## Neurosurgery

and permits movement of the head relative to the tracking cameras, or vice versa, without loss of registration.

### Accuracy Considerations

When performing point-based registration, there are a number accuracy metrics that can be described. It is very important when talking about the accuracy of a particular system that the measurements used are clear and that their meaning is understood. In a paper by Fitzpatrick et al., the three main error metrics associated with point-based registration are described and a derivation of the most important statistic is given [7]. We will describe their results and the implications thereof for image-directed neurosurgery in this section. It is vital that any surgeon using point landmarks as a means of registration for image guidance understands these results.

### Error Metrics

We will call the point landmarks "fiducials". The first statistical measure of error we will describe is the "fiducial localization error" (FLE). This is simply the accuracy with which one can generally locate a given fiducial. An estimate of FLE for a particular fiducial must take into account the accuracy with which the point can be found by the user in the images and on the patient, as well as the intrinsic accuracy of the localization device.

The second metric is the "fiducial registration error" (FRE). This is the root mean square (rms) residual error on the fiducials after transformation. For example, if we have a set of points in image coordinates and their corresponding physical locations, we can calculate a transformation from image to physical space. By transforming the image points, we have two sets of points that should coincide: the transformed image points and their measured physical positions. Because there are errors in our measurements, these points do not coincide exactly and the distances between them provide the FRE. It is common, because it is easy to calculate, for commercial systems to quote FRE either as an rms or as an error on each point. As we shall see, however, FRE is not a good measure of registration accuracy.

The third, and most clinically relevant, metric is the "target registration error" (TRE). This is the accuracy with which a point other than our fiducials can be located. If we are performing an electrode placement heading for a specific target, the TRE is a measure of the accuracy with which we can locate that target given the registration we have obtained from our fiducials. This is clearly the error in which we are most interested.

Fitzpatrick et al. [7] have found a formula relating TRE to FLE and the configuration of the landmarks, as follows:

where there are n fiducial points, where fk is the rms distance of the fiducials to the principal axis, k, of the point distribution, and where dk is the distance from this same axis to the target point, r. In image-guided neurosurgery we are interested in reducing the TRE. From this equation we can see that there are two methods of achieving this. One is to increase the number of fiducials used; the other is to increase the spread of these fiducials.

For systems that quote FRE only, there may be a temptation to ignore landmarks that have a high FRE and reduce the set until the mean FRE falls below a given value. This is a very poor method of achieving registration. It will tend to mean that a poor configuration of landmarks will remain, perhaps all being close together or all close to lying along a line. Though a low FRE may result from this process, the associated TRE, especially at a distance from these landmarks, may be very poor indeed. Landmarks with high FRE should only be discarded if there is a good reason for thinking that they are outliers, e.g. if a skin marker has clearly moved.

Manufacturers of IGS systems should be encouraged to incorporate the above equation into accuracy assessments provided to the surgeon. Until this is the case, it is paramount that surgeons are aware of the issues affecting the true target accuracy of navigation.