Semi-automatic and robust determination of dental arch form in dental cone-beam CT with B-spline approximation

Background and objective The dental arch form is generally used as a base for planning orthodontic treatments. It is, therefore, vital to determine the proper individual dental arch form for more accurate orthodontic treatment. We aimed to develop and validate a robust algorithm for semi-automatic determination of the dental arch form in dental cone-beam CT (CBCT) images with the cubic B-spline approximation. Methods Our algorithm consists of tooth segmentation, determination of an occlusal plane, and generation of intersection points between the teeth and the offset plane from the occlusal plane in CBCT images. By fitting a curve to the intersection points using the cubic B-spline curve approximation, the dental arch form was finally determined. The accuracy of the dental arch forms was evaluated by comparison with gold standards determined by an expert orthodontist. Results Thirteen dental CBCT scans from nine subjects were enrolled in this study. From the CBCT scans, 13 maxillary arch forms and 11 mandibular arch forms with Class I occlusion were determined by our proposed algorithm and evaluated for validation. The mean error between the dental arch forms of gold standards and our method using the cubic B-spline was 0.413 ± 0.092 mm (range, 0.264–0.587 mm). Conclusions Our proposed method showed reliable accuracy of determining the dental arch forms for the maxilla and mandible. These results suggested that this method might be used for planning automatic tooth setup for individual patients.