Computation of tooth axes of existent and missing teeth from 3D CT images

Orientations of tooth axes are important quantitative information used in dental diagnosis and surgery planning. However, their computation is a complex problem, and the existing methods have respective limitations. This paper proposes new methods to compute 3D tooth axes from 3D CT images for existent teeth with single root or multiple roots and to estimate 3D tooth axes from 3D CT images for missing teeth. The tooth axis of a single-root tooth will be determined by segmenting the pulp cavity of the tooth and computing the principal direction of the pulp cavity, and the estimation of tooth axes of the missing teeth is modeled as an interpolation problem of some quaternions along a 3D curve. The proposed methods can either avoid the difficult teeth segmentation problem or improve the limitations of existing methods. Their effectiveness and practicality are demonstrated by experimental results of different 3D CT images from the clinic.