## June 03, 2010

### SPM2 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
```

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