Mathematical shape matching as a tool in tooth wear assessment--development and conduct

The quantitative assessment of restoration and tooth wear usually requires fixed reference points from which measurements are made. In longitudinal patient follow-up the loss or erosion of such points may preclude measurement and an alternative approach is to seek regions of coincidence and conflict in digital models of before and after wear surfaces, with a continuous refinement of the parameters of the coordinate transformations, until the closest correspondence between them is found. A computer program has been written to implement the algorithm and assess the technique's capacity to find the match between surfaces both artificially generated and from tooth replicas recorded from patients at different epochs. The program was able to achieve the desired ends, demonstrating the utility of the technique in tooth wear assessment but identifying the need to refine the program further to enhance both its difference detection capabilities and level of automation. Examination of the theory and practical experience highlighted certain situations when user understanding is invaluable to ensure a satisfactory solution. This strengthened the investigators' resolve against reliance upon commercially based surface fitting programs whose basis may not be fully understood. Notwithstanding this surface matching is a powerful tool in the investigation of dental wear.