Registration method

The experimental setting used in our method is illustrated at figure . It is based on a Isotrack 3D localization device. It uses two probes, "p" and "h", whose location and orientation relatively to the base station "b" is known at all times. Probe "h" is attached to the forehead of the patient and provides a local coordinate system for the head. Probe "p" is first used to digitize the scalp surface for the registration, then to localize the magnet during the stimulation.

  

Figure 7.2: Experimental setting.

The first step of the registration process is the segmentation of the scalp from the MR image. For this, the image is thresholded and median-filtered. Then, the background of the image is found as the largest connected component below the threshold level. The scalp is the edge of the background.

  

Figure 7.3: Matching criterion as a function of the translation or rotation errors.

The surface of the head in the physical space is defined as the set S of points p digitized by the "p" probe and transformed into the "h" coordinate system. The registration matching criterion is defined as the mean square distance between this set of points and the MRI-derived scalp surface O. Hence, the best transformation T from the set $\Re$ of rigid transformations is

$$T = \arg\min_{T \in \Re} \{ \sum_{p \in S} dist_E(T(p),O) \}$$ (7.1)

In this equation, dist_E(q,O) is of course pre-computed using a 3D Euclidean distance transformation. Because T(p) is not necessarily located on the integer grid, the value of dist_E(T(p),O) is tri-linearly interpolated from the distance map.
Figure studies the evolution of the matching criterion's value as a function of the mis-registration. It is a smooth function of the transformation parameters, so that we use a simple gradient-based minimization algorithm to find the optimal translation and rotation parameters.