sMRI Spatial Normalization
Overview
Teaching: 30 min
Exercises: 15 minQuestions
What are reference coordinate systems
What are ‘templates’, ‘atlases’?
What is spatial normalization?
Objectives
Understand reference spaces and registration process
You Are Here!
Why do we need spatial normalization
Compare and combine brain images across modalities, individuals, and studies
What do we need for spatial normalization
1. A reference frame: A 3D space that assigns x,y,z coordinates to anatomical regions (independent of voxel dimensions!).
2. A common template: a single or an average image volume as an alignment target
3. An image registration algorithm
1. Coordinate systems and spaces
 World coordinates
 Anatomical coordinates
 Image coordinates
Image source
World coordinates
The world coordinates refer to a Cartesian coordinate system in which a MRI (or other modality) scanner is positioned.
Anatomical coordinates
The anatomical space is coordinate system (X,Y,Z) that consists of three planes to describe the standard anatomical position of a human
 Axial plane is parallel to the ground and separates the head (Superior) from the feet (Inferior)
 Coronal plane is perpendicular to the ground and separates the front (Anterior) from the back (Posterior)
 Sagittal plane separates the Left from the Right
The origin and directions of anatomical coordinate system are defined by conventions. In neuroimaging the most commonly used definition is the stereotaxic space.
Stereotaxic space
 A 3dimensional coordinate reference frame based on anatomical landmarks  originally used to guide neurosurgical procedures.
 A/P means anterior/posterior
 L/R means left/right
 S/I means superior/inferior
 Example: RAS
 First dimension (X) points towards the right hand side of the head
 Second dimension (Y) points towards the Anterior aspect of the head
 Third dimension (Z) points towards the top of the head
 Directions are from the subject’s perspective. In the RAS coordinate system, a point to the subject’s left will have a negative x value.
 Talairach space
 Derived from a single 60yr old female cadaver brain
 MNI space(s)
 Similar to the original Talairach space but the Zcoordinate has approximately +3.5 mm offset relative to the Talairach coordinate.
Image coordinates
The image coordinate system (i,j,k) describes the acquired image (voxels) with respect to the anatomy. The MR images are 3D voxel arrays (i.e. grids) whose origin is assigned at the upper left corner. The i axis increases to the right, the j axis to the bottom and the k axis backwards.
The MR image metadata stores the anatomical location of the image origin and the spacing between two voxels (typically in mm).
For examples:
 image coordinate: (0,0,0) ~ anatomical location: (100mm, 50mm, 25mm)
 The spacing between voxels along each axis: (1.5mm, 0.5mm, 0.5mm)
Image source
Quiz: coordinate systems
What happens when you downsample a MR image?
Solution
Downsampling reduces the number of total voxels in the image. Consequently the voxelspacing is increased as more anatomical space is “sampled” by any given voxel. Note that the new intensity values of the resampled voxels are determined based on the type of interpolation used.
2. MR image templates

An anatomical template is an average MR volume whose voxels encode the average probability of different tissue classes (e.g. WM, GM, and CSF) at particular spatial location. The template creation is an iterative process comprising normalization, alignment, and averaging of a set of MR images from several different subjects.

Structural T1‐weighted templates serve as a common reference space and allow researchers to combine and compare data from multiple subjects.
 Templates play an important role in a variety of neuroimaging tasks:
 Target image for spatial normalization in voxel‐wise analyses
 Automated intensity based WM, GM, and CSF tissue‐segmentation of MR images
 Anatomical atlas creation for region of interest analyses
 Automated seed selection for connectivity analyses

A good template is supposed to be a representative average of the study cohort. However for computational reasons (template creation is a computationally intensive process), and to maintain comparability across studies, image processing pipelines typically use publicly available templates.
 Commonly used templates:
 MNI 305
 an average of 305 T1weighted MRI scans from young healthy adults
 305 normal MRI brains were linearly coregistered (9param) to 241 brains that had been coregistered (roughly) to the Talairach atlas.
 Collin27
 One individual scanned 27 times and the images linearly registered to create an average with high SNR and structure definition
 Linearly registered to the MNI 305
 MNI152 linear a.k.a. ICBM152 (International Consortium for Brain Mapping)
 An average of 152 T1weighted MRI scans from young adults
 Linearly coregistered (9param) to the MNI 305
 Higher resolution and better contrast than the MNI305
 Used by SPM
 MNI152 nonlinear
 Version of MNI152 nonlinearly registered to MNI 305
 Updated versions
 MNI152NLin6Asym: used by FSL
 MNI152NLin2009cAsym: used by fMRIprep
 MIITRA
 An average of 222 T1weighted MRI scans from older adults
 Nonlinearly registered to MNI/ICBM152 2009 version.
 fsaverage
 Surface template characterized by “vertices and faces/triangles”
 Spherical alignment of 40 participants
 163,842 vertices per hemispheres
 MNI 305
T1 templates (MNI305, Collin27, MNI152 (linear), MNI152 (nonlinear))
Multimodal MNI/ICBM152 atlas
3. Image registration
A process that aligns an image from one coordinate space to another.
 Purpose
 building templates
 native (subject) space to templatespace alignment (normalization)
 intersubject alignment (typically for cohort specific)
 intrasubject alignment (coregistration of image modalities or longitudinal analyses)
 Image similarity metrics
 correlation ratio (CR)
 crosscorrelation (CC)
 mutual information (MI)
 Transforms
 Linear: global feature aligment
 Rigid (6 parameters): rotation, translation
 Affine (12 parameters): rotation, translation, scaling, skewing
 Nonlinear (a.k.a elastic): local feature aligment via warping
 Computationally intensive deformation models with large number of parameters
 Employ diffeomorphic models that preserve topology and sourcetarget symmetry
 Linear: global feature aligment
Note: Linear registrations are often used as an initialization step for nonlinear registration.
 Commonly used algorithms
Algorithm  Deformation  ~ parameters 

FSL FLIRT  Linear  9 
ANIMAL  Nonlinear (Local translation)  69K 
DARTEL Toolbox  Nonlinear (diffeomorphic)  6.4M 
ANTs (SyN)  Nonlinear (bidirectional diffeomorphic)  28M 
 Rigid registration example (source: SimpleITK):
 The figure below shows the source image being registered to the target (left) in an iterative process. The optimized loss is shown on the right.
 Nonlinear deformation example (source: 3D Slicer publication, wiki)
 The figure below shows local deformation (i.e. warping) of source image due to nonlinear registration.
Quiz: Image registration
What would the information encoded in the nonlinear deformation tell you about the subject?
Solution
The deformation fields encode information regarding local morphometric brain changes. These can be quantified using “Jacobians” of the deformation field, and can be used to assess subtle morphometric differences between groups or timepoints.
Python snippet (see ../code/3_sMRI_spatial_norm.ipynb for detailed example.)
from nilearn import plotting
from nilearn import image
from nibabel.affines import apply_affine
cut_coords = (40,10,0)
A = np.array([[1.053177, 0.061204, 0.060685, 90.310684],
[0.070210, 1.009246, 0.117766, 9.806847],
[0.023069, 0.117785, 1.186777, 13.209366],
[0. ,0. , 0., 1.]])
cut_coords_affine_transformed = apply_affine(A, cut_coords)
x,y,z = cut_coords_affine_transformed
cut_coords_affine_transformed_str = "({},{},{})".format(int(x),int(y),int(z))
print("Subject space to refernce space mapping:\n {} > {}".format(cut_coords,cut_coords_affine_transformed_str))
Subject space to refernce space mapping:
(40, 10, 0) > (47,2,11)
Subject space vs reference space: use cases
Key Points
Reference coordinate spaces and spatial normalization offer a way to map and compare brain anatomy across modalities, individuals, and studies