Shape model of the maxillary dental arch using Fourier descriptors with an application in the rehabilitation for edentulous patient.

The knowledge of teeth positions on the maxillary arch is useful in the rehabilitation of the edentulous patient. A combination of angular (θ), and linear (l) variables representing position of four teeth were initially proposed as the shape descriptor of the maxillary dental arch. Three categories of shape were established, each having a multivariate normal distribution. It may be argued that 4 selected teeth on the standardized digital images of the dental casts could be considered as insufficient with respect to representing shape. However, increasing the number of points would create problems with dimensions and proof of existence of the multivariate normal distribution is extremely difficult. This study investigates the ability of Fourier descriptors (FD) using all maxillary teeth to find alternative shape models. Eight FD terms were sufficient to represent 21 points on the arch. Using these 8 FD terms as an alternative shape descriptor, three categories of shape were verified, each category having the complex normal distribution.

A probability distribution of shape for the dental maxillary arch using digital images.

Selected landmarks from each of 47 maxillary dental casts were used to define a Cartesian-coordinate system from which the positions of selected teeth were determined on standardized digital images. The position of the i-th tooth was defined by a line of length (l(i)) joining the tooth to the origin, and the angle (θ(i)) of this line to the horizontal Cartesian axis. Four teeth, the central incisor, lateral incisor, canine and first molar were selected and their position were collectively used to represent the shape of the dental arch. A pilot study using clustering and principal component analysis strongly suggest the existence of 3 groups of arch shape. In this study, the homogeneity of the 3 groups was further investigated and confirmed by the Dunn and Davies-Bouldein validity indices. This is followed by an investigation of the probability distribution of these 3 groups. The main result of this study suggests 3 groups of multivariate (MV) normal distribution. The MV normal probability distribution of these groups may be used in further studies to investigate the issues of variation of arch shape, which is fundamental to the practice of prosthodontics and orthodontics.

A novel shape representation of the dental arch and its applications in some dentistry problems.

Standardized digital images of maxillary dental casts of 47 subjects were analyzed using MATLAB software whereby the two hamular notches and the incisive papilla defines the Cartesian vertical and horizontal axes, as well as the origin. The angle and length of the midpoints of the anterior teeth, mesiobuccal and distobuccal cusp of the posterior teeth were measured from the origin and denoted as θ(1), …, θ(18) and l(1), …, l(18) respectively. These values were collectively used to represent the shape of each dental cast. Clustering and principal component analyses were employed to find possible groups of dental arches using the above measure of shape. The main result of this study is that the 3 groups of dental arch shape may be represented by the novel feature vector v(k) = (θ(k)(1), l(k)(1), θ(k)(3), l(k)(3), θ(k)(5), l(k)(5), θ(k)(13), l(k)(13)), k = 1, 2, 3. Knowledge of v(k) implies three impression trays should be sufficient in a particular prosthetic dentistry application for Malaysian patients. Further, given that v(k) are accurately measured they may be potential candidates as evidence in specific application of forensic dentistry.