Image registrationin

BrainVoyager QX

March 21, 2008

Contents

1 Principles of image registration 11.1 The image registration process . . . . . . . . . . . . . . . . . . . . . . 1

1.1.1 Estimation of the transformation . . . . . . . . . . . . . . . . . 21.1.2 Applying the transformation . . . . . . . . . . . . . . . . . . . 17

2 Artifacts 182.1 Pre-existent artifacts . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

2.1.1 Subject-based . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182.1.2 Scanner-based . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

2.2 Possibly introduced artifacts . . . . . . . . . . . . . . . . . . . . . . . . 192.2.1 Transformation models . . . . . . . . . . . . . . . . . . . . . . 192.2.2 Measures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 202.2.3 Optimization . . . . . . . . . . . . . . . . . . . . . . . . . . . . 202.2.4 Interpolation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 202.2.5 Resampling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

3 Evaluation and validation of the registration 223.1 Criteria for evaluation . . . . . . . . . . . . . . . . . . . . . . . . . . . 223.2 Validation measures . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

3.2.1 Gold standard . . . . . . . . . . . . . . . . . . . . . . . . . . . . 233.2.2 Fiducials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 233.2.3 Labeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

3.3 Evaluation, validation in BrainVoyager QX . . . . . . . . . . . . . . . 243.3.1 Visual evaluation . . . . . . . . . . . . . . . . . . . . . . . . . . 243.3.2 Labeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 263.3.3 Quantification of registration accuracy . . . . . . . . . . . . . . 26

4 Comparison studies and benchmarks 274.1 Motion correction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 274.2 Image registration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

5 Conclusions about image registration situations 285.1 Conclusions from the literature . . . . . . . . . . . . . . . . . . . . . . 28

5.1.1 Affine transformation . . . . . . . . . . . . . . . . . . . . . . . 285.1.2 Spatial normalization / Talairach transformation . . . . . . . 285.1.3 High-dimensional warping vs. alignment along cortex cur-

vature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 285.1.4 Performing group statistics . . . . . . . . . . . . . . . . . . . . 295.1.5 Performing independent component analysis (ICA) . . . . . . 29

5.2 Optimizing registration in BrainVoyager QX . . . . . . . . . . . . . . 315.2.1 Atypical subject morphology and manual alignment . . . . . 315.2.2 Optimizing motion correction . . . . . . . . . . . . . . . . . . . 31

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5.2.3 Alternative for motion correction . . . . . . . . . . . . . . . . . 365.2.4 Improve the quality of the automated image registration . . . 365.2.5 Improve the quality of the anatomical image (*.vmr) . . . . . 365.2.6 Improve the quality of inter-subject alignment . . . . . . . . . 36

A Affine transformation matrices 37

B Optimization 40

C Interpolation methods 42

D Metric spaces 44

E Constraints on the transformation 46E.1 Diffeomorphisms (differentiable mappings) . . . . . . . . . . . . . . . 46

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Abstract

Outline This document is created in order to provide an overview of the imageregistration methods that are available in BrainVoyager QX so that the optimalimage registration method can be selected for each situation (motion, intra-modal,inter-modal, etc).Thanks to Armin Heinecke, Bettina Sorger and Joost Mulder who contributed tothis document.

Document version : 0.3. This document has a draft status. Therefore, it currentlyserves merely as a pointer to relevant literature and tools because the informationcan be incomplete and/or may contain errors.Before starting the data analysis, please always consult the original literature thatis referred to in this document and the official documentation for BrainVoyager QXwritten by prof. dr. Rainer Goebel.See for example the online BrainVoyager QX User’s Guide

http://www.brainvoyager.com/bvqx/doc/UsersGuide/WebHelp/BrainVoyagerQXUsersGuide.htmhttp://web.mac.com/rainergoebel/RainersBVBlog/Rainers_BV_Blog/Rainers_BV_Blog.html

and “Rainer’s BV Blog”.

Hester Breman, Brain Innovation B.V., 2008

Chapter 1

Principles of image registration

1.1 The image registration process

To transform one image to another, we need to estimate the parameters to trans-form the image. Then the parameters can be applied to transform the image. For adepiction of the image registration process, see figure 1.1.

Figure 1.1: The global image registration process

Examples of image registration in BrainVoyager QX are the motion correction,the FMR to VMR coregistration (see figure 1.2, the transformation to Talairachspace and the cortex-based alignment (CBA). These are all instances of intensity-based or landmark-based image registration.

Figure 1.2: Example of the image registration process in BrainVoyager QX

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1.1.1 Estimation of the transformation

The parameter estimation process consist of the following steps (see figure 1.3):

1. Select a transformation model.

2. Initialize the transformation parameters.

3. Compute the similarity between the images using a metric (repeat)

4. Increase the similarity between the images using optimization (repeat)

5. Interpolate to compute new intensity values on each position of the image(repeat)

6. If the images are similar enough, stop.

First, the image that consists of discrete pixels or voxels is made continuous sothat the intensity at a position in space is a function of the coordinates: f(x, y, z)(see Young et al, [54]; see also figures 1.5 and 2.1).Then, with or without computing the image derivatives, the parameters are slightlychanged to make the images more similar; then the new distance between the im-ages is computed. This distance is computed using a metric (see section 1.1.1).Then, the image is changed from continuous to discrete by computing the new in-tensity values at the voxel center positions via interpolation and resampling (seesection 1.1.1).An image registration process starts with an initialization of the parameters, i.e.an initial guess for the rotation, translation and scaling parameters. Often they arejust set to zero. After the initialization, a cyclic process is applied until the shortestdistance between the images has been found (see figure 1.3).

Figure 1.3: The image registration process

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Selecting a transformation model

Via the transformation model is defined how many parameters are used to trans-form or deform the source image to the target image (see figure 1.5). In the transfor-mation function or mapping is defined how many of parameters should be usedfor the transformation; this is the search space for the optimizer. For rigid bodytransformations, this are 6 parameters: translation in x, y, z and rotation over x,y and z-axis. During the registration process, the parameters are updated to theoptimal transformation via an iterative process.

Figure 1.4: Transformation models according to Lester and Arridge (1999)

Rigid and affine transformations are global transformations (the same trans-formation applies to all coordinates). Non-linear transformations/warps are local(transformations locally defined:spatially varying deformations).

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Linear or global transformationsCoordinate changes for a 3-dimensional object in vector space can be classified

as global or local (see figure 1.6 and 1.5). When the coordinates of an object arechanged, this can be represented in a matrix (see appendix A).

Figure 1.5: Possible models to transform an image to another

For a 3-dimensional brain image, a 4x4 (homogeneous) matrix can be used fora global coordinate change. This involves a coordinate change along all axes orsome of the axes. Changes can be translations (shifts to a certain direction), rota-tions, scaling (change of size, sometimes referred to as zooms), shears (skewnesstowards one direction) and perspective transformations (vanishing horizon in asingle point).

Figure 1.6: Types of transformations after Woods (2001)

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Rigid body transformations In case of rotations and/or translations, the geomet-rical transformation is called rigid body.

Affine transformations When scaling is involved as well, it is called an affine trans-formation. Affine transformations map parallel lines to parallel lines [22, p.112].For affine transformations, 4 types of parameters are possible, which are rotation,translation, scaling and shearing (see figure 1.1.1).

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Hierarchical transformation modelThe hierarchical transformation model using increasing data complexity (see fig-

ure 1.4) mentioned by Lester & Arridge (1999, [31] is applied in BrainVoyager QXto register functional to anatomical images (see figures 1.7 and 1.8).First, low-resolution images are taken from the original images and registered toeach other.Then the resolution is gradually increased. This method is called Gaussian/Laplacianscale pyramidal registration.

Figure 1.7: Select the 2D-3D hierarchical transformation method via the 3D VolumeTools in BrainVoyager QX

Figure 1.8: BrainVoyager QX creating Gaussian/Laplacian scale pyramids

Piecewise linear transformationsFrom Holden (2008, [22, par.K]):

... the source image is divided into a number of rectangular subim-ages or blocks and these are individually registered to the target image.

In BrainVoyager QX, the spatial normalization to the Talairach & Tournoux at-las [46] is based on a piecewise linear transformation model. There are twelvepieces, according to the proportional grid.

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Non-linear or local transformations (warps)Non-rigid transformations map straight lines to curves [22, p.112], which is de-

picted in the lower part of figure 1.9.

Figure 1.9: Global vs. local mappings

When local coordinate changes are allowed, a larger matrix is required thanthe 4x4 matrix used for affine transformation, for example a 9x4 matrix. Thistransformation does not only involve linear coordinate changes (multiplication,f.e. x′ = a ∗ x + b ∗ y + c ∗ z + d) but also second-order factors (f.e. e04x2), usinga second-order polynomial in the equation. When transformations are non-linear,they are called warps. Non-linear transformations account for local expansion andcontraction; these phenomena can for example be observed when a BrainVoyagermesh (*.srf) is being morphed.Because the coordinate changes concern real objects in a 3-dimensional Euclideanspace R3, concepts used in digital image processing originate from mechanics (cf.[35]); therefore Holden (2008), see below has based part of his transformationmodel categorization on physically based models.For more information about geometrical transformations in image processing, goodreferences are Foley et al (1996, [15]) and Woods (2000, [51]).

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Holden (2008, [22]) categorizes geometric transformations in the types physi-cally based models and basis function expansions (see figure 1.10).

Figure 1.10: Transformation categories by Holden (2008)

The physically based models refer to transformation processes of substances orfluids like rubber resp. water and originate from continuum mechanics (cf. Mars-den & Ratiu [35, ch.15]). These are the elastic and fluid flow transformations (see leftside of image 1.10).The basis function expansions are derived from approximation and informationtheory (cf. MacKay [32]). The basis function expansions can be radial basis func-tions (RBF), splines and wavelets.The unknowns in the elastic deformation system of equations are stress, strain anddisplacement [22]. They result in a Navier-Cauchy partial differential equation(PDE).

The Navier-Cauchy PDE [...] is essentially an optimisation prob-lem that involves balancing the external forces (image similarity) withthe internal stresses that impose smoothness constraints [...]. It can besolved using variational [...], finite difference [...], [...], FEM models [...],basis function expansion [...] and Fourier transform methods [...].

From Holden [22, p.114]. For an elaborate description of the implementation of anelastic model, see Davatzikos (1997, [12]).

Figure 1.11: Mesh morphing forces in BrainVoyager QX

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In BrainVoyager QX, elastic transformations are typically found in mesh mor-phing. The elastic transformation process is guided by the smoothing, surfacefinding and distortion reduction forces (see figure 1.11).

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Compute image similarity via the registration metric

“A registration metric takes two images as input and returns a real value that in-dicates how well the images are aligned” [22]. So the registration or similaritymetric describes the distance between two images in a metric space (see appendixD). The metric describes how well the parameters fit to the data. Synonyms are ob-jective function, or cost function. The distance can be based on geometrical featuresor on intensity measures.

Examples of similarity measures are (see [45]):statistical: correlation ratio, sum of squared differences (SSD), ratio image unifor-mity (RIU, by Woods)information theory based: mutual information (MI), normalized mutual information(NMI), asymmetric gradient based multi feature mutual information (AMMI), en-tropyspectral: energy of the histogram (H)

A metric is a distance function, describing the closeness of two points in space,or the similarity of the images. Because the metric describes how different or sim-ilar the images are, this number should be minimized resp. maximized; this isperformed by the optimization part of the registration process.

Similarity based on geometrical featuresRohr (2004, [43]) shows the existence of the 3D anatomical landmarks tip/peak,

tip/cusp, saddle, junction (3 surfaces), junction (2 curves) via figure 1.12).

Figure 1.12: 3D anatomical landmarks

Paragios & Deriche (2005, [39]) use optical flow and level set methods to trackboundaries for motion estimation. Mangin et al (2004, [34]) use a graph structureto characterize the cortical folding pattern.In BrainVoyager QX, landmark-based registration can be performed for point-based registration of 3D to 3D volumes and spatial normalization to the Talairach& Tournoux atlas [46]. Another feature-based registration method in BrainVoyagerQX is the cortex-based alignment.

Similarity based on intensityThe estimation based on intensities is performed by computing the image gra-

dients. For an explanation, see for example Mulders (2007, [37]).

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Estimation in BrainVoyager QXTable 1.1 shows the functions that can be used in BrainVoyager QX to estimate

parameters for transforming one image to another.

Function Estimation typeMotion estimation Intensity/entropy basedIntra-session alignment (ISA) Intensity/entropy basedAnatomical to functional registration, fine Intensity/entropy basedCortex-based alignment Geometry/feature-basedAnatomical to AC-PC Geometry/feature-basedAnatomical to Talairach Geometry/feature-basedCorresponding points Geometry/feature-based

Table 1.1: Transformation parameter estimation functions in BrainVoyager QX

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Optimization

The source or floating image needs to be moved to the target image in order tomake it more similar. The direction for the movement is usually found using gra-dients, although this is not necessarily so (see figure 1.13, based on [41, ch. 15]).

Figure 1.13: Optimization methods

Optimization in BrainVoyager QXIn BrainVoyager QX, the intensity-based parameter determination for motion es-

timation can be inspected via a log file (*_3DMC_verbose.log). In BrainVoyagerQX, the Levenberg-Marquardt optimization is used for determination of the mo-tion parameters. The process is depicted in appendix B. For details, please consultPress et al (2002, [41]).

Figure 1.14: The computation of parameters for motion correction can be saved toa BrainVoyager QX log file

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Interpolation and resampling

During interpolation, the new intensity values at the voxel center positions arecomputed.Meijering et al (2001, [36]) classify interpolation methods into the categories shapeor morphology-based, Fourier-based and convolution-based (see appendix C).The convolution-based methods are divided in SINC and SINC approximationmethods. These SINC approximation methods compute the intensity values withdifferent weighting functions for neighboring voxel values. Because the SINC can-not be fully computed because it has infinite support, in practice the SINC ap-proximation interpolation methods are used (1. symmetrical piecewise polynomi-als: nearest neighbour, linear, Lagrange; 2. generalized; 3. piecewise polynomials(splines); 4. windowed/apodized SINC).

Figure 1.15: A spline is a curve composed of piecewise presentations or polynomi-als. They are connected via knots and the shape is controlled via the control points.The control points can be stored in a coefficient matrix.

For a comparison study of interpolation methods and details on generalizedand spline-based interpolation, see Thevenaz et al [47].

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Interpolation in BrainVoyager QXThe interpolation methods that are offered in BrainVoyager QX for each regis-

tration function are shown in table 1.1.1.

Function Nearest neighbour (Tri)linear Windowed SINC Cubic splineSlice scan time correction - yes yes yesSlice scan time correction , scripting (QX1.9) - yes yes yesMotion correction - yes yes -Motion correction via scripting 0 yes - -Intra-session alignment (ISA) 0 yes - -Intra-session alignment, scripting 0 yes - -Anatomical to functional registration 0 0 0 0Anatomical to AC-PC yes yes yes yesAnatomical to Talairach yes yes yes -Functional to Talairach (VTC) yes yes yes -Functional to Talairach, scripting yes yes yes -Diffusion to Talairach (VDW) yes yes yes -Cortical thickness analysis yes yes - -Cortex based alignment 0 0 0 0

Table 1.2: Interpolation methods available in BrainVoyager QX

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Stopping criterion

The cyclical parameter estimation process will stop when the similarity measurematches the stopping criterion. This means that the current parameters to trans-form the source image to the floating image cannot be improved any more. Thestopping criterion can be specified in two ways [41]:

1. Iterate until the algorithm has found the minimum or maximum (conver-gence)

2. Use a parameter that indicates when to stop. This parameter is then usedto stop the process when a new iteration round makes only a very smalldifference to the found minimum or maximum, for example 0.01 or 10−3, orwhen a maximum number of iterations has been reached (see figure 1.16).

Figure 1.16: For motion estimation in BrainVoyager QX, the maximum number ofiterations per volume can be adapted

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Saving estimation parameters in BrainVoyager QX

The parameters resulting from the estimation process can mostly be saved in Brain-Voyager QX, except in cases where the estimation and transformation is appliedimmediately, in case of high-dimensional warping. Details can be found in table1.1.1.

Saving affine transformation parametersAffine estimation parameters are usually saved in a 4x4 transformation matrix

that can be found in a transformation file (*.trf)(see figure 1.17).

Figure 1.17: Affine transformation matrix in BrainVoyager QX transformation file

More information about affine transformation matrices can be found in ap-pendix A.

Function Can be saved File format Re-application or inversionMotion correction Yes *3DMC.rtc and *3DMC verbose.log Yes (via GLM modeling)Motion correction via scripting Yes *3DMC.rtc and *3DMC verbose.log Yes (via GLM modeling)Intra-session alignment (ISA) No - -Intra-session alignment, scripting No - -Anatomical to functional registration, initial Yes *IA.trf Yes (via 3D Volume Tools)Anatomical to functional registration, fine Yes *FA.trf Yes (via 3D Volume Tools)Anatomical to functional registration, manual Yes *MAN.trf Yes (via 3D Volume Tools)Corresponding points registration Yes *.cps YesAnatomical to AC-PC Yes *ACPC.trf Yes (via 3D Volume Tools)Anatomical to Talairach Yes *.tal and in VMR header YesCortex based alignment Yes *.vmp (curvature), *.ssm (mappings) 0

Table 1.3: Saving estimation parameters in BrainVoyager QX

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1.1.2 Applying the transformation

After the parameters to transform the image to another image have been estimated(and possibly saved), the transformation can be applied at that timepoint or at alater timepoint.An example of the application of a transformation in BrainVoyager QX is the cre-ation of VTC files, where the transformation that has been estimated during theinitial and fine alignment coregistration, is now applied by creating a volumetime course file (*.vtc). The same is valid for the creation of normalized diffusionweighted files (*.vdw) from *.dmr→ *.vmr coregistration.

Figure 1.18: Applying a rigid body or affine transformation via the BrainVoyagerQX 3D Volume Tools

Another example is the application of a manually specified transformation.This can be performed via the Spatial Transformations tab of the BrainVoyagerQX 3D Volume Tools (see figure 1.18).

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Chapter 2

Artifacts

2.1 Pre-existent artifacts

The following artifacts can be already present in the data at the moment that theyare acquired. Therefore it cannot be said without doubts that the original acquiredimage is the “true” image. The artifacts that are already in the data are dependentof the subject and the scanner. The severity of the artifacts can also be dependentof the type of gradient (imaging modality).

2.1.1 Subject-based

MotionHemmendorf states [21]:

movement within scans should lead to apparent deformations ofthe object during the scan/scans within which movement occurs. Inthe temporal domain this should yield effects related to the temporalderivative of the movement parameters, and in the spatial domain itshould be pronounced along edges in the image. The exact appearancewould depend on the specific type of movement.

Freire & Mangin report that least-square (LS) based similarity measures aresensitive to outliers [16]. They state that

If our interpretation is correct, LS-SPM correction, and to a smallerextent LS-AIR, creates spurious clusters of activated voxels along high-contrast brain edges.

They suggest to use a more robust estimator like mutual information (MI).For a quantification study of head motion in stroke patients, young and elderly

people see Seto et al [44]. For interaction with other artifacts, see [23], [7].

SusceptibilitySusceptibility artifacts are inhomogeneities in the strength of the static magnetic

field caused macroscopic susceptibility differences in the human head. These fieldinhomogeneities can cause geometrical distortions in the image (e.g. pixel shift) ac-quired with an Echo-Planar Imaging (EPI) sequence. Also, an interaction betweenmotion and the susceptibility artifact exists. For correction of this combination ofartifacts, see Hutton et al [23, 24].In worst cases, drop-out will occur, which involves signal loss that cannot be

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recovered; for optimal parameter settings reducing distortions and dropout, seeWeiskopf et al (2006, [49]).In future, distortion correction tools will be available in BrainVoyager QX (see Bre-man et al, 2007 [8]).

2.1.2 Scanner-based

Gradient non-linearitiesThe gradients (B1) cannot be precisely as linear as they were designed, which

causes intensity inhomogeneities in the data. In BrainVoyager, this can be correctedvia computation of an additive or multiplicative bias field [19].

ShimmingShimming can only reduce first order (and sometimes second order) field inho-

mogeneities. Remaining field inhomogeneities and deviations in the shims willintroduce geometrical distortions in the data, mostly in the phase encoding direc-tion (posterior → anterior). For a study on shimming, see Balteau (2005, [6]). Toimprove shimming by changing head position, see Heberlein & Hu (2001, [20]).

Scanner manufacturerGartus et al (2007, [17]) claim that the data quality of the Philips scanner exceeds

the quality of the Bruker scanner.

Type of gradientThe occurrence of artifacts is partly dependent of the type of gradient. In case

of Diffusion Weighted Imaging (DWI), susceptibility artifacts and eddy currentscan occur; for correction, see Andersson & Skare [1, 2]. In future, an eddy currentcorrection tool will be available in BrainVoyager QX (ask Pim Pullens).In Echo-Planar Imaging (EPI), susceptibility artifacts are worse than in non-gradientbased sequences, for example spin-echo (SE). For a detailed description of EPI ar-tifacts, see Fischer & Ladebeck [13].

2.2 Possibly introduced artifacts

It is possible that some applied methods come with drawbacks in the form of in-troducing artifacts. This is not necessarily the case, however, but it is better tobe aware of the possible risks of certain methods before selecting a transformationmodel and an interpolation method, than discovering afterwards that the data con-tain artifacts.

2.2.1 Transformation models

Rigid body transformations

Be aware of stimulus-related motion and residual artifacts after correction becauseof the interaction between motion and the susceptibility artifact (see Hutton et al,2004 [23]). See also “Head motion and its correction” by Brammer (2001, [7]).

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Affine transformations

Non-linear transformations

In non-linear transformations, errors can be introduced via physically impossi-ble transformations. This can be prevented by using a regularization parameteror penalty function (which is for example used in the Levenberg-Marquardt opti-mization (see appendix B)) and transformation constraints (see appendix E).

2.2.2 Measures

For artifacts in mutual information (MI), see “Interpolation Artefacts in MutualInformation-Based Image Registration” (Pluim, 2000 [40]).

2.2.3 Optimization

Jenkinson et al (2002, [25]) report that optimization processes can get stuck in localminima. They recommend the methods (1) to apodize the cost function and (2) toemploy a hybrid globallocal optimization method, to avoid this problem.

2.2.4 Interpolation

IntroductionWhen performing image registration, the image is assumed to be in continuous

space, i.e. at each arbitrary point in space, a value would be present. After com-puting the new position, interpolation is needed to compute the intensity values atthe voxel centers or mesh coordinates, so that the elements are discrete again (seefigure 2.1). For a comparison study of interpolation methods, see Meijering et al(2001, [36]).

Figure 2.1: BrainVoyager image volumes (*.amr, *.dmr, *.fmr, *.vmr) and surfaces(*.srf) consist of discrete elements: voxels and triangles

Advantages and disadvantages of interpolation methods

Nearest neighbour: Disadvantages of nearest neighbor are that aliasing may oc-cur and edges may appear jagged [37].

(Tri)linear: The aliasing effect caused by nearest neighbor interpolation mostlydisappears with linear interpolation but this anti-aliasing is at the cost ofblurring the image. Therefore, when repeated resampling of an image is re-quired, the process will gradually smooth image details [37].

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Cubic: The amount of blurring is a little less than with linear interpolation. Sinceblurring is already deliberately introduced in the multi scale approach, theoverall effect of intentional blurring and blurring by linear interpolation canbe fine-tuned to get the desired effect. This way linear interpolation can beused to speed up registration [37].

ConclusionAfter an elaborate comparison study, Thevenaz et al (2000, [47]) state:

We conclude from both theoretical and practical concerns that themost important index of quality is the approximation order of the basisfunction, its support being the most important parameter with respectto efficiency.

According to Thevenaz et al, using splines for interpolation is a preferable option.Cubic spline interpolation is also available in BrainVoyager QX; for a detailed list,see the table 1.1.1.

2.2.5 Resampling

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Chapter 3

Evaluation and validation ofthe registration

3.1 Criteria for evaluation

The following criteria for evaluation of image registration algorithms can be de-fined (Goshtashby, CVPR’04):

Accuracy: The difference between estimated and true values.

Reliability: The rate of success of an algorithm.

Robustness: The degree of stability of the accuracy or reliability of an algorithmunder variations in its input parameters.

Computational complexity: Speed.

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3.2 Validation measures

See “Validation of Registration Accuracy” [52], Crum et al (2003, [11]), Maintz& Viergever (1998, [33]) and the Nonrigid Image Registration Evaluation Project(NIREP) (Christensen, [9]).

See “Evaluation of Similarity Measures for Non-rigid Registration” (Skerl, Likar,Pernus, WBIR 2006):

Accuracy (ACC): Root mean square of distances between origin and pointsDistinctiveness of optimimum (DO): uncertainty of optimum for pair of pointsCapture range (CR): smallest of distances between optima and closest minimaNumber of minima (NOM): sum minima within distance of global optimaRisk of non-convergence (RON)

Jenkinson et al [25] use the median absolute residual variation (MARV).For DTI the following validation measures can be used [27]:

(a) quantitative parameters: tensor-fitting error (Ef), mean dispersion index (MDI),mean fractional anisotropy (MFA) and mean variance (MV) within 11 regions ofinterest (ROI) defined from homogeneous fiber bundles(b) fiber tractography through the uncinate fasciculus and the corpus callosum.

3.2.1 Gold standard

When a stereotactic frame is used (cf. the Brown-Roberts-Wells Stereotactic HeadFrame System, [42]), the Target Registration Error (TRE) is regularly used as vali-dation measure (West et al, 1997 [50]) by using the root-mean-square (rms).

3.2.2 Fiducials

In case no stereotactic frame is used but fiducials have been attached to the head,the Fiducial Localization Error (FLE) and Fiducial Registration Error (FRE) canbe computed as validation measures (Woods, 2000, [51]) by using the root-mean-square (rms).

3.2.3 Labeling

If no frame or fiducials are present, labels of brain structures are needed to comparethe registration accuracy via overlays. Labeling can be achieved via segmentationor automatic labeling procedures.

The following validation accuracy measures were defined by Christensen et al[9]:

• Relative/fractional overlap: The relative overlap (RO) [9]) or fractional over-lap [11] measure

• Intensity variance (IV)

• Cumulative inverse consistency error (CICE)

• Cumulative transitivity error (CTE)

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3.3 Evaluation, validation in BrainVoyager QX

3.3.1 Visual evaluation

Evaluate registration of 3D images: overlay

Open the first 3D image (*.vmr) via File → Open. Add the second 3D image viaFile→ Load Secondary VMR. On the “Coregistration” tab of the 3D Volume Toolsdialog, select the mode “VMR → VMR”. Then, click “Blend: Transparent”. Nowthe spatial correspondence of the images can be compared (see figure 3.3.1).

Evaluate alignment of 4D data: time course movie

To visually check the alignment of the volumes in a 4D functional file (*.fmr and*.stc) after motion correction and intra-session alignment, the Time Course Movieoption can be used (see figure 3.3.1). This function can be found via the “Options”entry of the BrainVoyager QX main menu.

Evaluate alignment of 4D data: extended log file

To numerically check the alignment of the volumes in a 4D functional file (*.fmrand *.stc) after motion correction, the option “Extended log file” can be used. The

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values obtained via the Levenberg-Marquardt optimization procedure [41, ch.15]are logged to this file. In case settings are optimized for sudden movement arti-facts, the log files of default and optimized motion correction can be compared.

Evaluate normalization of 3D data: superimpose Talairach grid

For visual evaluation of the success of the Talairach transformation, the Talairachgrid can be superimposed on the transformed anatomical image (*.vmr). This op-tion is available on the “Talairach” tab of the “3D Volume Tools” dialog (see fig-ure 3.3.1). For more information on the Talairach grid, please consult Talairach &Tournoux (1988, [46]) and Lancaster & Fox (2000, [30]).

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3.3.2 Labeling

Labeling by defining regions-of-interest (ROI/VOI/POI)See the documents “Overview of the capabilities of the ROI Analysis tool” , “De-

scription of steps to create and use an anatomically defined region of interest”and/or “POI definition and usage in BrainVoyager QX” by Armin Heinecke.

Automatic labeling of surface patchesIn the Meshes menu option of BrainVoyager QX, navigate to ’Cortex Based Align-

ment...’ and select the ’Align pair’ tab. To activate the automatic labeling function,click the ’Copy labels...’ button (see figure 3.3.2).

To select labels from a mesh, click the ’Browse...’ button. In the subfolder ’At-lasbrains’ of the folder ’BrainVoyager QX’ are labeled anatomical regions in theform of patches of interest (POIs) available (see figure 3.3.2).

For an extended explanation, please see the document “How to use the CopyLabels Option in BV QX” by Armin Heinecke.

3.3.3 Quantification of registration accuracy

In case the spatial correspondence needs to be quantified, there are several optionsavailable on the ‘Segmentation’ tab of the 3D Volume Tools dialog that enable tomark voxels with a color and then to count them (Volumetry), or to mask and per-form some image calculations or use the morphological tools. For evaluation ofthe Talairach transformation, the BrainTalMask.vmr in the “BrainVoyager QX”directory could be useful when applying morphological operations.

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Chapter 4

Comparison studies andbenchmarks

4.1 Motion correction

At the W.M.Keck Lab for Functional Brain Imaging (University of Wisconsin-Madison,USA) a project for the “Comparison of fMRI Analytic Tools” is/was being per-formed [38]. Participants in the project are Terry Oakes, Tom Johnstone, AndyAlexander, Moo Chung, Larry Greischer, Kathleen Ores and Richie Davidson.

4.2 Image registration

In a study of Gartus et al (2007, [17], the image registration accuracy difference be-tween experts and software (not including BrainVoyager) for healthy subjects andpatients was quantified.

A future image registration evaluation project is NIREP of Gary Christensen(website: http://www.nirep.org/).

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Chapter 5

Conclusions about imageregistration situations

5.1 Conclusions from the literature

5.1.1 Affine transformation

In a comparison between spline-based, [...] and affine registration, Holden (2002)(in Crum et al, 2003, [11, p.1430]) concludes the following:

As expected, the affine registration performs relatively poorly com-pared with the other nonrigid registrations. What would not be appar-ent by reporting fidelity for 0 alone is that the overlap for the coarseand fine registrations rises from 0.76 to 0.95 for τ 1 and to 0.99 for τ 2.

This might indicate that for certain circumstances, it can be preferable to use a hier-archical affine registration method, like the FMR-VMR Gaussian scale pyramids inBrainVoyager QX, instead of direct affine registration (like the manual registrationin BrainVoyager QX).

5.1.2 Spatial normalization / Talairach transformation

In a comparison study between the landmark-based methods thin-plate splines(TPS), multiquadrics (MQ), weighted mean (WMN) and piecewise linear (PL) fromZagorchev and Goshtashby (1986, in Holden (2008, [22, p.124])) is reported that thepiecewise linear (PL) method, also used in BrainVoyager (for the Talairach trans-formation), is most suitable for local differences:

Generally, PL (piecewise linear) was the most suitable method forimages with local geometrical differences because the local supportproperty ensures that errors are not propagated globally.

5.1.3 High-dimensional warping vs. alignment along cortex cur-vature

Crivello et al (2002, [10]) conclude that a precise spatial correspondency is requiredfor associative areas:

It has been demonstrated that the macroscopic anatomical variabil-ity is highly related to the microstructural one in primary cortices [Geyer

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et al., 1996], but this tight relationship seems to disappear for associa-tive areas [Amunts et al., 1999]. The large variability of the architecturalorganization of the cerebral cortex that exists at every scale requires usto approach this issue through probabilistic schemes and atlases ratherthan through single individual observations (as was the case for thepioneer, Brodmanns map). Such studies are based on the hypothesisof sulcal anatomical standardization and therefore require all datasetsto be accurately normalized in a probabilistic space at a macroscopiclevel. The most accurate brain is likely to provide the most relevantconclusions regarding the relative positions of functional landmarksand cytoarchitectural areas.

Also Fischl et al [14] state that:

Since gyral and sulcal landmarks are typically accurate predictorsof the location of functional areas, it seems likely that using these fea-tures to drive the registration of the cortical surfaces will result in amore accurate alignment of corresponding functional areas than can beachieved using volume-based deformation methods.

A project to investigate morphogenesis and the variability in cortical folding pat-terns is described in Mangin et al (2004, [34]).

5.1.4 Performing group statistics

Dependent from a number of factors, including the design, it can be useful forgroup studies to include the motion estimates as covariates in the General Lin-ear Model (GLM) instead of removing the estimated motion from the images; fora thorough study and concrete recommendations, please consult Johnstone et al(2006, [26]).Goebel et al ([19]) state that in case group statistics are being computed, the inter-subject cortical alignment improve results substantially, a finding supported byVan Atteveldt (2004, [4]):

While functional areas do not precisely follow cortical landmarks, ithas been shown for areas V1 and motor cortex that a cortical alignmentapproach substantially improves statistical group results by reducinganatomical variability [Fischl et al., 1999]. In BrainVoyager QX, a high-resolution, multiscale version of such a cortical mapping approach hasbeen developed [Goebel et al., 2002, 2004], which automatically alignsbrains using curvature information of the cortex.Since the curvature of the cortex reflects the gyral/sulcal folding pat-tern of the brain, this brain matching approach essentially aligns corre-sponding gyri and sulci across subjects brains. The implemented high-resolution, multiscale cortex alignment procedure has been proven tosubstantially increase the statistical power and spatial specificity of groupanalyses [e.g., Van Atteveldt et al., 2004].

5.1.5 Performing independent component analysis (ICA)

After the results of Goebel et al (2006, [19]), if independent component analysis(ICA) is performed in a group-wise fashion, using inter-subject cortical registrationmay improve the statistical results:

Limiting our description to the two task-related components, cortex-based ICA provided a much more anatomically detailed picture of the

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same two-component model at the group level than the Talairach spaceICA.

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5.2 Optimizing registration in BrainVoyager QX

5.2.1 Atypical subject morphology and manual alignment

According to Gartus et al (2007, [17]), in a comparative study, manual image regis-tration of functional (EPI) to anatomical data by 3 experts proved to be better thanautomated registration in 90% of 10 patient cases and 70% of the 10 normal sub-jects. Although BrainVoyager was not included in this comparative study, theseresults indicate that in case of an atypical morphology of the brain, extra attentionneeds to be paid to the image registration. In case one is an expert, this could meanthat manual alignment is preferred, with the remark that the:

[...] precision of manual alignment, however, depends strongly onacquired expertise [18].

Manual alignment for affine transformations can be performed by adapting the’Rotation’, ’Translation’ and ’Scale (FOV)’ parameter values on the ’Coregistration’tab of the 3D Volume Tools dialog. This procedure has been briefly described inthe document “ManualRegistrationInBVQX” by Hester Breman.Alternatively, one could try the landmark-based image registration. After indicat-ing corresponding points in both MRI images, BrainVoyager QX will determinethe rotation, translation and scaling parameters. Please consult the topic ’Corre-sponding Points Alignment’ of the ’Coregistration’ chapter in the BrainVoyagerQX User’s Guide for useful suggestions for the selection of points.

5.2.2 Optimizing motion correction

When the movement of the subject is not too large to make the data useless, it ispossible to change the default settings to a more time-consuming procedure. Forproblematic data this might result in higher accuracy. To optimize motion correc-tion, it is possible to change the interpolation and the data sampling parameters.For comparing the differences, see section 3.3.1.

InterpolationWhen computing, the image is considered as an object in continuous space. This

means that at any arbitrary point, an intensity value is available. However, af-ter each estimation iteration, and also when applying a transformation, a discretevalue needs to be obtained so that one new intensity value per voxel can be savedto disk. Computing these new intensity values at particular points is performedvia interpolation.When a higher degree interpolation (cubic spline, SINC) is selected, more inten-sity values are taken into account to compute the intensity of a target voxel. ForSINC, a window of 7 is used in BrainVoyager, for example. Also, the weightingof the intensity values of these neighboring voxels is different. In linear interpola-tion methods (low-degree), all values are weighted equally (see left side of figure5.1). In higher-degree interpolation methods, closer voxels are considered moreimportant than intensity values of voxels that are further away. On the right sideof figure 5.1, a general example is provided: the closer voxels are weighted with2/n and the intensity values of more distant voxels only with weights 0.5/n. In thisexample, n, the total number of voxels taken into account to compute the intensityvalue for the target voxel, is 8 (4 voxels close, 4 voxels further away). Please notethat this is just a general example to clarify the principle and the weights depictedare not real.

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The fact that the weighting method in higher-degree interpolation does reflect bet-ter the spatial distribution of intensity values, this might improve the motion cor-rection in case of sudden movement effects in the data.

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Figure 5.1: (a) On the left side is shown that in linear interpolation methods (low-degree), all values are weighted equally (b) On the right side one can see that closervoxels are considered more important in higher-degree interpolation methods. n isthe total number of voxels taken into account for the computation of new intensityvalue for the target voxel.

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Data samplingSimilarly to interpolation, the data sampling is used to compute the new values,

in this case to estimate the motion (for more information about estimation, see sec-tion 1.1.1). In case of sudden intensity changes, unchecking the option “Reduceddata” might improve the detection of the motion (see right side of figure 5.2).

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Figure 5.2: (a) On the left side of the figure, reduced data sampling is selected; theconsequence is that not every voxel is taken into account for estimation of motion,which is no problem with smooth transitions of the value. (b) on the right side ofthe figure no reduced data sampling is applied. In this case, each voxel is takeninto account for estimating the motion.

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5.2.3 Alternative for motion correction

Instead of removing motion from the functional data (*.fmr/*.stc), it is also pos-sible to use the estimated motion parameters in the general linear model (GLM).For instructions, please consult the document “Usage of motion parameters in theGLM model” by Armin Heinecke. The optimal conditions for including the mo-tion estimation parameters in the GLM have been studied by Johnstone et al [26].

5.2.4 Improve the quality of the automated image registration

The following suggestions were made by Armin Heinecke to improve the qualityof the automated image registration.

1. Perform inhomogeneity correction (see also next paragraph) on the anatom-ical image (*.vmr).

2. Optimize AMR contrast and brightness. Open the AMR separately and changethe contrast and brightness.

3. Perform brain peeling (via the BrainVoyager QX menu “Volumes” → “Seg-ment Brain From Head Tissue”).

5.2.5 Improve the quality of the anatomical image (*.vmr)

The following suggestions were made by Bettina Sorger to improve the quality ofthe anatomical image (*.vmr) in Talairach space.

1. Perform inhomogeneity correction take time and be very precise never in-clude grey matter in presegmentation (in case of doubt: include to less ratherthan to much) repeat 2-3 times if necessary

2. Optimize gray matter intensity value set grey matter intensity value to 100′

optimal segmentation setting in BV QX

3. Combine multiple 3D data sets same subject, scanner, MR sequence (ownpositive experience) same subjects, different scanners, different MR sequences(Henk Jansma) perform ACPC-/Talairach transformation only once useautomatic 3D-3D alignment (for creating *_ACPC.trf files) following in-homogeneity correction and brain peeling use *_ACPC.tal (for creating*_TAL.vmr) use re-apply function (for improving data quality) averagemultiple *_TAL.vmr in BV QX

5.2.6 Improve the quality of inter-subject alignment

When performing group statistics, the accuracy of the inter-subject alignment vianormalization to Talairach space may be improved by performing cortical align-ment (see section 5.1). For instructions, please consult the topic “Cortex-BasedAlignment” in the BrainVoyager QX User’s Guide. An Cortex-Based Alignmentexercise and sample data are available on our ftp server.

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Appendix A

Affine transformation matrices

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38

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Appendix B

Optimization

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Appendix C

Interpolation methods

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Appendix D

Metric spaces

In a metric space the distance between two points can be computed using a metricfor that space, or the norm for the absolute distance (see for example figure D.1).

Figure D.1: Transformation or mapping in a metric space

For the Euclidean space R3, this is for example the L2 norm (see figure D.2).

Figure D.2: Topological vs. metric space

In a topological space (see image D.2), instead of inferring distances, it is im-portant to know how the areas are connected. The connectedness of a space can beindicated by genus λ, Euler characteristic χ or winding number. A simply connectedspace does not have holes. Anything that can be transformed to a sphere without

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cutting is topologically equivalent to a sphere, c.q. simply connected. This is genus0. So after accurate bridge removal in BrainVoyager QX [29], also the cortex hasgenus 0. A cortex reconstruction with a hole in it has genus 1 and is topologicallyequivalent to a torus (donut shape).

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Appendix E

Constraints on thetransformation

E.1 Diffeomorphisms (differentiable mappings)

A homeomorphism maps one differentiable manifold to another [22]. In otherwords, if the mapping preserves structure (is invertible), the mapping is a home-omorphism; when the mapping preserves structure and is differentiable, it is a dif-feomorphism [28]. (A manifold is a curved object or an object in curved space; thiscauses the distance function to be variable instead of constant. In this case, themetric tensor gij can be used to characterize the distance).

In figure E.1, the arrows represent the mapping between manifolds A and B.The bidirectionality of the arrow indicates that the mapping is invertible, c.q. isa homeomorphism. The bidirectional arrow with Jacobian and Hessian matricesattached indicate that the mapping is invertible and differentiable.The Jacobian matrix consists of a partial derivatives which represent the rate ofchange of the parameters (velocity); the Jacobian can be interpreted as a matrix thatindicates for a point in the input space how much its mapping on the output spacewill change as a response to a small variation in one of the transform parameters.The Hessian parameters, the second derivatives, represent the acceleration.For applications, see Toga & Thompson [48], Woods [53], Avants & Gee [5] and

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Ashburner [3].

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