affine + nonlinear registeredSix affine + nonlinear registeredSix affine + nonlinear registered
Insufficieny of Affine-only normalisationInsufficieny of Affine-only normalisationInsufficieny of Affine-only normalisationInsufficieny of Affine-only normalisation
Stage 2. Nonlinear WarpsStage 2. Nonlinear Warps Stage 2. Nonlinear WarpsStage 2. Nonlinear Warps
• Deformations consist of a linear Deformations consist of a linear combination of smooth combination of smooth basis imagesbasis images
• These are the lowest frequency basis These are the lowest frequency basis images of a 3-D discrete cosine transformimages of a 3-D discrete cosine transform
• Brain masks can be applied (eg for lesions)Brain masks can be applied (eg for lesions)
Affine Registration(2 = 472.1)
Affine Registration(2 = 472.1)
Templateimage
Templateimage
Non-linearregistration
withoutregularisation(2 = 287.3)
Non-linearregistration
withoutregularisation(2 = 287.3)
Non-linearregistration
withregularisation(2 = 302.7)
Non-linearregistration
withregularisation(2 = 302.7)
Without the Bayesian formulation, the non-linear spatial normalisation can introduce unnecessary warping into the spatially normalised images
Bayesian ConstraintsBayesian ConstraintsBayesian ConstraintsBayesian Constraints
• Using Bayes rule, we can constrain (“regularise”) the nonlinear fit by incorporating prior knowledge of the likely extent of deformations:
p(p|e) p(e|p) p(p) (Bayes Rule)
p(p|e) is the a posteriori probability of parameters p given errors ep(e|p) is the likelihood of observing errors e given parameters pp(p) is the a priori probability of parameters p
• For Maximum a posteriori (MAP) estimate, we minimise (taking logs):
H(p|e) H(e|p) + H(p) (Gibbs potential)
H(e|p) (-log p(e|p)) is the squared difference between the images (error)H(p) -log p(p)) constrains parameters (penalises unlikely deformations) is “regularisation” hyperparameter, weighting effect of “priors”
Bayesian ConstraintsBayesian ConstraintsBayesian ConstraintsBayesian Constraints
• Algorithm simultaneously minimises:Algorithm simultaneously minimises:
– Sum of squared difference Sum of squared difference between template and objectbetween template and object
– Squared distance between the Squared distance between the parameters and their expectation parameters and their expectation
• Bayesian constraints applied to both:Bayesian constraints applied to both:
1) affine transformations1) affine transformations
– based on empirical prior rangesbased on empirical prior ranges
2) nonlinear deformations2) nonlinear deformations
– based on smoothness constraint based on smoothness constraint (minimising (minimising membrane energymembrane energy))
Empirically generated priors
Bayesian ConstraintsBayesian ConstraintsBayesian ConstraintsBayesian Constraints
1. Realignment (motion correction)
2. Normalisation (to stereotactic space)
3. Smoothing
4. Between-modality Coregistration
5. Segmentation (to gray/white/CSF)
6. Morphometry (VBM/DBM/TBM)
1. Realignment (motion correction)
2. Normalisation (to stereotactic space)
3. Smoothing
4. Between-modality Coregistration
5. Segmentation (to gray/white/CSF)
6. Morphometry (VBM/DBM/TBM)
OverviewOverviewOverviewOverview
Reasons for SmoothingReasons for SmoothingReasons for SmoothingReasons for Smoothing
• Potentially increase signal to noise (matched filter theorem)Potentially increase signal to noise (matched filter theorem)
• Inter-subject averagingInter-subject averaging (allowing for residual differences after normalisation)(allowing for residual differences after normalisation)
• Increase validity of statistics (more likely that errors distributed normally)Increase validity of statistics (more likely that errors distributed normally)
• Potentially increase signal to noise (matched filter theorem)Potentially increase signal to noise (matched filter theorem)
• Inter-subject averagingInter-subject averaging (allowing for residual differences after normalisation)(allowing for residual differences after normalisation)
• Increase validity of statistics (more likely that errors distributed normally)Increase validity of statistics (more likely that errors distributed normally)
Gaussian smoothing kernel
• Kernel defined in terms of FWHM (full width at half maximum) of filter - Kernel defined in terms of FWHM (full width at half maximum) of filter - usually ~16-20mm (PET) or ~6-8mm (fMRI) of a Gaussianusually ~16-20mm (PET) or ~6-8mm (fMRI) of a Gaussian
• Ultimate smoothness is function of Ultimate smoothness is function of appliedapplied smoothing and smoothing and intrinsicintrinsic image image smoothness (sometimes expressed as smoothness (sometimes expressed as “resels”“resels” - RESolvable Elements) - RESolvable Elements)
• Kernel defined in terms of FWHM (full width at half maximum) of filter - Kernel defined in terms of FWHM (full width at half maximum) of filter - usually ~16-20mm (PET) or ~6-8mm (fMRI) of a Gaussianusually ~16-20mm (PET) or ~6-8mm (fMRI) of a Gaussian
• Ultimate smoothness is function of Ultimate smoothness is function of appliedapplied smoothing and smoothing and intrinsicintrinsic image image smoothness (sometimes expressed as smoothness (sometimes expressed as “resels”“resels” - RESolvable Elements) - RESolvable Elements)
FWHM
1. Realignment (motion correction)
2. Normalisation (to stereotactic space)
3. Smoothing
4. Between-modality Coregistration
5. Segmentation (to gray/white/CSF)
6. Morphometry (VBM/DBM/TBM)
1. Realignment (motion correction)
2. Normalisation (to stereotactic space)
3. Smoothing
4. Between-modality Coregistration
5. Segmentation (to gray/white/CSF)
6. Morphometry (VBM/DBM/TBM)
OverviewOverviewOverviewOverview
Between Modality Co-registrationBetween Modality Co-registrationBetween Modality Co-registrationBetween Modality Co-registration
• Because different modality images have Because different modality images have different properties (e.g., relative intensity different properties (e.g., relative intensity of gray/white matter), cannot simply of gray/white matter), cannot simply minimise difference between imagesminimise difference between images
• Two main approaches:Two main approaches:
I. Via Templates:I. Via Templates:
1) Simultaneous affine registrations 1) Simultaneous affine registrations between between each image and same-modality each image and same-modality templatetemplate
2) Segmentation into grey and white matter2) Segmentation into grey and white matter
3) Final simultaneous registration of segments3) Final simultaneous registration of segments
II. Mutual InformationII. Mutual Information
• Because different modality images have Because different modality images have different properties (e.g., relative intensity different properties (e.g., relative intensity of gray/white matter), cannot simply of gray/white matter), cannot simply minimise difference between imagesminimise difference between images
• Two main approaches:Two main approaches:
I. Via Templates:I. Via Templates:
1) Simultaneous affine registrations 1) Simultaneous affine registrations between between each image and same-modality each image and same-modality templatetemplate
2) Segmentation into grey and white matter2) Segmentation into grey and white matter
3) Final simultaneous registration of segments3) Final simultaneous registration of segments
II. Mutual InformationII. Mutual Information
EPI
T2 T1 Transm
PD PET
• Useful, for example, to display Useful, for example, to display functional results (EPI) onto high functional results (EPI) onto high resolution anatomical image (T1)resolution anatomical image (T1)
• Useful, for example, to display Useful, for example, to display functional results (EPI) onto high functional results (EPI) onto high resolution anatomical image (T1)resolution anatomical image (T1)
3. Registration of Partitions3. Registration of Partitions3. Registration of Partitions3. Registration of Partitions
1. Affine Registrations1. Affine Registrations1. Affine Registrations1. Affine Registrations
• Both images are registered - using 12 parameter affine Both images are registered - using 12 parameter affine transformations - to their corresponding templates...transformations - to their corresponding templates...
• … … but only the rigid-body transformation parameters allowed to but only the rigid-body transformation parameters allowed to differ between the two registrationsdiffer between the two registrations
• This gives:This gives:
– rigid body mapping between the imagesrigid body mapping between the images
– affine mappings between the images and the templatesaffine mappings between the images and the templates
• Both images are registered - using 12 parameter affine Both images are registered - using 12 parameter affine transformations - to their corresponding templates...transformations - to their corresponding templates...
• … … but only the rigid-body transformation parameters allowed to but only the rigid-body transformation parameters allowed to differ between the two registrationsdiffer between the two registrations
• This gives:This gives:
– rigid body mapping between the imagesrigid body mapping between the images
– affine mappings between the images and the templatesaffine mappings between the images and the templates
2. Segmentation2. Segmentation2. Segmentation2. Segmentation
• ‘‘Mixture Model’ cluster Mixture Model’ cluster analysis to classify MR analysis to classify MR image as GM, WM & CSFimage as GM, WM & CSF
• Additional information is Additional information is obtained from obtained from a priori a priori probability images - probability images - see latersee later
• ‘‘Mixture Model’ cluster Mixture Model’ cluster analysis to classify MR analysis to classify MR image as GM, WM & CSFimage as GM, WM & CSF
• Additional information is Additional information is obtained from obtained from a priori a priori probability images - probability images - see latersee later
Between Modality Co-registration: I. Via TemplatesBetween Modality Co-registration: I. Via TemplatesBetween Modality Co-registration: I. Via TemplatesBetween Modality Co-registration: I. Via Templates
• Grey and white matter Grey and white matter partitions are registered using a partitions are registered using a rigid body transformation rigid body transformation
• Simultaneously minimise sum Simultaneously minimise sum of squared differenceof squared difference
• Grey and white matter Grey and white matter partitions are registered using a partitions are registered using a rigid body transformation rigid body transformation
• Simultaneously minimise sum Simultaneously minimise sum of squared differenceof squared difference
Between Modality Coregistration: II. Mutual InformationBetween Modality Coregistration: II. Mutual Information Between Modality Coregistration: II. Mutual InformationBetween Modality Coregistration: II. Mutual Information
PET T1 MRI
Another way is to maximise Another way is to maximise the the Mutual InformationMutual Information in in the 2D histogram (plot of the 2D histogram (plot of one image against other)one image against other)
For histograms normalised For histograms normalised to integrate to unity, the to integrate to unity, the Mutual Information is:Mutual Information is:
iijj h hijij log h log hijij
kk h hikik ll h hljlj
Another way is to maximise Another way is to maximise the the Mutual InformationMutual Information in in the 2D histogram (plot of the 2D histogram (plot of one image against other)one image against other)
For histograms normalised For histograms normalised to integrate to unity, the to integrate to unity, the Mutual Information is:Mutual Information is:
iijj h hijij log h log hijij
kk h hikik ll h hljlj
New inSPM2
1. Realignment (motion correction)
2. Normalisation (to stereotactic space)
3. Smoothing
4. Between-modality Coregistration
5. Segmentation (to gray/white/CSF)
6. Morphometry (VBM/DBM/TBM)
1. Realignment (motion correction)
2. Normalisation (to stereotactic space)
3. Smoothing
4. Between-modality Coregistration
5. Segmentation (to gray/white/CSF)
6. Morphometry (VBM/DBM/TBM)
OverviewOverviewOverviewOverview
Image SegmentationImage SegmentationImage SegmentationImage Segmentation
• Partition into gray matter (GM), white matter (WM) and cerebrospinal fluid (CSF)Partition into gray matter (GM), white matter (WM) and cerebrospinal fluid (CSF)
• ‘‘Mixture ModelMixture Model’ cluster analysis used, which assumes each voxel is one of a number ’ cluster analysis used, which assumes each voxel is one of a number of distinct tissue types (clusters), each with a (multivariate) normal distributionof distinct tissue types (clusters), each with a (multivariate) normal distribution
• Further Bayesian constraints fromFurther Bayesian constraints from prior probability imagesprior probability images, which are overlaid, which are overlaid
• Additional correction for intensity inhomogeniety possibleAdditional correction for intensity inhomogeniety possible
• Partition into gray matter (GM), white matter (WM) and cerebrospinal fluid (CSF)Partition into gray matter (GM), white matter (WM) and cerebrospinal fluid (CSF)
• ‘‘Mixture ModelMixture Model’ cluster analysis used, which assumes each voxel is one of a number ’ cluster analysis used, which assumes each voxel is one of a number of distinct tissue types (clusters), each with a (multivariate) normal distributionof distinct tissue types (clusters), each with a (multivariate) normal distribution
• Further Bayesian constraints fromFurther Bayesian constraints from prior probability imagesprior probability images, which are overlaid, which are overlaid
• Additional correction for intensity inhomogeniety possibleAdditional correction for intensity inhomogeniety possible
.
Intensity histogramfit by multi-Gaussians
Priors:
Image:
Brain/skullCSFWMGM
1. Realignment (motion correction)
2. Normalisation (to stereotactic space)
3. Smoothing
4. Between-modality Coregistration
5. Segmentation (to gray/white/CSF)
6. Morphometry (VBM/DBM/TBM)
1. Realignment (motion correction)
2. Normalisation (to stereotactic space)
3. Smoothing
4. Between-modality Coregistration
5. Segmentation (to gray/white/CSF)
6. Morphometry (VBM/DBM/TBM)
OverviewOverviewOverviewOverview
Morphometry Morphometry (Computational Neuroanatomy)(Computational Neuroanatomy)
Morphometry Morphometry (Computational Neuroanatomy)(Computational Neuroanatomy)
• Voxel-by-voxelVoxel-by-voxel: : where are the where are the differences between populations?differences between populations?
– Univariate: e.g, Voxel-Based Univariate: e.g, Voxel-Based Morphometry (VBM)Morphometry (VBM)
– Multivariate: e.g, Tensor-Based Multivariate: e.g, Tensor-Based Morphometry (TBM)Morphometry (TBM)
• Volume-basedVolume-based: : is there a difference is there a difference between populations?between populations?
– Multivariate: e.g, Deformation-Multivariate: e.g, Deformation-Based Morphometry (DBM)Based Morphometry (DBM)
• Continuum:Continuum:
– perfect normalisation => all perfect normalisation => all information in Deformation field information in Deformation field (no VBM differences)(no VBM differences)
– no normalisation => all in VBMno normalisation => all in VBM
• Voxel-by-voxelVoxel-by-voxel: : where are the where are the differences between populations?differences between populations?
– Univariate: e.g, Voxel-Based Univariate: e.g, Voxel-Based Morphometry (VBM)Morphometry (VBM)
– Multivariate: e.g, Tensor-Based Multivariate: e.g, Tensor-Based Morphometry (TBM)Morphometry (TBM)
• Volume-basedVolume-based: : is there a difference is there a difference between populations?between populations?
– Multivariate: e.g, Deformation-Multivariate: e.g, Deformation-Based Morphometry (DBM)Based Morphometry (DBM)
• Continuum:Continuum:
– perfect normalisation => all perfect normalisation => all information in Deformation field information in Deformation field (no VBM differences)(no VBM differences)
– no normalisation => all in VBMno normalisation => all in VBM
Spatial Normalisation
Original Template
Normalised Deformation field
VBM TBM DBM
Originalimage
Spatiallynormalised
Segmentedgrey matter
Smoothed
“Optimised” VBM involves segmenting images before normalising, so as to normalise gray matter / white matter / CSF separately...
A voxel by voxel statistical analysis is used to detect regional differences in the amount of grey matter between populations
Voxel-Based Morphometry (VBM)Voxel-Based Morphometry (VBM)Voxel-Based Morphometry (VBM)Voxel-Based Morphometry (VBM)
SPM
Affine registration
Apply deformation
Segmentation & Extraction
Affine transform
Segmentation & extraction
Spatial normalisation
priors
Modulation
smooth
smoothSTATSvolume
STATSconcentration
template
Normalised T1
T1 image
Optimised VBMOptimised VBMOptimised VBMOptimised VBM
Grey matter volume loss with age
superior parietalpre and post central
insulacingulate/parafalcine
VBM Examples: AgingVBM Examples: AgingVBM Examples: AgingVBM Examples: Aging
Males > FemalesFemales > Males
L superior temporal sulcusR middle temporal gyrus
intraparietal sulci
mesial temporaltemporal pole
anterior cerebellar
VBM Examples: Sex DifferencesVBM Examples: Sex DifferencesVBM Examples: Sex DifferencesVBM Examples: Sex Differences
Right frontal and left occipital petalia
VBM Examples: Brain AsymmetriesVBM Examples: Brain AsymmetriesVBM Examples: Brain AsymmetriesVBM Examples: Brain Asymmetries
Deformation-based Morphometrylooks at absolute displacements
Tensor-based Morphometry looks at local shapes
Morphometry on deformation fields: DBM/TBMMorphometry on deformation fields: DBM/TBMMorphometry on deformation fields: DBM/TBMMorphometry on deformation fields: DBM/TBM
Vector field Tensor field
Deformationfields ...
Parameter reduction using principal component analysis (SVD)
Multivariate analysis of covariance used to identify differences between groups
Canonical correlation analysis used to characterise differences between groups
Remove positional and size information - leave shape
Deformation-based Morphometry (DBM)Deformation-based Morphometry (DBM)Deformation-based Morphometry (DBM)Deformation-based Morphometry (DBM)
Non-linear warps of sex differences characterised by
canonical variates analysis
Mean differences (mapping from an average female to
male brain)
DBM Example: Sex DifferencesDBM Example: Sex DifferencesDBM Example: Sex DifferencesDBM Example: Sex Differences
If the original Jacobian matrix is donated by A, then this can be decomposed into: A = RU, where R is an orthonormal rotation matrix, and U is a symmetric matrix containing only zooms and shears.
TemplateTemplateWarpedOriginal
Strain tensors are defined that model the amount of distortion. If there is no strain, then tensors are all zero. Generically, the family of Lagrangean strain tensors are given by: (Um-I)/m when m~=0, and log(U) if m==0.
Relative volumes
Strain tensor
Tensor-based morphometry
References
Friston et al (1995): Spatial registration and normalisation of images.Human Brain Mapping 3(3):165-189
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.IPMI’95 pp 263-274
Ashburner et al (1997): Incorporating prior knowledge into image registration.NeuroImage 6(4):344-352
Ashburner et al (1999): Nonlinear spatial normalisation using basis functions.Human Brain Mapping 7(4):254-266
Ashburner & Friston (2000): Voxel-based morphometry - the methods.NeuroImage 11:805-821