Automatic Teeth Axes Calculation for Well-Aligned Teeth Using Cost Profile Analysis Along Teeth Center Arch

In dental implantology and virtual dental surgery planning using computed tomography (CT) images, the examination of the axes of neighboring and/or biting teeth is important to improve the performance of the masticatory system as well as the aesthetic beauty. However, due to its high connectivity to neighboring teeth and jawbones, a tooth and/or its axis is very elusive to automatically identify in dental CT images. This paper presents a novel method of automatically calculating individual teeth axes. The planes separating the individual teeth are automatically calculated using cost profile analysis along the teeth center arch. In this calculation, a novel plane cost function, which considers the intensity and the gradient, is proposed to favor the teeth separation planes crossing the teeth interstice and suppress the possible inappropriately detected separation planes crossing the soft pulp. The soft pulp and dentine of each individually separated tooth are then segmented by a fast marching method with two newly proposed speed functions considering their own specific anatomical characteristics. The axis of each tooth is finally calculated using principal component analysis on the segmented soft pulp and dentine. In experimental results using 20 clinical datasets, the average angle and minimum distance differences between the teeth axes manually specified by two dentists and automatically calculated by the proposed method were 1.94° ± 0.61° and 1.13 ± 0.56 mm, respectively. The proposed method identified the individual teeth axes accurately, demonstrating that it can give dentists substantial assistance during dental surgery such as dental implant placement and orthognathic surgery.