In the above formula it is assumed that the volume of integration is centred about . If this is not the case (when the origin of the world coordinates is not at the centre of the brain) then the matrix can be simply modified to include a general centre.

That is, let be the desired centre, and define a new coordinate

(33) |

Therefore,
, giving
. This implies that and
so that

Mark Jenkinson 2003-02-11