Mathematical analysis of tooth and restoration contour using image analysis

The aim of this study was to develop a methodology for comparison of the contour of artificial crowns in the mid bucco-lingual plane with their equivalent natural teeth on the opposing side of the same arch (antimeres) using a novel application of image analysis software. The objective was to determine whether artificial crowns were overcontoured.

Specimens consisted of thin sections of silicone putty impressions of the buccal and lingual surfaces of 55 full crown restorations and their natural antimeric teeth. A thin slice of the putty was obtained in the mid-tooth bucco-lingual plane and a digital image was captured and this was analysed to produce a data set (x, y) representing the curvature of the tooth surface. Further analysis was performed in order to describe the profile in optimum mathematical terms.

The curves were best represented by three equations: y = a + bx(0.5), ln(y) = a + bx2, and y2 = a + bx. In all equations parameter (b), which expresses the contour curvature, was used as a deciding factor in comparing the degree of contour of the crown restorations with their natural antimeres. Most artificial crowns were found to be either similarly or undercontoured when compared with their natural antimeres. When overcontouring was present in the artificial crowns this tended to occur on the lingual aspects of anterior and posterior crowns.

Simplifying tooth contour into a mathematical model can be useful in determining whether restorations are overcontoured. Clinically, particular attention should be directed towards the lingual aspects of restorations which were more likely to be overcontoured.