Image Processing for fmri John Ashburner. Wellcome Trust Centre for Neuroimaging, 12 Queen Square, London, UK.

Transcription

1 Iage Processing for fmri John Ashburner Wellcoe Trust Centre for Neuroiaging, 12 Queen Square, London, UK.

2 Contents * Preliinaries * Rigid-Body and Affine Transforations * Optiisation and Objective Functions * Transforations and Interpolation * Within Subject: Realignent & Coregistration * Between Subject: Spatial Noralisation & Soothing

3 Rigid-Body Transforations * Assue that brain of the sae subject doesn t change shape or size in the scanner. * Head can ove, but reains the sae shape and size. * Soe exceptions: * Iage distortions. * Brain slops about slightly because of gravity. * Brain growth or atrophy over tie. * If the subject s head oves, we need to correct the iages. * Do this by iage registration.

4 Iage Registration Two coponents: Registration - i.e. Optiise the paraeters that describe a spatial transforation between the source and reference iages Transforation - i.e. Re-saple according to the deterined transforation paraeters

5 2D Affine Transfors * Translations by t x and t y * x 1 = x + t x * y 1 = y + t y * Rotation around the origin by radians * x 1 = cos() x + sin() y * y 1 = -sin() x + cos() y * Zoos by s x and s y * x 1 = s x x * y 1 = s y y *Shear *x 1 = x + h y *y 1 = y

6 2D Affine Transfors * Translations by t x and t y * x 1 = 1 x + y + t x * y 1 = x + 1 y + t y * Rotation around the origin by radians * x 1 = cos() x + sin() y + * y 1 = -sin() x + cos() y + * Zoos by s x and s y : * x 1 = s x x + y + * y 1 = x + s y y + *Shear *x 1 = 1 x + h y + *y 1 = x + 1 y +

7 3D Rigid-body Transforations * A 3D rigid body transfor is defined by: * 3 translations - in X, Y & Z directions * 3 rotations - about X, Y & Z axes * The order of the operations atters 1 1 cos sin sin cos 1 cos sin 1 sin cos 1 cos sin sin cos 1 1 Zt 1 Y 1 X 1 rans trans trans Ω Ω Ω Ω Θ Θ Θ Θ Φ Φ Φ Φ Translations Pitch about x axis Roll about y axis Yaw about z axis

8 Voxel-to-world Transfors * Affine transfor associated with each iage * Maps fro voxels (x=1..n x, y=1..n y, z=1..n z ) to soe world coordinate syste. e.g., * Scanner co-ordinates - iages fro DICOM toolbox * T&T/MNI coordinates - spatially noralised * Registering iage B (source) to iage A (target) will update B s voxel-to-world apping * Mapping fro voxels in A to voxels in B is by * A-to-world using M A, then world-to-b using M B -1 * M B -1 M A

9 Left- and Right-handed Coordinate Systes * NIfTI forat files are stored in either a left- or right-handed syste * Indicated in the header * Talairach & Tournoux uses a right-handed syste * Mapping between the soeties requires a flip * Affine transfor has a negative deterinant

10 Optiisation * Iage registration is done by optiisation. * Optiisation involves finding soe best paraeters according to an objective function, which is either iniised or axiised * The objective function is often related to a probability based on soe odel Objective function Most probable solution (global optiu) Local optiu Local optiu Value of paraeter

11 Objective Functions * Intra-odal * Mean squared difference (iniise) * Noralised cross correlation (axiise) * Inter-odal (or intra-odal) * Mutual inforation (axiise) * Noralised utual inforation (axiise) * Entropy correlation coefficient (axiise)

12 Siple Interpolation * Nearest neighbour * Take the value of the closest voxel * Tri-linear * Just a weighted average of the neighbouring voxels * f 5 = f 1 x 2 + f 2 x 1 * f 6 = f 3 x 2 + f 4 x 1 * f 7 = f 5 y 2 + f 6 y 1

13 B-spline Interpolation A continuous function is represented by a linear cobination of basis functions 2D B-spline basis functions of degrees, 1, 2 and 3 B-splines are piecewise polynoials Nearest neighbour and trilinear interpolation are the sae as B-spline interpolation with degrees and 1.

14 Contents * Preliinaries * Within Subject: Realignent & Coregistration * Realignent by iniising ean-squared difference * Residual artifacts and distortion correction * Coregistration by axiising utual inforation * Between Subject: Spatial Noralisation & Soothing

15 Processing Overview Statistics or whatever fmri tie-series Anatoical MRI Teplate Soothed Estiate Spatial Nor Motion Correct Sooth Coregister Spatially noralised Deforation

16 Mean-squared Difference * Miniising ean-squared difference works for intraodal registration (realignent) * Siple relationship between intensities in one iage, versus those in the other * Assues norally distributed differences

17 Residual Errors fro aligned fmri * Re-sapling can introduce interpolation errors * especially tri-linear interpolation * Gaps between slices can cause aliasing artefacts * Slices are not acquired siultaneously * rapid oveents not accounted for by rigid body odel * Iage artefacts ay not ove according to a rigid body odel * iage distortion * iage dropout * Nyquist ghost * Functions of the estiated otion paraeters can be odelled as confounds in subsequent analyses

18 Moveent by Distortion Interaction of fmri *Subject disrupts B field, rendering it inhoogeneous * distortions in phase-encode direction *Subject oves during EPI tie series *Distortions vary with subject orientation *shape varies

19 Moveent by distortion interaction

20 Correcting for distortion changes using Unwarp Estiate reference fro ean of all scans. Estiate oveent paraeters. Estiate new distortion fields for each iage: estiate rate of change of field with respect to the current estiate of oveent paraeters in pitch and roll. Unwarp tie series. + B B Andersson et al, 21

21 Coregistration Inter-odal registration. Match iages fro sae subject but different odalities: anatoical localisation of single subject activations achieve ore precise spatial noralisation of functional iage using anatoical iage.

22 Coregistration axiises Mutual Inforation * Used for between-odality registration * Derived fro joint histogras * MI= ab P(a,b) log 2 [P(a,b)/( P(a) P(b) )] * Related to entropy: MI = -H(a,b) + H(a) + H(b) * Where H(a) = - a P(a) log 2 P(a) and H(a,b) = - a P(a,b) log 2 P(a,b)

23 Contents * Preliinaries * Within Subject: Realignent & Coregistration * Between Subject: Spatial Noralisation & Soothing * Segentation for spatial noralisation * Soothing

24 Processing Overview Statistics or whatever fmri tie-series Anatoical MRI Teplate Soothed Estiate Spatial Nor Motion Correct Sooth Coregister Spatially noralised Deforation

25 Alternative Pipeline fmri tie-series Teplate Statistics or whatever Soothed Motion Correct Estiate Spatial Nor Sooth Spatially noralised Deforation

26 Spatial Noralisation * Brains of different subjects vary in shape and size. * Need to bring the all into a coon anatoical space. * Exaine hoologous regions across subjects * Iprove anatoical specificity * Iprove sensitivity * Report findings in a coon anatoical space (eg MNI space)

27 Spatial Noralisation * This is the sae algorith as for tissue segentation. * Cobines: * Mixture of Gaussians (MOG) * Bias Correction Coponent * Warping (Non-linear Registration) Coponent

28 Spatial Noralisation * Default spatial noralisation in SPM12 estiates nonlinear warps that atch tissue probability aps to the individual iage. * Spatial noralisation achieved using the inverse of this transfor.

29 Modelling deforations * Tissue probability aps are warped to align with tissues identified in iage.

30 Modelling deforations

31 Modelling a bias field * A bias field is odelled as a linear cobination of basis functions. Corrupted iage Bias Field Corrected iage

32 Iterative optiisation schee Update tissue estiates Update deforation estiates Update bias field estiates No Converged? Yes

33 Evaluations of nonlinear registration algoriths

34 Sooth Blurring is done by convolution. Each voxel after soothing effectively becoes the result of applying a weighted region of interest (ROI). Before convolution Convolved with a circle Convolved with a Gaussian

35 References * Friston et al. Spatial registration and noralisation of iages. Huan Brain Mapping 3: (1995). * Collignon et al. Autoated ulti-odality iage registration based on inforation theory. IPMI 95 pp (1995). * Thévenaz et al. Interpolation revisited. IEEE Trans. Med. Iaging 19: (2). * Andersson et al. Modeling geoetric deforations in EPI tie series. Neuroiage 13: (21). * Ashburner & Friston. Unified Segentation. NeuroIage 26: (25). * Klein et al. Evaluation of 14 nonlinear deforation algoriths applied to huan brain MRI registration. NeuroIage 46(3): (29).