coreg and spatial

7/29/2019 Coreg and Spatial

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Co-registration and Spatial

Normalisation

Nazanin Derakshan

Eddy DavelaarSchool of Psychology, Birkbeck University of

London


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What is Spatial Normalisation?

It is a registration method that allows us towarp images from a number of individuals

into roughly the same standard space: this

allows signal averaging across individuals.

It is useful for determining what happens

generically over individuals.

The method results in spatially normalised

images.


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Why are spatially normalised images

useful?

They are useful because activation sites

can be reported according to their

Euclidian coordinates within a standardspace (Fox, 1995).

The most commonly adopted coordinatesystem within the brain imaging

community is that described by Talairach

& Toumoux (1988).


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How does the method work?

Normalisation usually begins by matching

the brains to a template image using

transformations. This is then followed byintroducing nonlinear deformations

described by a number of smooth basis

functions (Friston et al.1995a).


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So the method

Warps the images such that functionallyhomologous regions from different subjects are

as close together as possible

Problems: No exact match between structure and function

Different brains are organised differently

Computational problems (local minima, not enough

information in the images, computationally expensive)

Compromise by correcting gross differences

followed by smoothing of normalised images


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Affine and Non-linear Registration


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Affine registration

The objective is to fit the source image fto a

template image g, using a twelve parameter

affine transformation. The images may be scaled

quite differently, so an additional intensityscaling parameter is included in the model.

Make sure you have plenty of slices


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When the error for a particular fitted parameter is

known to be large, then that parameter will be

based more upon the prior information.

In order to adopt this approach, the prior

distribution of the parameters should be known.

This can be derived from the zooms and shears

determined by registering a large number of

brain images to the template.


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Affine Registration The first part is a 12 parameter

affine transform 3 translations

3 rotations

3 zooms

3 shears

Fits overall shape and size

z Algorithm simultaneously minimises

y Mean-squared difference between template and

source image

y Squared distance between parameters and their

expected values (regularisation)


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Affine Registration

Minimise mean squared difference fromtemplate image(s)

Affine registration

Affine registration

matches positionsand sizes of images.


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Non-Linear Spatial Normalisation

Assumes that the image has already beenapproximately registered with the template

according to a twelve-parameter affine

registration.

It is used when the parameters describing

global shape differences are not accountedfor by affine registration.


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The model for defining nonlinear warps

uses deformations consisting of a linear

combination of low-frequency periodic

basis functions.


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Non-linear registration

Affine + Non-linear

Size and global shape of

the brain is normalised.


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Without regularisation, the non-

linear spatial normalisation can

introduce unnecessary warps.

Regularisation


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Regularization is achieved by minimizingthe sum of squared difference between the

template and the warped image, while

simultaneously minimizing some function of

the deformation field. The principles are

Bayesian and make use of

the MAP (Maximum A Posteriori) scheme


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Template

image

Affine

registration

(2 = 472.1)

Non-linear

registration

without

regularisation.

(2 = 287.3)

Non-linear

registration

using

regularisation.

(2 = 302.7)

Over-fitting


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Algorithm simultaneously minimises

Mean squared difference between

template and source image

Squared distance between parameters

and their known expectation

Deformations consist of a linear combination of

smooth basis functions

These are the lowest frequencies of a 3D

discrete cosine transform (DCT)


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Co-registration

Matching of two images of different modalities

(e.g., T1 with T2) by finding the transformation

parameters

Why co-registration? Realigning functional images can be greatly

facilitated by having high-res structural images

Allows a more precise spatial normalization asthe warps computed from structural images can

be applied to the functional images.


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co-registration maximizes the mutual

information between two images

MI is a measure of the dependence

between images


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Now a tiny bit more technical


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Spatial normalization: procedure that

warps images from a number of

individuals into roughly the same standard

space to allow signal averaging acrosssubjects.


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Purpose of spatial normalization is to

maximize the sensitivity to neuro-

physiological change elicited by

experimental manipulation of sensorimotoror cognitive state

may imply that condition-dependent

effects should be incorporated in theoptimization procedure


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Techniques I

Label-based techniques: identify

homologous features in the source and

reference images and find the

transformations that best superpose them. Labels: (discrete) points, lines, surfaces

Identified manually, time-consuming,

subjective


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Techniques II

Intensity-based techniques identify a

spatial transformation that optimizes some

voxel-similarity measure between a source

and reference image, where both aretreated as unlabelled continuous

processes.

Hybrid approaches: combine intensitybased methods with matching user-

defined features (typically sulci)


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Warping: high-dimensional problem, but

much of the spatial variability can be

captured using just a few parameters.

Warping transformations are arbitrary and

regularization schemes are necessary to

ensure that voxels remain close to their

neighbors.


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Regularization is often incorporated in a

Bayesian scheme, using maximum a posteriori

(MAP) or minimum variance estimate (MVE).

(elastic: convolving a deformation field is a formof linear regularization)

An alternative to Bayesian methods is using a

viscous fluid model to estimate the warps.(plastic: not the deformation field is regularized,

but the increments to the deformations at each

iteration)


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Bayesian registration scheme to obtain

MAP estimate of registration parameters

usespriorknowledge of variability in

brain size/shapes


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Bayes here as well? - Yes.


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Assumptions

qMAP=mode[p(q|b)], p(q|b) ~ p(b|q)p(q)

All D(p) approx. multi-normal distributions

equal variance for each observation:estimated from SSE from current iteration

Exact form of p(q) is known

not strictly correct, but close enough


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Affine registration

Determine 9 or 12 parameter affine

transformation that registers images

together by minimizing some mutual

function

Aim is to fit source image f to template g

with using ourpriorknowledge about

those q-parameters (courtesy of nicepeople giving their knowledge)


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Nonlinear registration/spatial

normalization (i.e., doing the curvy stuff)

Assumes image already approx registered with

template

Model for defining nonlinear warps uses

deformations consisting of linear combinationsof low-frequency periodic basis functions

(because HF is lost during smoothing)

Discrete (co)sine transform

Optimize q-parameters that weight the various

basis functions


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Lowest basis functions of a 2D DCT

Different boundary conditions

(DST, DCT/DST, DCT)

Getting the curvy stuff


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Linear regularization

Regularization achieved by minimizing

SSE between template and warped image,

while minimizing some function of the

deformation field.

MAP approach assumes prior estimate

with mean zero. Choice of prior affects

energy Membrane, bending, linear-elastic energy

(read more in Chapter 2 by Ashburner & Friston)


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Chapter 1, Figure 2 by Friston

Can you read this now???


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Cool, however

Fitting method not optimal when there is

no linear relationship between images,

e.g., intensities vary (across modalities)

By taking intensity into account, many

reference images can be used for

registration

Co-registration: matching differentmodalities on the corresponding templates


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Caveats of MAP

No guarantee to get the global optimum

No one-to-one match for small structures

MVE may be more appropriate: is theaverage of all possible solutions, weighted

by their individual posterior probabilities

If errors are Normal, MAP=MVE. This is

partially satisfied by smoothing before

registering


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Further references

Friston, K. J. Introduction: Experimental

design and statistical parametric mapping

Ashburner, J., & Friston, K. J. Chapter 2

Rigid body registration.

Ashburner, J., & Friston, K. J. Chapter 3

Spatial normalization using basis

functions.

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