Similarity Measure 73

proposed algorithm that the set of sample points should be as compact as possible in order to increase the speed. This forms a limitation when we want to use smaller down-sampled images to increase the speed. One possible solution to this problem is using other simi-larity measures such as cross-correlation. Cross-correlation (CC) is a simisimi-larity measure which is robust against the variability of brightness and contrast as well as inhomogeneity.

It can be correctly computed using relatively few sample points when compared with CR.

The only disadvantage of CC is it can only handle uni-modal registrations. But when an application only involves uni-modal registrations, CC may be a better similarity measure of choice since it imposes stronger constraints to the intensity relationship between source and target image.

The second limitation of CR is its flexibility in terms of handling multi-modal registra-tions. Although CR can handle most multi-modal registration schemes through its hypoth-esis of functional relationship of intensity, we must point out that there are still cases in which this assumption fails, that is, CR cannot handle all types of multi-modal registra-tions. For example, there is no functional intensity relationship between a T1-weighted MR image and a diffusion weighted image. In a T1-weighted MR image, the intensity of white matters is generally uniform throughout the image (ignoring the factors such as intensity non-uniformity). In a diffusion-weighted image, however, the intensity of white matters varies tremendously due to different directions of the fibers. In such cases when no functional relationship exists, similarity measures imposing more general assumptions are more preferable (e.g. mutual information).

Another limitation of the similarity measure used in our work is that the similarity is determined solely by the intensity of the images, and no anatomical knowledge is incor-porated. One possible way to remove this limitation is by incorporating anatomical infor-mation in the similarity measure. For example, in the work by Hellier et al. [17], sulcal patterns are extracted and used as constraints for non-rigid brain registration. Liu et al. [23]

proposed a hybrid registration method for cortical surfaces. It consists of a volumetric warping followed by an attribute-based surface warping. Incorporating anatomical infor-mation such as the cortical surfaces during the registrations may result in better alignment

74 Discussion

of tissues. This may be a promising direction for the improvement of the proposed algo-rithm.

Chapter 7

Conclusion

76 Conclusion

In this work, we have developed an efficient non-rigid registration algorithm which is symmetric and diffeomorphic. In the proposed algorithm, diffeomorphism is ensured by us-ing the log-Euclidean framework. An symmetric correlation ratio combined with weighted Laplacian model is used as the objective function. To increase efficiency, we used a greedy local optimization approach based on radial basis functions. A hierarchical framework is used to further improve the speed and accuracy. The proposed algorithm can incorporate results of symmetric affine registrations without losing overall symmetry. The performance of the proposed algorithm was evaluated using the result of pairwise registration of LPBA40 dataset. The result of evaluation shows that the proposed algorithm is fully diffeomorphic and has sub-voxel accuracy in terms of symmetry. The proposed algorithm is faster than most diffeomorphic registration methods while maintaining high accuracy. According to the evaluation framework by Klein et al. [18], the proposed algorithm is more accurate than all 14 non-rigid registration algorithms listed by Klein et al. [18], and is faster than the top-ranked diffeomorphic registration algorithm. Although the result of the evaluation appears to be promising, more evaluations are still needed before any solid conclusion is made. Fu-ture works include further improvements in terms of accuracy and more evaluations based on different datasets and evaluation methods.

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