In orthodontics superimposition is an important technique allowing for accurate diagnosis and treatment planning. Lower radiation, three-dimensional, cone-beam computed tomography allows for acquisition of three-dimensional patient scans. New superimposition methods are used compared to the traditional methods used for two-dimensional scans. A new superimposition method is designed in this thesis.

A review of the current methods of superimposition used in orthodontics was performed. The review found that voxel-based, surface-based, and point-based superimposition methods are used. The most commonly used superimposition method is maximization of mutual information.

A cone-beam computed tomography machine is tested to find any inherent machine properties that may influence superimposition. The testing found that cone-beam computed tomography preserves and allows for highly accurate linear measurements. When greyscale values are viewed on a global scale there is not much change between scans. An issue arises when greyscale values are only viewed and compared between scans for a very small region of interest. Voxel-based superimposition methods must ensure they use a large enough region for the superimposition.

A full mathematical proof is contained within this thesis, outlining the techniques used in the superimposition method as well as the method itself. This includes proofs of the relevant techniques used, such as shift invariance for Fourier transform or finding the shift between two images using phase correlation. The algorithm works by taking two three-dimensional images and converting them to the frequency domain using Fourier transforms. The Fourier transform removes the translation differences between the two images while preserving any differences due to rotation. The rotational changes are then converted to translations using a coordinate transform from Cartesian to cylindrical coordinates. The translational difference between the two volumes is found using phase correlation. This corresponds to a rotational shift between the two images about a single axis that can then be corrected. The entire process is then iterated through to correct for all rotational differences between the images. A final phase correlation allows for correction of all translations to fully register two images. A simple validation is included.

The algorithm is tested against patient scans. This is done in two manners, finding the registrations ability to register scans with known error, and registering time one and time two scans of real patient data with unknown initial error between the scans. The algorithm is also compared to the 6 point superimposition method found in literature. The new registration algorithm had comparable, or superior, accuracy in 4 out of 10 tests. The new algorithm had a 57% faster runtime compared to the six point method. The new registration algorithm required less user involvement than the six point method, only requiring a rough selection of the cranial base for each patient scan versus measuring multiple points accurately for the six point method.