Assessment of 3-D Hemimandible Boundary Shape Differences Using Elliptical Fourier Analysis and Procrustes Superimposition Methods

Objectives: The purpose of this research is twofold: [1] derive a visual depiction of the boundary outline differences between superimposed images and [2] assess whether statistically significant differences are present.
Methods: A sample of (n=15) was collected for each of the three groups. Using Dolphin software, the hemi-mandible (HMD) of each member of the three groups was digitized to generate a 3-D boundary outline. These files were used as input for elliptical Fourier function analysis (EFF). Five superimposition procedures were utilized: [1] Superimposition of the original three groups using the Frankfort Horizontal (FH), [2] Use of EFFs to rotate the original data about the centroid so that the principal axis of the first harmonic is parallel with the X-axis as advocated by Khul and Giardina, [3] Size-standardize the original data ([1] above) and superimpose on the centroid, [4] Rotate the size-standardized data about the centroid (as in [2] above), and [5] Procrustes superimposition.
Results: The 1^st superimposition on the FH depicts the Brachyfacial and Mesofacial groups as closely similar in contrast to the Dolichofacial group, suggesting the presence of significant differences. However, the Dolichofacial difference is based on the FH orientation that uses two cranial landmarks which are independent of the mandible making these shape changes misleading with respect to the mandible. The 4^th superimposition shows that the three groups are quite similar in overall shape. Procrustes superimposition shows that the shapes of the HMD groups are also similar with most of the differences limited to the gonial region.
Conclusions: The 4^th and 5^th superimposition approaches, in particular, provide a good visual assessment of shape differences along the boundary outline.