In this section, we compare the performance of our new integrated algorithm to our previous point-based only method as well as a standard non-linear intensity-only based method. We evaluate the accuracy of the algorithms in matching cortical landmarks in a set of 17 normal controls.
All images used in this work were high resolution (1.2 × 1.2 × 1.2mm) 3D SPGR images acquired using a GE 1.5 T scanner (2 NEX, TR= 24msec, TE = 5msec, flip = 45°). The scans were of excellent quality and without movement artifacts. The brains were next stripped and the following four sulci were manually traced (a) left central sulcus, (b) right central suclus, (c) left superior frontal sulcus and (d) right superior frontal sulcus, as shown in . For the purpose of both the integrated and the point-only based methods, labeled point sets for each subject were constructed using approximately 5000 points for the outer cortical surface and 250 points for each sulcus resulting in a total point set of approximately 6000 points/subject. All subjects were registered to a normal control reference subject, an example registration is shown in
Fig. 1 Sulci used in the evaluation of the registration methods. Note that these are major sulci, hence the matching error of the intensity based method is smaller that what is reported by Hellier et al. 
Fig. 2 Example registration result. In this close-up of the central sulcus overlaid on a volume rendered stripped brain, the target surface is shown in white. The warped template is shown for three different registrations RPM − red, Integrated λ (more ...)
For the purpose of comparison, the registrations were computed using (a) our point-based method RPM[12
] and (b) our implementation of the non-linear intensity (NMI) based method of Rueckert et al [13
]. To test the effect of the tradeoff parameter λ
, the integrated algorithm was applied using seven different values of λ
). We used the following measures to evaluate the quality of the registration:
1. Cross-Correlation Coefficient (CC)
This measures the degree of intensity similarity. We use this measure rather than NMI as it was not explicitly optimized by methods (ii) and (iii). In practice, though, there was found to be a monotonic relationship between CC and NMI. The values of CC for all registration methods are shown in .
Fig. 3 Average intensity similarity for the point-based registration method (RPM), the new integrated algorithm (INT-λ) with seven different values of the weight of adherence to the point correspondences λ and the intensity only similarity algorithm (more ...)
2. Average Sulcal matching error
This was the mean distance of all points from the reference sulcus to the target sulcus using correspondences estimated by a nearest-neighbor matching method. The results for this are shown in . We also report the total bending energy of the calculated transformations to give a sense of the extent of the deformation in each case. Note that the bending energy in RPM is very low as there are no sub-cortical features and hence the registration is very smooth away from the cortical surface and the sulci. The integrated algorithms with high values of λ also have low bending energy; the bending energy gradually increased and approaches that of the NMI method a λ goes to zero. The average total bending energy for all the registration methods is shown in the chart in .
Average sulcal matching error for the point-based registration method (RPM), the new integrated algorithm (INT-λ) as above and the intensity only similarity algorithm (NMI) as computed from N = 17 normal controls.
Average bending energy for the registrations computed by the point-based registration method (RPM), the new integrated algorithm (INT-λ) and the intensity only similarity algorithm (NMI) as computed from N = 17 normal controls.
The intensity similarity metric results shown in indicate that the integrated method approaches the intensity-based method as the value of λ goes to zero as expected, especially for λ < 0.05. As expected the RPM algorithm is superior in terms of sulcal distance error point matching Note that in particular for λ = 0.1 or 0.05, the performance of the integrated algorithm the integrated method performs almost as well as the individual components (i.e. RPM and NMI) in their area of respective strengths, i.e. it produces an optimal tradeoff between sulcal matching error and intensity similarity.