Quantifying 3-Dimensional Cephalometric Measurements: An Exploratory Approach using Fourier Descriptors

Cephalometric measurements aid in orthodontic diagnosis and treatment planning by providing the clinician a general description of the patient’s skeletal and dental malocclusion, as well as its deviation from the norm. Such measurements are derived from 2-dimensional (2-D) cephalograms, a compressed view of 3-dimensional (3-D) structure. These measurements are linear measurements, consisting of lines, angles and ratios. Using such an approach can introduce measurement errors due to magnification, anatomical asymmetries, improper head positioning etc. Moreover, information between point A and point B is completely lost because of the inherent deficiency in linear measurements. This deficiency is exponentially magnified when applied to 3-D images, CT scans, etc. Objectives: To overcome limitations of current linear measurement system in 2-D and 3-D images by developing a method to quantify 3-D image of mandible using Fourier Descriptors. Methods: Using dry skull mandible, a brass wire outline of boundary of mandible was formed. It was then converted into a set of points, which when joined together, recreated the original outline. A medical CT scan of human mandible was uploaded into Dolphin software. Points were digitized on scanned image of mandible in 3 planes of space. Using Dolphin, co-ordinates of these points were converted into format compatible with Elliptical Fourier Functions (EFF). EFF analysis was executed on this data, generating a Fourier equation fitting those points. Using PsiPlot software, the points were plotted to form a curve. A pilot study using 10 sample cases was performed, and mean data was generated. Results: A quantifiable 3-D outline of mandible was created by points digitized in 3 planes of space. Conclusions: Measurement errors using 2-D method were eliminated. Anatomical variations, mandibular asymmetries, changes due to growth, and pre- and post-treatment changes can be clearly defined with this approach.