1. Coregistration and Spatial Normalisation
Ana Saraiva
Britt Hoffland

2. (Co-registration and) Spatial
Overview
Motion
correction
Smoothing
kernel
(Co-registration and) Spatial
normalisation
Standard
template
fMRI time-series
Statistical Parametric Map
General Linear Model
Design matrix
Parameter Estimates

3. Between modality co-registration
PET
T1 MRI
Refers to any method for realigning images, like realignment for motor correction (last week), however we can also realign images from two different modalities like combining morphological information assessed by MRI with functional information of for example PET

4. Why is between-modality co-registration useful?
Significant advantages in research and clinical settings
Co-registration maximizes the mutual information between two images
clinical setting: anatomical identification (MRI) with local pathologies (PET), compensation for atrophy
research: better anatomical identification of local areas, normalisation benefits from high-res images

5. Principles of co-registration
Registration  Transformation
6 Parameters for motion correction
When several images of the same subject are acquired it is useful to have them al in register; image registration involves estimating a set of parameters describing a spatial transformation that best matches these images (and then resampling according to determined transformation parameters)

6. Different for between-modality coregistration
Shape
Signal intensities
EPI T2 T1
Transm PD
PET
However with between-modality coregistration we cannot simply mimise the differences between different images because of the different shape and signal intensities (relative intensities of grey/white matter vary between functional and structural, no voxel to voxel match, no simple subtraction signal intensities)

7. Between modality registration
Manually (homologous landmarks)
I via templates
II mutual information
Manual identification of homologous landmarks in both images (time consuming, requires degree of experience, subjective)

8. Via Templates 12 parameter affine transformations
Templates conform to the same anatomical space
Simultaneous registration
Both images are simultaneously registered to their corresponding template (templates conform to the same anatomical space) using 12 parameter affine transformations
Affine transformation is a linear transformation followed by a translation ax+b

9. 1. Affine Registration 12 parameter affine transform
3 translations
3 rotations
3 zooms
3 shears
Fits overall shape and size
Algorithm simultaneously minimises
Mean-squared difference between template and source image
Squared distance between parameters and their expected values (regularisation)
However, while the images are both realigned to their corresponding template, only the 6 rigid body transformation parameters (bold on the screen: 3 translations and 3 rotations) are allowed between these two registrations

10. However… Image MRI  Template MRI Scaling/shearing parameters
Rigid body transformation parameters
Image PET  Template PET
However… only the rigid body transformation parameters are allowed to differ… because we now know the rigid body parameters for image MRI to fit template MRI and image PET to template PET AND because the template confirm to the same anatomical space we now know the rigid body mappings between the MRI and PET image

11. 2. Segmentation Partition in GM, WM, CSF Priors: Image: Brain/skull
Images consists of number of disctinct tissue types (clusters) from which every voxel has been drawn, intensities of these voxels belong to one of these clusters and confirm to a multivariate normal distribution (generalization of the one-dimensional normal distribution to higher dimensions)
Therefore we overlay these images on probability images (images from a largen number of subjects segmented in GM, WM, CSF normalized in same space using affine transformations) this gives us the a priori probability of a voxel being GM, WM or CSF

12. Registration of partitions
Grey and white matter partitions are registered using a rigid body transformation,
Simultaneously minimise sum of squared difference…

13. Between Modality Coregistration: II. Mutual Information
PET
T1 MRI

14. Co-registration in SPM

15. Co-registration in SPM
Make selection
NB Why would you reslice? What does this mean?
Explains each option

16. Template: image that remains stationary
Image that is ‘jiggled about’ to match template
Defaults used by SPM for estimating the match, including Normalised Mutual Information
Run
Reslice options: choose from the menu for each of the three options (usually just defaults)

17. Spatial Normalisation

18. fMRI pre-processing sequence
Realignment
Motion correction: Adjust for movement between slices
Coregistration
Overlay structural and functional images: Link functional scans to anatomical scan
Normalisation
Warp images to fit to a standard template brain
Smoothing
To increase signal-to-noise ratio
Extras (optional)
Slice timing correction; unwarping

19. What is spatial normalisation?
Establishes a one-to-one correspondence between the brains of different individuals by matching each subject to a standard template
Allows:
Signal averaging across subjects
Determination of what happens generically over individuals
Identify commonalities and differences between groups (e.g. patients vs. healthy individuals)
Advantages:
Activation sites can be reported according to their Euclidian coordinates within a standard space (e.g. MNI or Tailarach & Tournoux, 1988)
Increases statistical power
It mainly concerns with mapping a single subjects brain image into a standard space – the brain of a subject is transformed to better match the brain or another subject or template
Allows for generalising findings to a population level
Make results from different studies comparable by aligning them to standard space
e.g. The T&T convention, using the MNI template
The MNI template follows the convention of T&T, but doesn’t match the particular brain
SPM 96 and later use standard brains from the Montreal Neurological Institute. The MNI defined a new standard brain by using a large series of MRI scans on normal controls. The current standard MNI template is the ICBM152, which is the average of 152 normal MRI scans that have been matched to the MNI305 using a 9 parameter affine transform
Montreal Neurological Institute

21. Methods of registering images
Label-based
Identifies homologous features (points, lines and surfaces) in the image and template and finds the transformations that best superimpose them
Limitations: few identifiable features; features can be identified manually (time consuming & subjective)
Non-label based (aka intensity based)
Identifies a spatial transformation that optimizes some voxel-similarity between a source and image measure by:
Minimising the sum of squared differences between the object and template image
Maximising correlation coefficient between the images.
Limitation: susceptible to poor starting estimates
- Registering images of different subjects into roughly the same coordinate system, where the co-ordinate system is defined by a template image
Methods can be divided into 2 categories
Once labels are identified, the spatial transformation can be effected by bringing the homologies together
For this matching criterion to be successful, the template is a warped version of the image – that is, there must be a correspondence in the grey levels of the different tissue types between the image and template

22. Spatial Normalisation in SPM
2 steps involved in registering any pair of images:
Linear registration - 12-parameter affine transformation – accounts for major differences in head shape and position
Nonlinear registration – warping – accounts for smaller-scale anatomical differences
Registration – determines the parameters describing a transformation
Transformation – transforms one of the images according to the set of determined parameters

23. Priors/Constraints
Both linear and non-linear registrations use prior knowledge of the variability of the head and size to determine constraints
Priors/constraints are calculated using estimators such as the maximum a posteriori (MAP) or the minimum variance estimate (MVE)
In order to transform an image to the same space, constraints are necessary otherwise it would be possible to transform any image such that it matches another exactly which would not represent the true shape of the brain
MAP estimates work by estimating the optimum coefficients for a set of bases, by minimizing the sum of squared differences between the template and source image, while simultaneously minimizing the deviation of the transformation from its expected value.
Constraints and priors smooth out the image
You don’t want voxels to be all over the place therefore you need to set some constraints beforehand

24. Step 1 – Affine transformation (Linear)
Aim: to fit the source image f to a template image g, using a 12-parameter affine transformation
Performed automatically by minimizing squared distance between parameters and expected values
12 parameters =
3 translations and 3 rotations
(rigid-body) + 3 shears and 3 zooms
Accounts for overall shape, size,
position and orientation
rotation
sheer
The first step in registering images from different subjects involves determining the optimum12 parameter affine transformation.
Affine registration matches positions and sizes of images.
Zooms and shears are needed to register heads of different shapes and sizes. Prior knowledge of the variability of head sizes is included within a Bayesian framework in
order to increase the robustness and accuracy of the method.
Given the small number of parameters, it doesn’t allow every feature to be matched exactly but it allows a global shape of the head to be modelled
translation
zoom

25. Step 2 – Warping (non-linear)
Corrects gross differences in head shapes that cannot be accounted for by the affine transformation
Warps are modelled by linear combinations of smooth discrete cosine transform basis functions
Uses relatively small number of parameters (approx. 1000)
Deformations transform the image to the space
Assumes that the image has already been approximately registered with the template according to a twelve-parameter affine registration.
But not as little as 12-parameter affine transformation

26. Non-linear basis functions
Deformations are modelled with a linear combination of non-linear basis functions

27. Over-fitting Affine registration (linear) Template
Regularisation – necessary so that nonlinear registration does not introduce unnecessary deformations
Ensures voxels stay close to their neighbours
Affine registration (linear)
Template
Without regularization in the nonlinear registration, it is possible to introduce unnecessary deformations that only reduce the residual sum of squares by a tiny amount. This could potentially make the algorithm very unstable. Regularization is achieved by minimizing the sum of squared difference between the template and the warped image, while simultaneously minimizing some function of the deformation field.
Non-linear registration without regularisation
Non-linear registration with regularisation

28. Limitations
Difficult to attempt exact structural matches between subjects, due to individual anatomical differences
Even if anatomical areas were exactly matched, it does not mean functionally homologous areas are matched too
This is particularly problematic in patient studies with lesioned brains
Solution: To correct gross differences followed by spatial smoothing of normalised images…
Aim: To warp the images to match functionally homologous regions from different subjects
we don’t know the extent to which individuals may vary in their structure-function relationships.

29. Normalisation in SPM
Calculates warps needed to get from your selected images – saves in sn.mat file
Estimate will calculate what warps are needed to get from your selected image to the template, and will generate a file containing these images ending in “sn.mat”.
Estimate and Write will do the same, and then apply these warps to your selected image, producing a new image file with the same filename, but with an additional “w” at the front (standing for “warped”). Note that you can select multiple images to apply the warps to – so that you can normalize a set of coregistered images in one step.
Write can be used if you already have your specified sn.mat file from previously normalized data

30. Select the image that will be matched to the template
Select image(s) to be warped using the sn.mat calculated from the Source Image
Select SPM template
Select voxel sizes for warped output images

31. References
Ashburner & Friston – Spatial Normalisation Using Basis Functions, Chapter 3, Human Brain Function, 2nd Ed
Ashburner & Friston – Nonlinear Spatial Normalisation Using Basis Functions, Human Brain Mapping, 1999
Ashburner & Friston - Multimodal image coregistration and partitioning--a unified framework, Neuroimage, 1997
MFD slides from previous years