# Realignment – Motion Correction (gif from FMRIB at Oxford)

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Realignment – Motion Correction (gif from FMRIB at Oxford)

OverviewOverview Motion correction Smoothing kernel Spatial normalisation Standard template fMRI time-series Statistical Parametric Map General Linear Model Design matrix Parameter Estimates

Within-subject Registration Assumes there is no shape change, and motion is rigid-body (i.e. translations/rotations)Assumes there is no shape change, and motion is rigid-body (i.e. translations/rotations) The steps are:The steps are: *Registration - i.e. Optimising the parameters that describe a rigid body transformation between the source and reference images - Reference image can be mean image or first image in session *Transformation - i.e. Re-sampling according to the determined transformation Assumes there is no shape change, and motion is rigid-body (i.e. translations/rotations)Assumes there is no shape change, and motion is rigid-body (i.e. translations/rotations) The steps are:The steps are: *Registration - i.e. Optimising the parameters that describe a rigid body transformation between the source and reference images - Reference image can be mean image or first image in session *Transformation - i.e. Re-sampling according to the determined transformation

1. Registration Determine the rigid body transformation body transformation that minimises the sum of squared difference between images between images Determine the rigid body transformation body transformation that minimises the sum of squared difference between images between images TranslationsPitchRollYaw Rigid body transformations parameterised by: Squared Error

1. Registration – Mean Squared Difference Minimising mean-squared difference works for intra-modal registration (realignment)Minimising mean-squared difference works for intra-modal registration (realignment) Simple relationship between intensities in one image, versus those in the otherSimple relationship between intensities in one image, versus those in the other –Assumes normally distributed differences

1. Registration Iterative procedure (Gauss- Newton ascent)Iterative procedure (Gauss- Newton ascent) Additional scaling parameterAdditional scaling parameter Nx6 matrix of realignment parameters written to file (N is number of scans)Nx6 matrix of realignment parameters written to file (N is number of scans) Orientation matrices in *.mat file updated for each volume (do not have to be resliced)Orientation matrices in *.mat file updated for each volume (do not have to be resliced) Reslice now or later  each time degrades the imageReslice now or later  each time degrades the image Iterative procedure (Gauss- Newton ascent)Iterative procedure (Gauss- Newton ascent) Additional scaling parameterAdditional scaling parameter Nx6 matrix of realignment parameters written to file (N is number of scans)Nx6 matrix of realignment parameters written to file (N is number of scans) Orientation matrices in *.mat file updated for each volume (do not have to be resliced)Orientation matrices in *.mat file updated for each volume (do not have to be resliced) Reslice now or later  each time degrades the imageReslice now or later  each time degrades the image

3D Rigid-body Transformations A 3D rigid body transform is defined by:A 3D rigid body transform is defined by: –3 translations - in X, Y & Z directions –3 rotations - about X, Y & Z axes The order of the operations mattersThe order of the operations matters A 3D rigid body transform is defined by:A 3D rigid body transform is defined by: –3 translations - in X, Y & Z directions –3 rotations - about X, Y & Z axes The order of the operations mattersThe order of the operations matters Translations Pitch about x axis Roll about y axis Yaw about z axis

Application of registration parameters involves re-sampling the image to create new voxels by interpolation from existing voxelsApplication of registration parameters involves re-sampling the image to create new voxels by interpolation from existing voxels Interpolation can be nearest neighbour (0-order), tri-linear (1st-order), (windowed) fourier/sinc, or in SPM2, nth-order “b-splines”Interpolation can be nearest neighbour (0-order), tri-linear (1st-order), (windowed) fourier/sinc, or in SPM2, nth-order “b-splines” Application of registration parameters involves re-sampling the image to create new voxels by interpolation from existing voxelsApplication of registration parameters involves re-sampling the image to create new voxels by interpolation from existing voxels Interpolation can be nearest neighbour (0-order), tri-linear (1st-order), (windowed) fourier/sinc, or in SPM2, nth-order “b-splines”Interpolation can be nearest neighbour (0-order), tri-linear (1st-order), (windowed) fourier/sinc, or in SPM2, nth-order “b-splines” 2. Transformation (reslicing) Nearest Neighbour Linear Full sinc (no alias) Windowed sinc

B-spline Interpolation A continuous function is represented by a linear combination of basis functions A continuous function is represented by a linear combination of basis functions Nearest neighbour and trilinear interpolation are the same as B-spline interpolation with degrees 0 and 1.

Interpolation errors, especially with tri-linear interpolation and small-window sincInterpolation errors, especially with tri-linear interpolation and small-window sinc 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 within a scan (which cause non-rigid image deformation)Rapid movements within 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 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 within a scan (which cause non-rigid image deformation)Rapid movements within 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 Realignment

Sources & References & So On… Rik Henson’s SPM minicourse (where these slides where mostly stolen from)Rik Henson’s SPM minicourse (where these slides where mostly stolen from) John Ashburner’s lecture on spatial preprocessing (SPM course USA 2005)John Ashburner’s lecture on spatial preprocessing (SPM course USA 2005) Human Brain Function, 2 nd Edition (Edited by J Ashburner, K Friston, W Penny) – mostly chapter 2.Human Brain Function, 2 nd Edition (Edited by J Ashburner, K Friston, W Penny) – mostly chapter 2. Rik Henson’s SPM minicourse (where these slides where mostly stolen from)Rik Henson’s SPM minicourse (where these slides where mostly stolen from) John Ashburner’s lecture on spatial preprocessing (SPM course USA 2005)John Ashburner’s lecture on spatial preprocessing (SPM course USA 2005) Human Brain Function, 2 nd Edition (Edited by J Ashburner, K Friston, W Penny) – mostly chapter 2.Human Brain Function, 2 nd Edition (Edited by J Ashburner, K Friston, W Penny) – mostly chapter 2.

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