It is sometimes desirable to compare registrations between two spaces performed with two different methods or two different conditions of application of one single method. More interestingly, if one registration happens to be ``accurate'', as verified by independent measurements, the comparison with another method will give a direct measurement of the registration error for that approach.
In the case where two registrations are performed without knowing the
``true'' transformation, reg_error can still be used to find
the registration difference 
between them using:
and
where 
and 
are
the registration parameters of the two registrations.
It is more useful in practice to express the registration difference in terms of imaging space coordinates since the centre of the head is usually more or less aligned with the isocenter of the scanner (which is the origin of scanner space). In surgical space, the coordinate system is dependant on the relative position of the pointing device and the head. So, the origin of the surgical space can be away from the patient's head.