Linear interpolation error in measured surfaces in a dental erosion study

An extensive palatal erosion study, which is currently being undertaken at the University of Dundee, aims to detect erosion through the precise mapping of replicas of children's incisors. All perceived sources of error are being scrutinised closely. The error due to the interpolation of surface positions from discrete point measurements has been investigated so that its contribution to the erosion estimates can be gauged. The calculation of the error statistics made use of covariance functions to express the undulation of the tooth surfaces. It has been found that, for the measurement point spacing of 150 µm being used in the current project, the interpolation error for an incisor is typically about 25 µm, to be compared with the root-mean-square error due to tooth impression and replication procedures, assessed as being in the order of ±3 µm, and replica measurement, assessed as being in the order of ±5 µm. The interpolation error constitutes a surprisingly large proportion of the overall system error. The same error estimation technique can be applied usefully and without difficulty to other research studies concerning erosion or wear in natural or restorative dental surfaces.