# John's Gems 2

Please note that since 2010 I no longer update John's Gems, and have instead integrated them into my blog Neuroimaging Tips & Tools. Please use the John-Gems tag in the blog to find all the Gems.

## SPM2-Specific code snippets by John Ashburner

John Ashburner is an author of SPM and frequent contributor to the SPM email list. Many of his answers consist of short snippets of code that are incredibly useful for SPM2 analyses. Below are the most some of the best (the 'gems') in an accessible form. (The inspiration for this page is "Graphics Gems", a series of books containing short bits of useful code for computer graphics.)

We don't yet know about any undiscovered bugs, so we aren't sure if they exist or not.
-JA, Mar 21, 2003.

I haven't tested them all but I'll make bug fixes as I find them. I hope you find this useful.

See also the SPM99 gems page and New! the SPM5 gems page.

 1. M vs mat 2. MINC templates 3. Tabular dump 4. -log10 P-values from T images 5. Normalizing a point 6. Contrast SE computation 7. Movement parameter extraction 8. ImCalc Script 9. Masking w/ ImCalc 10. Creating a mask from XYZ list 11. Un-normalizing a point 12. fMRI Analysis threshold 13. Corrected cluster size threshold

## Gem 1: Transformation Matricies in SPM2 vs SPM99

```Subject: Re: spm2b: spm_header_edit.m
From: John Ashburner <john@FIL.ION.UCL.AC.UK>
Date: Fri, 7 Feb 2003 19:09:38 +0000 (14:09 EST)
To: SPM@JISCMAIL.AC.UK

> Following your previous answer it looks like the origin is indeed set to
> the new value in the header, but also the  .mat file is written. In this
> file, I find two matrices: M and mat. I noticed that they are identical if
> defaults.analyze.flip = 0 but if defaults.analyze.flip = 1 one of them is
> flipped (M(1,4)=-mat(1,4)). Why are there two transformation matrices?

Backwards compatibility.  The M variable is for compatibility with SPM99,
whereas the mat variable is the one used for SPM2.  Images produced by
SPM2b that have a .mat file should be compatible between analyses with
different defaults.analyze.flip settings.  In other words, reading the
orientation of images with .mat files containing the mat field does not
require identifying the value of defaults.analyze.flip.  However, if the
orientation etc is read from an SPM99 .mat file, or from the .hdr, then
the defaults.analyze.flip variable is consulted.

If a .mat file exists, then it is read, otherwise the relevant information
is taken from the .hdr and defaults.analyze.flip.  If a mat variable exists
in the mat file then it is used, otherwise the orientation is derived from
the M variable and defaults.analyze.flip.

Best regards,
-John

```

## Gem 2: Making your own MINC SPM2 templates

Subject: Re: FDP template --- SPM99 version
From: John Ashburner <john@FIL.ION.UCL.AC.UK>
Date: Thu, 27 Mar 2003 16:53:03 +0000 (11:53 EST)
To: SPM@JISCMAIL.AC.UK

> Those who use the FDG template should know that is was created for SPM99,
> and is thus in the standard orientation for that program, which is the
> opposite from that used in SPM2b.
>
> I believe that John Ashburner has agreed to convert to MINC format for use
> in SPM2b.

Converting from SPM99 to SPM2b templates can be pretty easy. In this case, the
command was (all one line):

rawtominc -transverse -short -signed -range 0 32767 -real_range 0 32767
-orange 0 32767 -xstep 2 -ystep 2 -zstep 2 -xstart -90 -ystart -126
-zstart -72 -xdircos 1 0 0 -ydircos 0 1 0 -zdircos 0 0 1 -pet FDG.mnc
91 109 91 < template_FDG_PET_OSEM_seg.img

rawtominc can be obtained from:
ftp://ftp.bic.mni.mcgill.ca/pub/minc/

Note that the simple conversion only applies to SPM99 templates in
Analyze format. If you do the same with SPM2b generated templates,
then you will need to do a left-right flip to them first.

Best regards,
-John
` `

## Gem 3: Finding p-value and statistics for all voxels

(Note: The program in this email was corrected; I have added the corrections to this message. Also, an additional typo was discovered in Sep 2003 and was fixed.)
```
Subject: Re: tabulate all voxels of a volume or cluster
From: John Ashburner <john@FIL.ION.UCL.AC.UK>
Date: Thu, 27 Mar 2003 14:26:56 +0000 (09:26 EST)
To: SPM@JISCMAIL.AC.UK

> Is there a possibility to tabulate the p-values and statistics for all
> voxels for the entire volume. (not only the peaks) ?
> Or which data file should I readout to get the desired
> values?

Copy and paste the following into Matlab, and select the appropriate
spmT or spmF images.  The first 3 columns are MNI coordinates.  The
fourth is the statistic.  I haven't included any p-values, but this
would be a relatively simple operation, provifing you can figure out
degres of freedom etc.  Use spm_Tcdf.m or spm_Fcdf.m to do this.

P=spm_get(1,'*.img','Select statistic image');
V=spm_vol(P);

[x,y,z] = ndgrid(1:V.dim(1),1:V.dim(2),0);
for i=1:V.dim(3),
z   = z + 1;
tmp = spm_sample_vol(V,x,y,z,0);
msk = find(tmp~=0 & finite(tmp));
if ~isempty(msk),
tmp = tmp(msk);
xyz1=[x(msk)'; y(msk)'; z(msk)'; ones(1,length(msk))];
xyzt=V.mat(1:3,:)*xyz1;
for j=1:length(tmp),
fprintf('%.4g %.4g %.4g\t%g\n',xyzt(1,j),xyzt(2,j),xyzt(3,j),tmp(j));
end;
end;
end;

Best regards,
-John
```

## Gem 4: -log10 P-values from T images

P-value images are difficult to visualize since "important" values are small and clumped near zero. A -log10 transformation makes for much better visualization while still having interpretability (e.g. a value of 3 cooresponds to P=0.001).

This function, T2nltP, will create -log10 P-value image based on either a contrast number (which must be a T contrast) or a T statistic image and the degrees of freedom.

This version for SPM2 was created Michael Moffitt, based on the SPM99 function of the same name for SPM99. Note that Michael's version can easily be changed to create P-values instead of -log10 P-values.

```
function T2nltP(a1,a2)
% Write image of P-values (spm_nltP_?) for a T image
%
% FORMAT T2nltP
% SPM will ask you which spmT_? file you want to convert to spm_nltP_?
%
% FORMAT T2nltP(Timg,df)
% Timg  Filename of T image
% df    Degrees of freedom
%
%
% As per SPM convention, T images are zero masked, and so zeros will have
% P-value NaN.
%
% @(#)T2nltP.m  1.2 T. Nichols 03/07/15
% Modified 04/01/20 by MAM - for SPM2 compatibility

if nargin==0

% Ask user for SPM.mat file and specific contrast
[SPM,xSPM]=spm_getSPM;

% If a 'T' contrast, get degrees of freedom (df) and fname of spmT_?
if xSPM.STAT ~= 'T', error('Not a T contrast'); end
df=xSPM.df(2);
Tnm=xSPM.Vspm.fname;

elseif nargin==2
Tnm = a1;
df  = a2;
end

Tvol = spm_vol(Tnm);

Pvol        = Tvol;
Pvol.dim(4) = spm_type('float');
Pvol.fname  = strrep(Tvol.fname,'spmT','spm_nltP');
if strcmp(Pvol.fname,Tvol.fname)
Pvol.fname = fullfile(spm_str_manip(Tvol.fname,'H'), ...
['nltP' spm_str_manip(Tvol.fname,'t')]);
end

Pvol = spm_create_vol(Pvol);

for i=1:Pvol.dim(3),
img         = spm_slice_vol(Tvol,spm_matrix([0 0 i]),Tvol.dim(1:2),0);
img(img==0) = NaN;
tmp         = find(isfinite(img));
if ~isempty(tmp)
% Create map of P values
%img(tmp)  = (max(eps,1-spm_Tcdf(img(tmp),df)));

% Create map of -log10(P values)
img(tmp)  = -log10(max(eps,1-spm_Tcdf(img(tmp),df)));
end
Pvol        = spm_write_plane(Pvol,img,i);
end;

spm_close_vol(Pvol);
```

## Gem 5: Normalizing [x y z]

An off-list email reports how to find the point in an normalized image that corresponds to a given un-normalized location. See also Un-normalizing a point.
```
From: John Ashburner <john@fil.ion.ucl.ac.uk>
To: Christophe Phillips <c.phillips@ulg.ac.be>
Subject: Re: Coordinates transform
Date: Wed, 4 Feb 2004 17:26:21 +0000

Hi Christophe,

> I've the coordinates [x y z] of a point (actually the location of a
> fitted current dipole) in an image 'img1'. This image was normalised
> into 'w_img1'. I'd like to have the dipoles coordinates [x y z]_w in
> the normalised image...
>
> Do you have a routine that can do that easily from the 'img1_sn.mat'
> file ?

The deformations in the sn.mat files map from points in normalised
space, to points in un-normalised space.  You therefore need to invert
them, which is a bit messy.  You would use the Deformations toolbox
for this (from the Toolbox pulldown).  First write out the deformation
field from the sn.mat.  Then call the Deformations toolbox again, and
choose the deformations inversion option.  This will be an iy*.img
file with three volumes.  This little script can then be used.

c = [x y z]'; % co-ordinates in mm (as shown by Display)
P = spm_get(1,'iy*.img','Select inverted warp');
P = [repmat(P,3,1) [',1';',2';',3']];
V = spm_vol(P);

vx = inv(V(1).mat)*[c ; 1];  % The voxel in the deformation to sample

w_coord = [...
spm_sample_vol(V(1),vx(1),vx(2),vx(3),1)
spm_sample_vol(V(2),vx(1),vx(2),vx(3),1)
spm_sample_vol(V(3),vx(1),vx(2),vx(3),1)]

I haven't tested it, so there may be things to fix.

All the best,
-John
```

## Gem 6: Contrast SE Computation

An email from Will Penny on how a contrast's standard error is computed.
```
Subject: Re: Beta SE in SPM2?
From: Will Penny <wpenny@FIL.ION.UCL.AC.UK>
Date: Fri, 27 Feb 2004 11:26:35 +0000
To: SPM@JISCMAIL.AC.UK

Tobias,

> How do I extract beta SE in SPM2?  As far as I can see I can only get
> y, Y, beta, and Bcov...have I missed something?

If you're referring to the Standard Error or the Standard deviation of the
parameter estimates then this isn't stored explicitly.

Its computed on the fly when one makes an inference about a contrast. See the
following lines (153-158) in spm_contrasts:

case 'T'                                  %-Compute SPM{t} image
%---------------------------------------------------------------
cB    = spm_get_data(xCon(ic).Vcon,XYZ);
l     = spm_get_data(VHp,XYZ);
VcB   = xCon(ic).c'*SPM.xX.Bcov*xCon(ic).c;
Z     = cB./sqrt(l*VcB);

So, if you did a contrast xCon(ic).c'=[1 0 0 0] to test the null
hypothesis that the first parameter is zero then cB will be equal to
beta1 and sqrt(l*VcB) will be equal to std(beta1) - the standard
deviation of the first parameter estimate.

Note that l is the residual sum of squares at that voxel which is
stored in the image ResMS.img and accessed via the file handle VHp.

In this way SPM does'nt have to store Standard Deviations/covariances
for every voxel and beta - so saving disk space. But its not that
handy for what you want !

Hope this helps, Will.

```

## Gem 7: Extracting realignment parameters

The referenced script is here save_parameters.m

```
Subject: Re: [SPM] realignment parameter
From: John Ashburner <john@FIL.ION.UCL.AC.UK>
Date: Fri, 23 Apr 2004 11:25:27 +0000 (07:25 EDT)
To: SPM@JISCMAIL.AC.UK

> I have switched from spm99 to spm2 and am learning new things.
> When I realign images interactively with GUI interface,
> the rp*.txt file is created. However, the parameter file
> is not created - or, I cannot find it -, when I realign
> with a batch script.
> I am sure I left out something, but I don't know it.
> Any suggestion will be very appreciated.

If you call spm_realign with output (left-hand) arguments, then no rp_*.txt
file is saved.  You could create a save_parameters.m file, containing:

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
function save_parameters(V)
fname = [spm_str_manip(prepend(V(1).fname,'rp_'),'s') '.txt'];
n = length(V);
Q = zeros(n,6);
for j=1:n,
qq     = spm_imatrix(V(j).mat/V(1).mat);
Q(j,:) = qq(1:6);
end;
save(fname,'Q','-ascii');
return;
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

and derive the values from your realigned images:

P = spm_get(Inf,'*.IMAGE','Select realigned images');
save_parameters(spm_vol(P))

Best regards,
-John
```

## Gem 8: ImCalc Script

SPM99 Gem 21 is the same (with minor changes).
```
Subject: Re: a script to use ImaCal
From: John Ashburner <john@FIL.ION.UCL.AC.UK>
Date: Thu, 16 Oct 2003 11:24:17 +0000 (07:24 EDT)
To: SPM@JISCMAIL.AC.UK

> Brain image for each subject to mask out CSF signal was generated by
> using MPR_seg1.img (i1) and MPR_seg2.img (i2) with (i1+i2)>0.5 in
> ImaCal.(called brainmpr.img for each subject)
>
> Then I have more than two-hundred maps, which need to mask out
> CSF. I think I can use ImaCal again with selecting brainmpr.img (i1)
> and FAmap.img (i1), and then calculating (i1.*i2) to generate a new
> image named as bFAmap.img.  Unfortunately, if I use the ImaCal, it
> take so long time to finish all subjects. Could anyone have a script
> to generate  a multiplication imaging with choosing a brain
> image(brainmpr.img, i1) and a map image (FAmap.img, i2) and writing
> an output image (bFAmap.img) from i1.*i2?

You can do this with a script in Matlab.  Something along the lines of the
following should do it:

P1=spm_get(Inf,'*.IMAGE','Select i1');
P2=spm_get(size(P1,1),'*.IMAGE','Select i2');

for i=1:size(P1,1),
P = strvcat(P1(i,:),P2(i,:)));
Q = ['brainmpr_' num2str(i) '.img'];
f = '(i1+i2)>0.5';
flags = {[],[],[],[]};
Q = spm_imcalc_ui(P,Q,f,flags);
end;

Note that I have not tested the above script.  I'm sure you can fix it if
it doesn't work.

Best regards,
-John
```

## Gem 9: Masking w/ ImCalc

This is an email from Rik Henson which references John. It addresses the fact that ImCalc defaults to writing out images in 2-byte signed integer format, which is can be problematic if you're masking statistic images (which should written with floating point precision).

```
From: Rik Henson <r.henson@UCL.AC.UK>
Date: Fri, 14 May 2004 08:24:25 +0100 (03:24 EDT)
To: SPM@JISCMAIL.AC.UK

analyses. This used to be possible using ImCalc in SPM99 (see Mailbase
archive). In SPM2 however, when ImCalc is called from the GUI, it
adopts various defaults, which include writing images as "uint16"
(rather than "float", which is the normal datatype for T/F imgs).
Thanks to John for pointing this out.

It is for this reason that the procedure of overwriting
spmT/F*imgs using ImCalc does not work from SPM2's GUI.

To override this default however, you can simply call
ImCalc from the command line instead, setting the
datatype to spm_type 'float':

spm_imcalc_ui([],[],'i1.*(i2>3.09)',{[],[],'float',0})

The empty 1st and 2nd arguments mean that SPM will prompt
you to select the input images and the output filename, as usual.
You will of course need to change the third argument to your
particular ImCalc equation for evaluation. The 4th argument
is a cell array of defaults, which includes the 'float' enforcement.

Rik

```
See also SPM2 Gem 8, and SPM99 Gems 3, 16, and 21.

## Gem 10: Creaging a mask from a XYZ list

This is a "Jan's Gem" from Jan Gläscher...

```
Subject: Re: [SPM] creating a mask from voxel coordinates
From: Jan Gläscher <glaescher@UKE.UNI-HAMBURG.DE>
Date: Tue, 15 Mar 2005 12:24:27 +0100
To: SPM@JISCMAIL.AC.UK

Dear Susana,

you can try the following recipe.  It might not be the easiest way, but it
should work.

Suppose your n MNI coordinates are saved in a 3xn matrix called mni.
(This is essential (not the name, but the format of 3xn), otherwise the
steps below won't work).

1. Create an spm_vol handle to the image, that you determined the
coordinates from

Vin = spm_vol(spm_get(1,'*.img','Select image'));

2. Read the information in the image. (The data are not needed, this is
done purely for the purpose of setting up a matrix of voxel coordinates.

3. Setup a matrix of zeros in the dimensions of the input image

4. Now loop over all voxels in your mni variable and set the corresponding
location in the mask matrix to 1:

for v = 1:size(mni,2)
end

5. Setup an spm_vol output file handle and change the filename

Vout = Vin;

6. Finally, write the new mask to the output file.

Cheers,
Jan
```

## Gem 11: Un-normalization

This script of John's will find the corresponding co-ordinate in un-normalised image: get_orig_coord2.m

## Gem 12: fMRI Analysis threshold

This is an update of Gem12 for SPM99, originally by Stefan Kiebel.

```
> Is it possible to instruct spm99 to search all voxels within a given
> mask image rather than all above a fixed or a %mean threshold?

Yes, with SPM2 it's possible to use several masking options.

To recap, there are 3 sorts of masks used in SPM2:
1. an analysis threshold

1: One can set this threshold for each image to -Inf to switch off this
threshold.
2: If the image allows this, NaN at a voxel position masks this voxel
from the statistics, otherwise the mask value is zero (and the user
can choose, whether implicit masking should be used at all).
3: Use mask image file(s), where NaN (when image format allows this) or
a non-positive value masks a voxel.

On top of this, SPM automatically removes any voxels with constant
values over time.

So what you want is an analysis, where one only applies an explicit

In SPM2 for PET, you can do this by going for the Full Monty and
choosing -Inf for the implicit mask and no 0-thresholding. Specify one
or more mask images. (You could also define a new model structure,
controlling the way SPM for PET asks questions).

With fMRI data/models, SPM2 is fully capable of doing explicit
masking, but the user interface for fMRI doesn't ask for it. One way
to do this type of masking anyway is to change the SPM.mat file
*after* you specify your model, but *before* clicking 'Estimate'.
Specifically:

set the SPM.xM.TH values all to -Inf,
SPM.xM.TH = -Inf*SPM.xM.TH;
and, in case that you have an image format not allowing NaNs,
set SPM.xM.I to 0
SPM.xM.I = 0;

2. If using a mask image, set SPM.xM.VM to a vector of structures,
where each structure element is the output of spm_vol. For instance:

3. Finally, save by
save SPM SPM

```

## Gem 13: Corrected cluster size threshold

This is a script that will tell you the corrected cluster size threshold for given cluster-defining threshold: CorrClusTh.m

The usage is pretty self explanatory:

```
Find the corrected cluster size threshold for a given alpha
function [k,Pc] =CorrClusTh(SPM,u,alpha,guess)
SPM   - SPM data structure
u     - Cluster defining threshold
If less than zero, u is taken to be uncorrected P-value
alpha - FWE-corrected level (defaults to 0.05)
guess - Set to NaN to use a Newton-Rhapson search (default)
Or provide a explicit list (e.g. 1:1000) of cluster sizes to
search over.
If guess is a (non-NaN) scalar nothing happens, except the the
corrected P-value of guess is printed.

Finds the corrected cluster size (spatial extent) threshold for a given
cluster defining threshold u and FWE-corrected level alpha.
```

To find the 0.05 (default alpha) corrected cluster size threshold for a 0.01 cluster-defining threshold:

```
>> CorrClusTh(SPM,0.01)
For a cluster-defining threshold of 2.4671 the level 0.05 corrected
cluster size threshold is 7860 and has size (corrected P-value) 0.0499926
```
Notice that, due to the discreteness of cluster sizes you cannot get an exact 0.05 threshold.

The function uses an automated search which may sometimes fail. If you specify a 4th argument you can manually specify the cluster sizes to search over:

```
>> CorrClusTh(SPM,0.01,0.05,6000:7000)

WARNING: Within the range of cluster sizes searched (6000...7000)

Try increasing the range or an automatic search.
```
```